Localization in abelian Chern-Simons theory
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed...
Abelian Chern-Simons theory and contact torsion
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas in ...... in quantum field theory. We compare the shift reduced partition function with other formulations of the abelian Chern-Simons partition function. This study naturally motivates an Atiyah-Patodi-Singer type index problem in contact geometry.......Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas...
Abelian Chern-Simons theory and linking numbers via oscillatory integrals
International Nuclear Information System (INIS)
Albeverio, S.; Schaefer, J.
1994-06-01
We introduce a rigorous mathematical model of abelian Chern-Simons theory based on the theory of infinite dimensional oscillatory integrals developed by Albeverio and Hoeegh-Krohn. We construct a gauge-fixed Chern-Simons path integral as a Fresnel integral in a certain Hilbert space. Wilson loop variables are defined as Fresnel integrable functions and it is shown in this context that the expectation value of products of Wilson loops w.r.t. the Chern-Simons path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops, as conjectured by Witten. We also propose a lattice Chern-Simons action which converges to the continuum limit. (orig.)
Non-existence of natural states for Abelian Chern-Simons theory
Dappiaggi, Claudio; Murro, Simone; Schenkel, Alexander
2017-06-01
We give an elementary proof that Abelian Chern-Simons theory, described as a functor from oriented surfaces to C∗-algebras, does not admit a natural state. Non-existence of natural states is thus not only a phenomenon of quantum field theories on Lorentzian manifolds, but also of topological quantum field theories formulated in the algebraic approach.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Energy Technology Data Exchange (ETDEWEB)
Di Bartolo, Cayetano; Grau, Javier [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Leal, Lorenzo [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Centro de Física Teórica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47270, Caracas 1041-A (Venezuela, Bolivarian Republic of)
2013-12-15
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
International Nuclear Information System (INIS)
Giavarini, G.; Martin, C.P.; Ruiz Ruiz, F.
1993-01-01
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in bbfR 3 can be defined so that its large-mass limit be the renormalized vaccum expectation value of the Wilson loop for abelian Chern-Simons theory also in bbfR 3 . (orig.)
Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field
Figueroa, Daniel G.; Shaposhnikov, Mikhail
2018-01-01
Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U (1) gauge sector, a (x)FμνF˜μν, reproducing the continuum limit to order O (dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K =FμνF˜μν that admits a lattice total derivative representation K = Δμ+ Kμ, reproducing to order O (dxμ2) the continuum expression K =∂μKμ ∝ E → ṡ B → . If we consider a homogeneous field a (x) = a (t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.
Anyons in discrete gauge theories with Chern-Simons terms
International Nuclear Information System (INIS)
Bais, F.A.; Driel, P. van; Wild Propitius, M. de
1993-01-01
A gauge theory with a discrete group H in (2+1)-dimensional space-time is known to describe (non-abelian) anyons. We study the effect of adding a Chern-Simons term to such a theory. As in a previous paper, we emphasize the algebraic structure underlying a discrete H gauge theory, namely the Hopf algebra D(H). For H≅Z N , we argue on physical grounds that a Chern-Simons term in the action leads to a non-trivial 3-cocycle on D(H). Accordingly, the physically inequivalent models are labeled by the elements of the cohomology group H 3 (H, U(1)). It depends periodically on the coefficient of the Chern-Simons term which model is realized. This establishes a relation with the discrete topological field theories of Dijkgraaf and Witten. We extrapolate these results to non-abelian H, and work out the representative example H≅anti D 2 . (orig.)
Chern-Simons theory from first principles
International Nuclear Information System (INIS)
Marino, E.C.
1994-01-01
A review is made of the main properties of the Chern-Simons field theory. These include the dynamical mass generation to the photon without a Higgs field, the statistical transmutation of charged particles coupled to it and the natural appearance of a transverse conductivity. A review of standard theories proposed for the Quantum Hall Effect which use the Chern-Simons term is also made, emphasizing the fact that this terms is put in an artificial manner. A physical origin for the Chern-Simons term is proposed, starting from QED in 3+1 D with the topological term and imposing that the motion of charged matter is restricted to an infinite plane. (author). 12 refs
On the quantization of the coefficient of the abelian Chern-Simons term
International Nuclear Information System (INIS)
Polychronakos, A.P.
1990-01-01
We point out that the coefficient of the abelian Chern-Simons term need not be quantized, even in the case of compact U(1) group. Instead, the quantum theory is qualitatively different for integer or rotational values of that coefficient. (orig.)
Canonical sectors of five-dimensional Chern-Simons theories
International Nuclear Information System (INIS)
Miskovic, Olivera; Troncoso, Ricardo; Zanelli, Jorge
2005-01-01
The dynamics of five-dimensional Chern-Simons theories is analyzed. These theories are characterized by intricate self couplings which give rise to dynamical features not present in standard theories. As a consequence, Dirac's canonical formalism cannot be directly applied due to the presence of degeneracies of the symplectic form and irregularities of the constraints on some surfaces of phase space, obscuring the dynamical content of these theories. Here we identify conditions that define sectors where the canonical formalism can be applied for a class of non-Abelian Chern-Simons theories, including supergravity. A family of solutions satisfying the canonical requirements is explicitly found. The splitting between first and second class constraints is performed around these backgrounds, allowing the construction of the charge algebra, including its central extension
Dimensional regularisation of Chern-Simons field theory
International Nuclear Information System (INIS)
Martin, C.P.
1990-01-01
We discuss the dimensional regularisation program as applied to a pure Chern-Simons theory in Minkowski space. In order to make this regularisation program feasible, we propose adding a Yang-Mills term to the pure Chern-Simons action. It is argued that the pure Chern-Simons theory is recovered in a certain limit. Explicit computations are carried out at the one-loop level in the background field gauge. (orig.)
Entanglement from topology in Chern-Simons theory
Salton, Grant; Swingle, Brian; Walter, Michael
2017-05-01
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.
4D edge currents from 5D Chern-Simons theory
International Nuclear Information System (INIS)
Gupta, K.S.; Stern, A.
1995-01-01
A class of two dimensional conformal field theories is known to correspond to three dimensional Chern-Simons theory. Here we claim that there is an analogous class of four dimensional field theories corresponding to five dimensional Chern-Simons theory. The four dimensional theories give a coupling between a scalar field and an external divergenceless vector field and they may have some application in magnetohydrodynamics. Like in conformal theories they possess a diffeomorphism symmetry, which for us is along the direction of the vector field, and their generators are analogous to Virasoro generators. Our analysis of the abelian Chern-Simons system uses elementary canonical methods for the quantization of field theories defined on manifolds with boundaries. Edge states appear for these systems and they yield a four dimensional current algebra. We examine the quantization of these algebras in several special cases and claim that a renormalization of the 5D Chern-Simons coupling is necessary for removing divergences. ((orig.))
Transport in Chern-Simons-matter theories
Energy Technology Data Exchange (ETDEWEB)
Gur-Ari, Guy; Hartnoll, Sean; Mahajan, Raghu [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2016-07-18
The frequency-dependent longitudinal and Hall conductivities — σ{sub xx} and σ{sub xy} — are dimensionless functions of ω/T in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of charged excitations of the theory and are basic experimental observables. We compute these conductivities for large N Chern-Simons theory with fermion matter. The computation is exact in the ’t Hooft coupling λ at N=∞. We describe various physical features of the conductivity, including an explicit relation between the weight of the delta function at ω=0 in σ{sub xx} and the existence of infinitely many higher spin conserved currents in the theory. We also compute the conductivities perturbatively in Chern-Simons theory with scalar matter and show that the resulting functions of ω/T agree with the strong coupling fermionic result. This provides a new test of the conjectured 3d bosonization duality. In matching the Hall conductivities we resolve an outstanding puzzle by carefully treating an extra anomaly that arises in the regularization scheme used.
Chern-Simons forms in gravitation theories
International Nuclear Information System (INIS)
Zanelli, Jorge
2012-01-01
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. In classical physics, the minimal coupling in electromagnetism and to the action for a mechanical system in Hamiltonian form are examples of CS functionals. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point like but an extended fundamental object, a membrane. They are found in relation with anomalies in quantum field theories, and as Lagrangians for gauge fields, including gravity and supergravity. A cursory review of the role of CS forms in gravitation theories is presented at an introductory level. (topical review)
Chern-Simons forms in gravitation theories
Zanelli, Jorge
2012-07-01
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. In classical physics, the minimal coupling in electromagnetism and to the action for a mechanical system in Hamiltonian form are examples of CS functionals. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point like but an extended fundamental object, a membrane. They are found in relation with anomalies in quantum field theories, and as Lagrangians for gauge fields, including gravity and supergravity. A cursory review of the role of CS forms in gravitation theories is presented at an introductory level.
Introductory lectures on Chern-Simons theories
Zanelli, Jorge
2012-02-01
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think. They are found in the studies of anomalies in quantum field theories and as Lagrangians for gauge fields, including gravity and supergravity. They seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point-like but an extended fundamental object, a membrane. A cursory review of these ideas is presented at an introductory level.
Wavefunction of the Universe and Chern-Simons perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soo Chopin [Department of Physics, National Cheng Kung University Tainan 70101, Taiwan (China)
2002-03-21
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Lorentz-violating Yang-Mills theory. Discussing the Chern-Simons-like term generation
Energy Technology Data Exchange (ETDEWEB)
Santos, Tiago R.S.; Sobreiro, Rodrigo F. [UFF-Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)
2017-12-15
We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable. (orig.)
Soliton condensation in some self-dual Chern-Simons theories
International Nuclear Information System (INIS)
Olesen, P.
1991-05-01
We show that the gauged non-linear Schroedinger equation has a closely packed soliton-condensate as a solution. We also show that the abelian Chern-Simons Higgs theory has a vortex condensate as an approximate solution whent he vortex cells are very small. (orig.)
Anyonic states in Chern-Simons theory
International Nuclear Information System (INIS)
Haller, K.; Lim-Lombridas, E.
1994-01-01
We discuss the canonical quantization of Chern-Simons theory in 2+1 dimensions, minimally coupled to a Dirac spinor field, first in the temporal gauge and then in the Coulomb gauge. In our temporal gauge formulation, Gauss's law and the gauge condition A 0 =0 are implemented by embedding the formulation in an appropriate physical subspace. We construct a Fock space of charged particle states that satisfy Gauss's law, and show that they obey fermion, not fractional statistics. The gauge-invariant spinor field that creates these charged states from the vacuum obeys the anticommutation rules that generally apply to spinor fields. The Hamiltonian, when described in the representation in which the charged fermions are the propagating particle excitations that obey Gauss's law, contains an interaction between charge and transverse current densities. We observe that the implementation of Gauss's law and the gauge condition does not require us to use fields with graded commutator algebras or particle excitations with fractional statistics. In our Coulomb gauge formulation, we implement Gauss's law and the gauge condition ∂ l A l =0 by the Dirac-Bergmann procedure. In this formulation, the constrained gauge fields become functionals of the spinor fields, and are not independent degrees of freedom. The formulation in the Coulomb gauge confirms the results we obtained in the temporal gauge: The ''Dirac-Bergmann'' anticommutation rule for the charged spinor fiels ψ and ψ degree that have both been constrained to obey Gauss's law is precisely identical to the canonical spinor anticommutation rule that generates standard fermion statistics. And we also show that the Hamiltonians for charged particle states in our temporal and Coulomb gauge formulations are identical, once Gauss's law has been implemented in both cases
Chern--Simons theory in the Schroedinger representation
International Nuclear Information System (INIS)
Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.
1989-01-01
We quantize the (2+1)-dimensional Chern--Simons theory in the functional Schroedinger representation. The realization of gauge transformations on states involves a 1-cocycle. We determine this cocycle; we show how solving the Gauss law constraint in the non-Abelian theory requires quantizing the parameter that normalizes the action; we trivialize the 1-cocycle with a spatially non-local cochain related to a 2-dimensional fermion determinant and we find the physical states that satisfy the Gauss law constraint. The quantum holonomy of physical states involves a contribution that is missed when the constraint is solved before quantization. We compute this quantity for the Abelian theory in Minkowski space, where it exhibits an interesting group theoretic structure. (In a note added in proof the corresponding non-Abelian computation is presented.) Also we consider coupling to external sources and offer yet another derivation of the anomalous statistics and spin of the charge and flux carrying particles---a calculation which is especially simple in the functional Schroedinger representation. copyright 1989 Academic Press, Inc
Lecture notes on Chern-Simons-Witten theory
Hu, Sen
2001-01-01
This invaluable monograph has arisen in part from E Witten's lectures on topological quantum field theory in the spring of 1989 at Princeton University. At that time Witten unified several important mathematical works in terms of quantum field theory, most notably the Donaldson polynomial, the Gromov-Floer homology and the Jones polynomials. In his lectures, among other things, Witten explained his intrinsic three-dimensional construction of Jones polynomials via Chern-Simons gauge theory. He provided both a rigorous proof of the geometric quantization of the Chern-Simons action and a very ill
The A-polynomial in Chern-Simons theory
DEFF Research Database (Denmark)
Malusà, Alessandro
One of the most amusing aspects of mathematical physics is the great variety of areas of mathematics it relates to, and builds bridges between. The world of TQFT’s, and in particular Chern-Simons, relates to algebraic geometry via the theory of moduli spaces: one example of this is given by the A......-polynomial. This knot invariant is obtained from the algebraic geometry of character varieties, and takes the meaning of the equation of a constraint central in Chern-Simons theory. In my poster I wish to expose the construction of this invariant, and highlight its strong ties with mathematical physics....
Chern-Simons as a geometrical set up for three dimensional gauge theories
International Nuclear Information System (INIS)
Lemes, V.E.R; Jesus, C. Linhares de; Sorella, S.P.; Villar, L.C.Q.; Ventura, O.S.
1997-12-01
Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field. (author)
Teichmüller TQFT vs. Chern-Simons theory
Mikhaylov, Victor
2018-04-01
Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2, ℝ) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conformal blocks. We propose that this theory can be defined by an analytically-continued Chern-Simons path-integral with an unusual integration cycle. On hyperbolic three-manifolds, this cycle is singled out by the requirement of invertible vielbein. Mathematically, our proposal translates a known conjecture by Andersen and Kashaev into a conjecture about the Kapustin-Witten equations. We further explain that Teichmüller TQFT is dual to complex SL(2, ℂ) Chern-Simons theory at integer level k = 1, clarifying some puzzles previously encountered in the 3d-3d correspondence literature. We also present a new simple derivation of complex Chern-Simons theories from the 6d (2,0) theory on a lens space with a transversely-holomorphic foliation.
Chern-Simons couplings for dielectric F-strings in matrix string theory
International Nuclear Information System (INIS)
Brecher, Dominic; Janssen, Bert; Lozano, Yolanda
2002-01-01
We compute the non-abelian couplings in the Chern-Simons action for a set of coinciding fundamental strings in both the type IIA and type IIB Matrix string theories. Starting from Matrix theory in a weakly curved background, we construct the linear couplings of closed string fields to type IIA Matrix strings. Further dualities give a type IIB Matrix string theory and a type IIA theory of Matrix strings with winding. (Abstract Copyright[2002], Wiley Periodicals, Inc.)
SU(2) Chern-Simons theory at genus zero
International Nuclear Information System (INIS)
Gawedzki, K.; Kupiainen, A.
1991-01-01
We present a detailed study of the Schroedinger picture space of states in the SU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae. (orig.)
Tertiary classes–after Chern-Simons theory
Indian Academy of Sciences (India)
J.N. Iyer Institute of Mathematical Sciences Chennai, India
2013-11-08
Nov 8, 2013 ... Euler characteristic class. In early twentieth century, the notion of local product structure, i.e. fiber spaces and their generalizations appeared, in the study of topological spaces (with additional structures). J.N. Iyer. IMSc, Chennai. Tertiary classes–after Chern-Simons theory ...
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Matrix model as a mirror of Chern-Simons theory
International Nuclear Information System (INIS)
Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2004-01-01
Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators. (author)
Asymptotic conformal invariance in a non-Abelian Chern-Simons-matter model
Energy Technology Data Exchange (ETDEWEB)
Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Campos e Particulas]. E-mail: acebal@cbpf.br
2002-08-01
One shows here the existence of solutions to the Callan-Symanzik equation for the non-Abelian SU(2) Chern-Simons-matter model which exhibits asymptotic conformal invariance to every order in perturbative theory. The conformal symmetry in the classical domain is shown to hold by means of a local criteria based on the trace of the energy-momentum tensor. By using recently exhibited regimes for the dependence between the several couplings in which the set of {beta}-functions vanish, the asymptotic conformal invariance of the model appears to be valid in the quantum domain. By considering the SU (n) case the possible non validity of the proof for a particular {eta} would be merely accidental. (author)
Chern-Simons theory and three-dimensional surfaces
International Nuclear Information System (INIS)
Guven, Jemal
2007-01-01
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space: one is constructed using the induced metric connection and involves only the intrinsic geometry? the other is extrinsic and uses the connection associated with the gauging of normal rotations. As such, the two theories appear to describe very different aspects of the surface geometry. Remarkably, at a classical level, they are equivalent. In particular, it will be shown that their stress tensors differ only by a null contribution. Their Euler-Lagrange equations provide identical constraints on the normal curvature. A new identity for the Cotton tensor is associated with the triviality of the Chern-Simons theory for embedded hypersurfaces implied by this equivalence
N = 4 Superconformal Chern-Simons theories with hyper and twisted hyper multiplets
International Nuclear Information System (INIS)
Hosomichi, Kazuo; Lee, Ki-Myeong; Lee, Sungjay; Lee, Sangmin; Park, Jaemo
2008-01-01
We extend the N = 4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C 2 /Z n ) 2 orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed.
Integrable lambda models and Chern-Simons theories
International Nuclear Information System (INIS)
Schmidtt, David M.
2017-01-01
In this note we reveal a connection between the phase space of lambda models on S 1 ×ℝ and the phase space of double Chern-Simons theories on D×ℝ and explain in the process the origin of the non-ultralocality of the Maillet bracket, which emerges as a boundary algebra. In particular, this means that the (classical) AdS 5 ×S 5 lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra psu(2,2|4) after a proper dependence of the spectral parameter is introduced. This offers a possibility for avoiding the use of the problematic non-ultralocal Poisson algebras that preclude the introduction of lattice regularizations and the application of the QISM to string sigma models. The utility of the equivalence at the quantum level is, however, still to be explored.
Integrable lambda models and Chern-Simons theories
Energy Technology Data Exchange (ETDEWEB)
Schmidtt, David M. [Departamento de Física, Universidade Federal de São Carlos,Caixa Postal 676, CEP 13565-905, São Carlos-SP (Brazil)
2017-05-03
In this note we reveal a connection between the phase space of lambda models on S{sup 1}×ℝ and the phase space of double Chern-Simons theories on D×ℝ and explain in the process the origin of the non-ultralocality of the Maillet bracket, which emerges as a boundary algebra. In particular, this means that the (classical) AdS{sub 5}×S{sup 5} lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra psu(2,2|4) after a proper dependence of the spectral parameter is introduced. This offers a possibility for avoiding the use of the problematic non-ultralocal Poisson algebras that preclude the introduction of lattice regularizations and the application of the QISM to string sigma models. The utility of the equivalence at the quantum level is, however, still to be explored.
Friedan-Shenker bundle from Chern-Simons theory
International Nuclear Information System (INIS)
Falceto, F.
1990-01-01
In this letter we present a proof of the invariance of the space of quantum states of the Chern-Simons (CS) theory in the presence of Wilson lines under parallel transport with respect to the Knizhnik-Zamolodchikov (KZ) connection for the case of a simple, simply connected, finite-dimensional group and genus-zero surface. The proof is based on the polynomial realization of the space of tensors in which these quantum states take values. (orig.)
Combinatorial quantization of the Hamiltonian Chern-Simons theory
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Grosse, H.; Schomerus, V.
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of ''functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional ω (''integration''). We prove that this data does not depend on the particular choices which have been made in the construction. The algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group. (orig.). With 1 fig
The dynamical structure of higher dimensional Chern-Simons theory
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G x U(1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion. (orig.)
Transgression forms and extensions of Chern-Simons gauge theories
International Nuclear Information System (INIS)
Mora, Pablo; Olea, Rodrigo; Troncoso, Ricardo; Zanelli, Jorge
2006-01-01
A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem
Analysis of observables in Chern-Simons perturbation theory
International Nuclear Information System (INIS)
Alvarez, M.; Labastida, J.M.F.
1993-01-01
Chern-Simons theory with gauge group SU(N) is analyzed from a perturbation theory point of view. Computations up to order g 6 of the vacuum expectation value of the unknot are carried out and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of the vacuum expectation value of an arbitrary knot factorizes in the form predicted by Witten. (orig.)
Super-Chern-Simons Theory as Superstring Theory
Grassi, P A
2004-01-01
Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with bosonic and fermionic strings. Here we present a common geometrical setting to develop systematically the prescription for amplitude computations. The geometrical origin of these difficulties is the theory of integration of superforms. We provide a translation between the theory of supermanifolds and topological strings with supertarget space. We show how in this formulation one can naturally construct picture changing operators to be inserted in the correlation functions to soak up the zero modes of commuting ghost and we derive the amplitude prescriptions from the coupling with an extended topological gravity on the worldsheet. As an application we consider a simple model on R^(3|2) leading to super-Chern-Simons theory.
BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields
Dai, Jialiang; Fan, Engui
2018-04-01
We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. We discuss four different cases: abelian, nonabelian, relativistic, and nonrelativistic situations and extend the system to the whole phase space including ghost fields. In addition, we obtain the BRST charge of the field system and check its nilpotence of the BRST transformation which plays an important role such as in topological quantum field theory and string theory.
A direct derivation of polynomial invariants from perturbative Chern-Simons gauge theory
International Nuclear Information System (INIS)
Ochiai, Tomoshiro
2003-01-01
There have been several methods to show that the expectation values of Wilson loop operators in the SU(N) Chern-Simons gauge theory satisfy the HOMFLY skein relation. We shall give another method from the perturbative method of the SU(N) Chern-Simons gauge theory in the light-cone gauge, which is more direct than already known methods
Chern-Simons-Rozansky-Witten topological field theory
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Minor Outlying Islands (United States); Saulina, Natalia [California Institute of Technology, Minor Outlying Islands (United States)], E-mail: saulina@theory.caltech.edu
2009-12-21
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kaehler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern-Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.
Shift versus no-shift in local regularization of Chern-Simons theory
International Nuclear Information System (INIS)
Giavarini, G.; Parma Univ.; Martin, C.P.; Ruiz Ruiz, F.
1994-01-01
We consider a family of local BRS-invariant higher covariant derivative regularizations of SU(N) Chern-Simons theory that do not shift the value of the Chern-Simons parameter k to k + sign(k) c v at one loop. (orig.)
On the non-renormalization properties of Gauge theories with Chern-Simons term
International Nuclear Information System (INIS)
Del Cima, Oswaldo M.; Piguet, Olivier
1997-12-01
Considering three-dimensional Chern-Simons theory, either coupled to matter or with a Yang-Mills term, we show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all orders of perturbation theory. From this we deduce the vanishing of the β-function associated to the Chern-Simons coupling constant and the full finiteness in the case of the Yang-Mills Chern-Simons theory. The main ingredient in the proof of the latter property is the non invariance of the Chern-Simons from under the gauge transformations. Our results hold for the three-dimensional Chern-Simons model in a general Riemannian manifold. (author)
Chern-Simons Theory, Matrix Models, and Topological Strings
International Nuclear Information System (INIS)
Walcher, J
2006-01-01
This book is a find. Marino meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge/gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. Here is a brief summary of the book. The journey begins with matrix models and an introduction to various techniques for the computation of integrals including perturbative expansion, large-N approximation, saddle point analysis, and the method of orthogonal polynomials. The second chapter, on Chern-Simons theory, is the longest and probably the most complete one in the book. Starting from the action we meet Wilson loop observables, the associated perturbative 3-manifold invariants, Witten's exact solution via the canonical duality to WZW models, the framing ambiguity, as well as a collection of results on knot invariants that can be derived from Chern-Simons theory and the combinatorics of U (∞) representation theory. The chapter also contains a careful derivation of the large-N expansion of the Chern-Simons partition function, which forms the cornerstone of its interpretation as a closed string theory. Finally, we learn that Chern-Simons theory can sometimes also be represented as a matrix model. The story then turns to the gravity side, with an introduction to topological sigma models (chapter 3) and topological string theory (chapter 4). While this presentation is necessarily rather condensed (and the beginner may
Framing and localization in Chern-Simons theories with matter
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Marco S. [Center for Research in String Theory - School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Griguolo, Luca [Dipartimento di Fisica e Scienze della Terra, Università di Parma andINFN Gruppo Collegato di Parma,Viale G.P. Usberti 7/A, 43100 Parma (Italy); Leoni, Matias [Physics Department, FCEyN-UBA & IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina); Mauri, Andrea [Dipartimento di Fisica, Università degli studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Penati, Silvia [Dipartimento di Fisica, Università degli studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Seminara, Domenico [Dipartimento di Fisica, Università di Firenze and INFN Sezione di Firenze,via G. Sansone 1, 50019 Sesto Fiorentino (Italy)
2016-06-22
Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.
Derivation of the Verlinde formula from Chern-Simons theory and the G/G model
International Nuclear Information System (INIS)
Blau, M.; Thompson, G.
1993-01-01
We give a derivation of the Verlinde formula for the G k WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function Z ΣxS 1 of Σ x S 1 with an arbitrary number of labelled punctures. By what is essentially a suitable gauge choice, Z ΣxS 1 is reduced to the partition function of an abelian topological field theory on Σ (a deformation of non-abelian BF and Yang-Mills theory) whose evaluation is straightforward. This relates the Verlinde formula to the Ray-Singer torsion of Σ x S 1 . We derive the G k /G k model from Chern-Simons theory, proving their equivalence, and give an alternative derivation of the Verlinde formula by calculating the G k /G k path integral via a functional version of the Weyl integral formula. From this point of view the Verlinde formula arises from the corresponding jacobian, the Weyl determinant. Also, a novel derivation of the shift k → k + h is given, based on the index of the twisted Dolbeault complex. (orig.)
On eleven-dimensional supergravity and Chern-Simons theory
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, Fernando, E-mail: fizaurie@ucsc.cl [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile); Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, Av. Insurgentes Sur s/n, D.F. (Mexico); Departament de Fisica Teorica, Universitat de Valencia, C/ Dr. Moliner 50, 46100 Burjassot, Valencia (Spain); Rodriguez, Eduardo, E-mail: edurodriguez@ucsc.cl [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-02-11
We probe in some depth into the structure of eleven-dimensional, osp(32|1)-based Chern-Simons supergravity, as put forward by Troncoso and Zanelli (TZ) in 1997. We find that the TZ Lagrangian may be cast as a polynomial in 1/l, where l is a length, and compute explicitly the first three dominant terms. The term proportional to 1/l{sup 9} turns out to be essentially the Lagrangian of the standard 1978 supergravity theory of Cremmer, Julia and Scherk, thus establishing a previously unknown relation between the two theories. The computation is nontrivial because, when written in a sufficiently explicit way, the TZ Lagrangian has roughly one thousand non-explicitly Lorentz-covariant terms. Specially designed algebraic techniques are used to accomplish the results.
Maxwell-Chern-Simons theory in covariant and Coulomb gauges
International Nuclear Information System (INIS)
Haller, K.; Lim-Lombridas, E.
1996-01-01
We quantize quantum electrodynamics in 2 + 1 dimensions coupled to a Chern-Simons (CS) term and a charged spinor field, in covariant gauges and in the Coulomb gauge. The resulting Maxwell-Chern-Simons (MCS) theory describes charged fermions interacting with each other and with topologically massive propagating photons. We impose Gauss's law and the gauge conditions and investigate their effect on the dynamics and on the statistics of n-particle states. We construct charged spinor states that obey Gauss's law and the gauge conditions and transform the theory to representations in which these states constitute a Fock space. We demonstrate that, in these representations, the nonlocal interactions between charges and between charges and transverse currents-along with the interactions between currents and massive propagating photons-are identical in the different gauges we analyze in this and in earlier work. We construct the generators of the Poincare group, show that they implement the Poincare algebra, and explicitly demonstrate the effect of rotations and Lorentz boosts on the particle states. We show that the imposition of Gauss's law does not produce any open-quotes exoticclose quotes fractional statistics. In the case of the covariant gauges, this demonstration makes use of unitary transformations that provide charged particles with the gauge fields required by Gauss's law, but that leave the anticommutator algebra of the spinor fields untransformed. In the Coulomb gauge, we show that the anticommutators of the spinor fields apply to the Dirac-Bergmann constraint surfaces, on which Gauss's law and the gauge conditions obtain. We examine MCS theory in the large CS coupling constant limit, and compare that limiting form with CS theory, in which the Maxwell kinetic energy term is not included in the Larangian. 34 refs
Non abelian Chern-Simons topological coupling from self-interaction
International Nuclear Information System (INIS)
Aragone, C.; Stephany, R.J.E.
1986-01-01
It is shown that the self-interaction mechanism drives in one step the topologically coupled-Maxwell-second rank antisymmetric tensor system into the Chern-Simons coupled -non abelian- (second rank) antisymmetric tensor action. Only one step is required to saturate the process because the action for the initial Maxwell-antisymmetric tensor system is given in its first-order form. The self-interaction mechanism works both for the original Chapline-Manton form of the action and for the dual form. (Author) [pt
Chern-Simons theories of symplectic super-diffeomorphisms
International Nuclear Information System (INIS)
Sezgin, E.; Sokatchev, E.
1989-04-01
We discuss the symplectic diffeomorphisms of a class of supermanifolds and the structure of the underlying infinite dimensional superalgebras. We construct a Chern-Simons (CS) gauge theory in 2+1 dimensions for these algebras. There exists a finite dimensional supersymmetric truncation which is the (2 n -1)-dimensional Hamiltonian superalgebra H-tilde(n). With a central charge added, it is a superalgebra, C(n), associated with a Clifford algebra. We find an embedding of d=3, N=2 anti-de Sitter superalgebra OSp(2|2)+OSp(2|2) in C(4), and construct a CS action for its infinite dimensional extension. We also discuss the construction of a CS action for the infinite dimensional extension of the d=3, N=2 superconformal algebra OSp(2,4). (author). 18 refs
Unification of gauge and gravity Chern-Simons theories in 3-D space-time
Energy Technology Data Exchange (ETDEWEB)
Saghir, Chireen A.; Shamseddine, Laurence W. [American University of Beirut, Physics Department, Beirut (Lebanon)
2017-11-15
Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such a unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3-dimensional space-time manifold on which they are defined. (orig.)
Chern-Simons theory, 2d Yang-Mills, and Lie algebra wanderers
International Nuclear Information System (INIS)
Haro, Sebastian de
2005-01-01
We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S 3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermionic formulation of Chern-Simons on S 3 which allows us to identify the Brownian particles as B-model branes moving on a noncommutative two-sphere, and construct 1- and 2-matrix models to compute Brownian motion ensemble averages
Chern-Simons theory with vector fermion matter
International Nuclear Information System (INIS)
Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman; Trivedi, Sandip P.; Wadia, Spenta R.; Yin, Xi
2012-01-01
We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at vertical stroke λvertical stroke =1; the conformal theory does not exist for vertical stroke λvertical stroke >1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. (orig.)
Chern-Simons gauge theory: Ten years after
International Nuclear Information System (INIS)
Labastida, J. M. F.
1999-01-01
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of the quantum field theory for three different gauge fixings leads to three different representations for Vassiliev invariants. Two of these gauge fixings lead to well known representations: the covariant Landau gauge corresponds to the configuration space integrals while the non-covariant light-cone gauge to the Kontsevich integral. The progress made in the analysis of the third gauge fixing, the non-covariant temporal gauge, is described in detail. In this case one obtains combinatorial expressions, instead of integral ones, for Vassiliev invariants. The approach based on this last gauge fixing seems very promising to obtain a full combinatorial formula. We collect the combinatorial expressions for all the Vassiliev invariants up to order four which have been obtained in this approach
Embedded graph invariants in Chern-Simons theory
International Nuclear Information System (INIS)
Major, Seth A.
1999-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices
Chern-Simons theory and atypical Hall conductivity in the Varma phase
Menezes, Natália; Smith, Cristiane Morais; Palumbo, Giandomenico
2018-02-01
In this article, we analyze the topological response of a fermionic model defined on the Lieb lattice in the presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gauge field, we first find the Landau-level spectrum by fixing the Landau gauge; then we compute the emergent Chern-Simons theory for a weak-electromagnetic-field regime. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice.
Integrable spin chain in superconformal Chern-Simons theory
International Nuclear Information System (INIS)
Bak, Dongsu; Rey, Soo-Jong
2008-01-01
N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS 4 x CP 3 . We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong 't Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|4; R)/SO(3, 1) x SU(3) x U(1) supercoset. We recall that the worldsheet theory is integrable classically by utilizing well-known results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we construct alternating spin chain Hamiltonian involving three-site interactions between 4 and 4-bar . At weak 't Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation. We further study new issues arising from the shortest gauge invariant operators TrY I Y † J = (15, 1). We observe that 'wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamiltonian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4-bar 's and of nonexistence of mesonic (44-bar ) bound-state.
Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
International Nuclear Information System (INIS)
Szabo, Richard J; Tierz, Miguel
2010-01-01
We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on S 2 . We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak-coupling phase. We study the strong-coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first-order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on S 3 , and hence to q-deformed Yang-Mills theory on S 2 . In particular, the ground-state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply laced gauge groups.
Maxwell-Chern-Simons theory for curved spacetime backgrounds
International Nuclear Information System (INIS)
Kant, E.; Klinkhamer, F.R.
2005-01-01
We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern-Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the geometrical-optics approximation. The corresponding light path is modified, which allows for new effects. In a Schwarzschild background, for example, there now exist stable bounded orbits of light rays and the two polarization modes of light rays in unbounded orbits can have different gravitational redshifts
Pure Lovelock gravity and Chern-Simons theory
Concha, P. K.; Durka, R.; Inostroza, C.; Merino, N.; Rodríguez, E. K.
2016-07-01
We explore the possibility of finding pure Lovelock gravity as a particular limit of a Chern-Simons action for a specific expansion of the AdS algebra in odd dimensions. We derive in detail this relation at the level of the action in five and seven dimensions. We provide a general result for higher dimensions and discuss some issues arising from the obtained dynamics.
International Nuclear Information System (INIS)
Ezawa, Z.F.; Iwazaki, A.
1991-01-01
It is shown that Chern-Simons gauge theories describe both the fractional-quantum-Hall-effect (FQHE) hierarchy and anyon superconductivity, simply by field-theoretically extracting the effects of vortex excitations. Vortices correspond to Laughlin's quasiparticles or bound states of anyons. Both of these phenomena are explained by the condensations of these vortices. We clarify why the anyon systems become incompressible (FQHE) or compressible (anyon superconductivity) depending on the statistics. It is to be emphasized that we can derive an effective Lagrangian describing fully the FQHE hierarchy from a basic Chern-Simons gauge theory
Vortex solutions of a Maxwell-Chern-Simons field coupled to four-fermion theory
International Nuclear Information System (INIS)
Hyun, S.; Shin, J.; Yee, J.H.; Lee, H.
1997-01-01
We find the static vortex solutions of the model of a Maxwell-Chern-Simons gauge field coupled to a (2+1)-dimensional four-fermion theory. Especially, we introduce two matter currents coupled to the gauge field minimally: the electromagnetic current and a topological current associated with the electromagnetic current. Unlike other Chern-Simons solitons the N-soliton solution of this theory has binding energy and the stability of the solutions is maintained by the charge conservation laws. copyright 1997 The American Physical Society
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector
Energy Technology Data Exchange (ETDEWEB)
Lozano, Gustavo [Departamento de Física, FCEYN Universidad de Buenos Aires & IFIBA CONICET,Pabellón 1 Ciudad Universitaria, 1428 Buenos Aires (Argentina); Mohammadi, Azadeh [Departamento de Física, Universidade Federal da Paraíba,58.059-970, Caixa Postal 5.008, João Pessoa, PB (Brazil); Schaposnik, Fidel A. [Departamento de Física, Universidad Nacional de La Plata/IFLP/CICBA,CC 67, 1900 La Plata (Argentina)
2015-11-06
In this paper we study a 2+1 dimensional system in which fermions are coupled to the self-dual topological vortex in U(1)×U(1) Chern-Simons theory, where both U(1) gauge symmetries are spontaneously broken. We consider two Abelian Higgs scalars with visible and hidden sectors coupled to a fermionic field through three interaction Lagrangians, where one of them violates the fermion number. Using a fine tuning procedure, we could obtain the number of the fermionic zero modes which is equal to the absolute value of the sum of the vortex numbers in the visible and hidden sectors.
Classical optics in generalized Maxwell Chern-Simons theory
International Nuclear Information System (INIS)
Burgess, M.; Leinaas, J.M.; Loevvik, O.M.
1993-03-01
The authors consider the propagation of electromagnetic waves in a two-dimensional polarizable medium endowed with Chern-Simons terms. The dispersion relation (refractive index) of the waves is computed and the existence of linear birefringence and anomalous dispersion is shown. When absorption is taken into account, the classic signature of a Voigt effect is found. In the case where linearly-polarized, three-dimensional waves pass through a two-dimensional plane, it is shown that there is optical activity, and the analogue of Verdet's constant is computed. 19 refs., 2 figs
Chern-Simons gauge theory on orbifolds: Open strings from three dimensions
Hořava, Petr
1996-12-01
Chern-Simons gauge theory is formulated on three-dimensional Z2 orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum of more complicated correlation functions in the simpler theory on manifolds. Chern-Simons theory on manifolds is known to be related to two-dimensional (2D) conformal field theory (CFT) on closed-string surfaces; here it is shown that the theory on orbifolds is related to 2D CFT of unoriented closed- and open-string models, i.e. to worldsheet orbifold models. In particular, the boundary components of the worldsheet correspond to the components of the singular locus in the 3D orbifold. This correspondence leads to a simple identification of the open-string spectra, including their Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding Chern-Simons theory. The correspondence is studied in detail, and some exactly solvable examples are presented. Some of these examples indicate that it is natural to think of the orbifold group Z2 as a part of the gauge group of the Chern-Simons theory, thus generalizing the standard definition of gauge theories.
A stringy origin of M2 brane Chern-Simons theories
International Nuclear Information System (INIS)
Aganagic, Mina
2010-01-01
We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity X 4 to type IIA string theory on a Calabi-Yau threefold X 3 fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on N D2 branes probing X 3 are the well-known quiver theories with N=2 supersymmetry in three dimensions. We show that turning on fluxes, and fibering the X 3 over a direction transverse to the branes, corresponds to turning on N=2 Chern-Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on X 3 in this background become N M2 branes on X 4 . This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of N=2 quiver Chern-Simons theories. We also provide a new N=2 Chern-Simons theory dual to AdS 4 xQ 1,1,1 . Type IIA/M-theory duality also relates IIA string theory on X 3 with only the RR fluxes turned on, to M-theory on a G 2 holonomy manifold. We show that this implies that the N M2 branes probing the G 2 manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing X 3 , except that now Chern-Simons terms preserve only N=1 supersymmetry in three dimensions.
What we think about the higher dimensional Chern-Simons theories
International Nuclear Information System (INIS)
Fock, V.V.; Nekrasov, N.A.; Rosly, A.A.; Selivanov, K.G.
1992-01-01
This paper reports that one of the most interesting developments in mathematical physics was the investigation of the so-called topological field theories i.e. such theories which do not need a metric on the manifold for their definition a d hence the observable of which are topologically invariant. The Chern-Simons (CS) functionals considered as actions give us examples the theories of such a type. The CS theory on a 3d manifold was firstly considered in the Abelian case by A.S. Schwartz and then after papers of E. Witten there has been an explosive process of publications on this subject. This paper discusses topological invariants of the manifolds (like the Ray-Singer torsion) computed by the quantum field theory methods; conformal blocks of 2d conformal field theories as vectors in the CS theory Hilbert space; correlators of Wilson loop and the invariants of 1d links in 3d manifolds; braid groups; unusual relations between spin and statistics; here we would like to consider the generalization of a part of the outlined ideas to the CS theories on higher dimensional manifolds. Some of our results intersect with
Chern-Simons term at finite density and temperature
International Nuclear Information System (INIS)
Sisakyan, A.N.; Shevchenko, O.Yu.; Solganik, S.B.
1997-01-01
The Chern-Simons topological term dynamical generation in the effective action is obtained at arbitrary finite density and temperature. By using the proper time method and perturbation theory it is shown that at zero temperature μ 2 = m 2 is the crucial point for Chern-Simons term. So when μ 2 2 , μ influence disappears and we get the usual Chern-Simons term. On the other hand, when μ 2 > m 2 , the Chern-Simons term vanishes because of nonzero density of background fermions. In particular for massless case parity anomaly is absent at any finite density or temperature. This result holds in any odd dimension both in Abelian and in non-Abelian cases
Abelian gauge theories on homogeneous spaces
International Nuclear Information System (INIS)
Vassilevich, D.V.
1992-07-01
An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S 3 is calculated. A generalization of the Chern-Simons action is suggested and analysed with the example of SU(3)/U(1) x U(1). (author). 11 refs
Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian
International Nuclear Information System (INIS)
Edelstein, Jose D.; Hassaine, Mokhtar; Troncoso, Ricardo; Zanelli, Jorge
2006-01-01
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions
Dynamics of Chern-Simons vortices
International Nuclear Information System (INIS)
Collie, Benjamin; Tong, David
2008-01-01
We study vortex dynamics in three-dimensional theories with Chern-Simons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern character of a suitable index bundle. We derive these results by integrating out massive fermions and following the fate of their zero modes.
Kaehler-Chern-Simons theory and symmetries of anti-self-dual gauge fields
International Nuclear Information System (INIS)
Nair, V.P.; Schiff, J.
1992-01-01
Kaehler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual instantons on a four-dimensional Kaehler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Baecklund transformations, previously related to 'hidden symmetries' of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to integrable two-dimensional theories is briefly discussed in this framework. (orig.)
Physically meaningful and not so meaningful symmetries in Chern-Simons theory
International Nuclear Information System (INIS)
Giavarini, G.
1993-01-01
We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift k → k + c v of the bare Chern-Simons parameter k in connection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift. (orig.)
Existence of local degrees of freedom for higher dimensional pure Chern-Simons theories
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
The canonical structure of higher dimensional pure Chern-Simons theories is analyzed. It is shown that these theories have generically a nonvanishing number of local degrees of freedom, even though they are obtained by means of a topological construction. This number of local degrees of freedom is computed as a function of the spacetime dimension and the dimension of the gauge group. copyright 1996 The American Physical Society
Perturbative expansion of Chern-Simons theory with non-compact gauge group
International Nuclear Information System (INIS)
Bar-Natan, D.; Witten, E.
1991-01-01
Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)
Skein relations and Wilson loops in Chern-Simons gauge theory
International Nuclear Information System (INIS)
Horne, J.H.
1990-01-01
We derive the skein relations for the fundamental representations of SO(N), Sp(2n), SU(mvertical stroken), and OSp(mvertical stroke2n). These relations can be used recursively to calculate the expectation values of Wilson lines in three-dimensional Chern-Simons gauge theory with these gauge groups. A combination of braiding and tying of Wilson lines completely describes the skein relations. (orig.)
On the phase of Chern-Simons theory with complex gauge group
Energy Technology Data Exchange (ETDEWEB)
Gibbs, R.; Mokhtari, S. [Dept. of Phys., Louisiana Tech. Univ., Ruston, LA (United States)
1995-10-07
We compute the eta function for Chern-Simons quantum field theory with complex gauge group. The calculation is performed using the Schwinger expansion technique. We discuss, in particular, the role of the metric on the field configuration space, and demonstrate that for a certain class of acceptable metrics the one-loop phase contribution to the effective action can be calculated explicitly. The result is found to be proportional to a gauge invariant part of the action. (author)
Exact solubility of Chern-Simons theory with compact simple gauge group
International Nuclear Information System (INIS)
Hayashi, Masahito
1993-01-01
We show that vacuum expectation values of Wilson loop operators in (2+1)-dimensional Chern-Simons theory satisfy algebraic equations. Interestingly enough, vacuum expectation values for unknotted Wilson loop operators in any representation of any compact and simple group are exactly computed by solving the equations. So-called 'skein relations', which give us algebraic equations among vacuum expectation values of different Wilson loop operators, are constructed. In our formalism, quantum group symmetry appears naturally. (orig.)
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
International Nuclear Information System (INIS)
Schmidt, Torsten
2009-01-01
The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)
International Nuclear Information System (INIS)
Sourrouille, Lucas; Casana, Rodolfo
2016-01-01
We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions, ω_1(|ϕ|) and ω(|ϕ|), which split the kinetic term of the Higgs field, |D_μϕ|"2→ω_1(|ϕ|)|D_0ϕ|"2-ω(|ϕ|)|D_kϕ|"2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether ω(|ϕ|)∝β|ϕ|"2"β"-"2 with β≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ω_1(|ϕ|) which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual |ϕ|"6-vortex solutions have been analyzed from both theoretical and numerical point of view.
Multi-boundary entanglement in Chern-Simons theory and link invariants
Energy Technology Data Exchange (ETDEWEB)
Balasubramanian, Vijay [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) andInternational Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Fliss, Jackson R.; Leigh, Robert G. [Department of Physics, University of Illinois,1110 W. Green Street, Urbana, IL 61801 (United States); Parrikar, Onkar [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States)
2017-04-11
We consider Chern-Simons theory for gauge group G at level k on 3-manifolds M{sub n} with boundary consisting of n topologically linked tori. The Euclidean path integral on M{sub n} defines a quantum state on the boundary, in the n-fold tensor product of the torus Hilbert space. We focus on the case where M{sub n} is the link-complement of some n-component link inside the three-sphere S{sup 3}. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level k (G=U(1){sub k}) we give a general formula for the entanglement entropy associated to an arbitrary (m|n−m) partition of a generic n-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod k) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod k). For G=SU(2){sub k}, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a “W-like' entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have “GHZ-like” entanglement (i.e., tracing out one torus does lead to a separable state).
Self-dual Maxwell-Chern-Simons theory on a cylinder
International Nuclear Information System (INIS)
Han, Jongmin; Kim, Seongtag
2011-01-01
In this paper, we study the relativistic Maxwell-Chern-Simons vortices on an asymptotically flat cylinder. A topological multivortex solution is constructed by variational methods, and the Maxwell and the Chern-Simons limits are verified.
Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals
International Nuclear Information System (INIS)
Drukker, Nadav; Plefka, Jan; Young, Donovan
2008-01-01
We study Wilson loops in the three-dimensional N = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS 4 x CP 3 . We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.
A Chern-Simons-like action for closed-string field theory
International Nuclear Information System (INIS)
Taylor, C.C.
1989-01-01
A Chern-Simons-like action is proposed for closed-string field theory. The action involves auxiliary fields of arbitrary ghost number and is defined in terms of the closed-string operations ∫, Q and *, analogous to those introduced by Witten in the construction of open-string field theory. The action is an extension of one proposed for free closed strings and bears a formal relationship to 2 + 1 gravity analogous to that between open-string field theory and (2 + 1)-dimensional Yang-Mills theory. (author)
Two-dimensional Lorentz-Weyl anomaly and gravitational Chern-Simons theory
International Nuclear Information System (INIS)
Chamseddine, A.H.; Froehlich, J.
1992-01-01
Two-dimensional chiral fermions and bosons, more generally conformal blocks of two-dimensional conformal field theories, exhibit Weyl-, Lorentz- and mixed Lorentz-Weyl anomalies. A novel way of computing these anomalies for a system of chiral bosons of arbitrary conformal spin j is sketched. It is shown that the Lorentz- and mixed Lorentz-Weyl anomalies of these theories can be cancelled by the anomalies of a three-dimensional classical Chern-Simons action for the spin connection, expressed in terms of the dreibein field. Some tentative applications of this result to string theory are indicated. (orig.)
Perturbed Chern-Simons theory, fractional statistics, and Yang-Baxter algebra
International Nuclear Information System (INIS)
Chatterjee, A.; Sreedhar, V.V.
1992-01-01
Topological Chern-Simons theory coupled to matter fields is analysed in the framework of Dirac's method of quantising constrained systems in a general class of linear, non-local gauges. We show that in the weak coupling limit gauge invariant operators in the theory transform under an exchange according to a higher dimensional representation of the braid group which is built out of the fundamental representation matrices of the gauge group and thus behave like anyons. We also discover new solutions of the Yang-Baxter equation which emerges as a consistency condition on the structure functions of the operator algebra of the matter fields. (orig.)
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, Leszek; Lindström, Ulf; Roček, Martin; von Unge, Rikard
2004-05-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
International Nuclear Information System (INIS)
Hadasz, Leszek; Lindstroem, Ulf; Rocek, Martin; Unge, Rikard von
2004-01-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space
Observables, skein relations, and tetrahedra in Chern-Simons gauge theory
International Nuclear Information System (INIS)
Martin, S.P.
1990-01-01
The observables in three-dimensional Chern-Simons gauge theory are Wilson lines and Wilson graphs. Skein relations are non-trivial identities between expectation values of distinct Wilson graphs. We discuss various kinds of skein relations and the relationships between them. By comparing different kinds of skein relations, we show how to calculate the expectation value of a general tetrahedral Wilson graph. This is shown to be the last and most difficult step in a systematic procedure for calculating the expectation values of arbitrary Wilson graphs in arbitrary representations of arbitrary gauge groups. (orig.)
Effective actions for gauge theories with Chern-Simons terms - I
International Nuclear Information System (INIS)
Bambah, B.A.; Mukku, C.
1989-01-01
The effective Lagrangian for a three-dimensional gauge theory with a Chern-Simons term is evaluated upto one-loop effects. It is shown to be completely finite. It also does not exhibit any imaginary part. The calculation is carried out in a background field analogue of the Feynman gauge and gauge invariance is maintained throughout the calculation. In an appendix an argument is presented as to why this Feynman gauge may be a 'good' gauge for our results to be applied to high temperature QCD and in particular to the quark-gluon plasma. (author). 12 refs
Charges and Energy in Chern-Simons Theories and Lovelock Gravity
Allemandi, G.; Francaviglia, M.; Raiteri, M.
2003-01-01
Starting from the SO(2,2n) Chern-Simons form in (2n+1) dimensions we calculate the variation of conserved quantities in Lovelock gravity and Lovelock-Maxwell gravity through the covariant formalism developed in gr-qc/0305047. Despite the technical complexity of the Lovelock Lagrangian we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal e...
Self-duality in Maxwell-Chern-Simons theories with non minimal coupling with matter field
Chandelier, F; Masson, T; Wallet, J C
2000-01-01
We consider a general class of non-local MCS models whose usual minimal coupling to a conserved current is supplemented with a (non-minimal) magnetic Pauli-type coupling. We find that the considered models exhibit a self-duality whenever the magnetic coupling constant reaches a special value: the partition function is invariant under a set of transformations among the parameter space (the duality transformations) while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying self-duality of the (2+1)-dimensional Z sub n - Abelian Higgs model with Chern-Simons and bare mass term.
A flat Chern-Simons gauge theory for (2+1)-dimensional gravity coupled to point particles
International Nuclear Information System (INIS)
Grignani, G.; Nardelli, G.
1991-01-01
We present a classical ISO (2,1) Chern-Simons gauge theory for planar gravity coupled to point-like sources. The theory is defined in terms of flat coordinates whose relation with the space-time coordinates is established. Though flat, the theory is equivalent to Einstein's as we show explicitly in two examples. (orig.)
International Nuclear Information System (INIS)
Chen Famin; Wu Yongshi
2010-01-01
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
Periodic electromagnetic vacuum in the two-dimensional Yang-Mills theory with the Chern-Simons mass
International Nuclear Information System (INIS)
Skalozub, V.V.; Vilensky, S.A.; Zaslavsky, A.Yu.
1993-06-01
The periodic vacuum structure formed from magnetic and electric fields is derived in the two-dimensional Yang-Mills theory with the Chern-Simons term. It is shown that both the magnetic flux quantization in the fundamental sell and conductivity quantization inherent to the vacuum. Hence, the quantum Hall effect gets its natural explanation. (author). 10 refs
Castro \\C
2003-01-01
Moyal noncommutative star-product deformations of higher dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(\\infty) gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional "knots" have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W_\\infty symmetries which are very relevant in the study of W_\\infty Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix mod...
Large N non-perturbative effects in N=4 superconformal Chern-Simons theories
International Nuclear Information System (INIS)
Hatsuda, Yasuyuki; Honda, Masazumi; Okuyama, Kazumi
2015-07-01
We investigate the large N instanton effects of partition functions in a class of N = 4 circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldsheet instanton corrections, which appear as quantum mechanical non-perturbative corrections in the Fermi-gas system.
A profusion of 1/2 BPS Wilson loops in N=4 Chern-Simons-matter theories
International Nuclear Information System (INIS)
Cooke, Michael; Drukker, Nadav; Trancanelli, Diego
2015-01-01
We initiate the study of 1/2 BPS Wilson loops in N=4 Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels k, −k and 0, and focus on loops preserving one of the two SU(2) subgroups of the R-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermultiplets have Wilson loops preserving another set of supercharges). We expect this classical pairwise degeneracy to be lifted by quantum corrections. In the case with nodes with vanishing Chern-Simons terms connected by twisted hypermultiplets, we find that the usual 1/4 BPS Wilson loops are automatically enlarged to 1/2 BPS, as happens also in 3-dimensional Yang-Mills theory. When the nodes with vanishing Chern-Simons levels are connected by untwisted hypermultiplets, we do not find any Wilson loops coupling to those nodes which are classically invariant. Rather, we find several loops whose supersymmetry variation, while non zero, vanishes in any correlation function, so is weakly zero. We expect only one linear combination of those Wilson loops to remain BPS when quantum corrections are included. We analyze the M-theory duals of those Wilson loops and comment on their degeneracy. We also show that these Wilson loops are cohomologically equivalent to certain 1/4 BPS Wilson loops whose expectation value can be evaluated by the appropriate localized matrix model.
N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
International Nuclear Information System (INIS)
Aharony, Ofer; Bergman, Oren; Maldacena, Juan; Jafferis, Daniel Louis
2008-01-01
We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) x U(N) and SU(N) x SU(N) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U(N) x U(N) theory at level k describes the low energy limit of N M2-branes probing a C 4 /Z k singularity. At large N the theory is then dual to M-theory on AdS 4 x S 7 /Z k . The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS 4 x CP 3 . For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) x SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
Superconformal Chern-Simons theories and AdS4/CFT3 correspondence
International Nuclear Information System (INIS)
Benna, Marcus; Klebanov, Igor; Klose, Thomas; Smedbaeck, Mikael
2008-01-01
We discuss the N = 2 superspace formulation of the N = 8 superconformal Bagger-Lambert-Gustavsson theory, and of the N = 6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N) x U(N) Chern-Simons theory. In particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then consider orbifold projections of this theory that give non-chiral and chiral (U(N) x U(N)) n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS 4 x S 7 /(Z n x Z k -tilde) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the N = 8 theory flow to a N = 2 superconformal gauge theory with a sextic superpotential. We conjecture that this gauge theory is dual to the U(1) R x SU(3) invariant extremum of the N = 8 gauged supergravity, which was discovered by N. Warner 25 years ago and whose uplifting to 11 dimensions was found more recently.
International Nuclear Information System (INIS)
Van de Wetering, J.F.W.H.
1992-01-01
Using perturbative Chern-Simons theory in the almost axial gauge on the euclidean manifold S 1 xR 2 , we give a prescription for the computation of knot invariants. The method gives the correct expectation value of the unknot to all orders in perturbation theory and gives the correct answer for the spectral-parameter-dependent universal R-matrix to second order. All results are derived for a general semi-simple Lie algebra. (orig.)
Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories
Zemba, Guillermo Raul
A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
Chern-Simons field theory of two-dimensional electrons in the lowest Landau level
International Nuclear Information System (INIS)
Zhang, L.
1996-01-01
We propose a fermion Chern-Simons field theory describing two-dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest-Landau-level constraint is enforced through a δ functional described by an auxiliary field λ. Unlike the field theory constructed directly with the states in the lowest Landau level, this theory allows one, utilizing the physical picture of open-quote open-quote composite fermion,close-quote close-quote to study the fractional quantum Hall states by mapping them onto certain integer quantum Hall states; but, unlike its application in the unconstrained theory, such a mapping is sensible only when interactions between electrons are present. An open-quote open-quote effective mass,close-quote close-quote which characterizes the scale of low energy excitations in the fractional quantum Hall systems, emerges naturally from our theory. We study a Gaussian effective theory and interpret physically the dressed stationary point equation for λ as an equation for the open-quote open-quote mass renormalization close-quote close-quote of composite fermions. copyright 1996 The American Physical Society
The integral form of D = 3 Chern-Simons theories probing C{sup n}/Γ singularities
Energy Technology Data Exchange (ETDEWEB)
Fre, P. [Dipartimento di Fisica, Universita di Torino (Italy); INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); National Research Nuclear University MEPhI, (Moscow Engineering Physics Institute), Moscow (Russian Federation); Grassi, P.A. [INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); DISIT, Universita del Piemonte Orientale, Alessandria (Italy); Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University (Japan)
2017-10-15
We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS{sub 4}/CFT{sub 3} correspondence. From the structural view-point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kaehler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS{sub 4}/CFT{sub 3} correspondence and more generally of M2-branes we emphasize the role of the Kaehler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non-compact Kaehler quotient K{sub 4} of some flat variety with respect to a suitable group. The crepant resolutions of C{sup n}/Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern-Simons Theory supposedly dual to the corresponding M2-brane solution. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Integrable spin chain of superconformal U(M) x U(N)-bar Chern-Simons theory
International Nuclear Information System (INIS)
Bak, Dongsu; Gang, Dongmin; Rey, Soo-Jong
2008-01-01
N = 6 superconformal Chern-Simons theory with gauge group U(M) x U(N)-bar is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C 4 /Z k orbifold singularity. We show that, much like its regular counterpart of M = N, the theory at planar limit have integrability structure in the conformal dimension spectrum of single trace operators. We first revisit the Yang-Baxter equation for a spin chain system associated with the single trace operators. We show that the integrability by itself does not preclude parity symmetry breaking. We construct two-parameter family of parity non-invariant, alternating spin chain Hamiltonian involving three-site interactions between 4 and 4-bar of SU(4) R . At weak 't Hooft coupling, we study the Chern-Simons theory perturbatively and calculate anomalous dimension of single trace operators up to two loops. The computation is essentially parallel to the regular case M = N. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation, but to the one preserving parity symmetry. We give several intuitive explanations why the parity symmetry breaking is not detected in the Chern-Simons spin chain Hamiltonian at perturbative level. We suggest that open spin chain, associated with open string excitations on giant gravitons or dibaryons, can detect discrete flat holonomy and hence parity symmetry breaking through boundary field.
Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model
International Nuclear Information System (INIS)
Paschoal, Ricardo C.; Helayel Neto, Jose A.
2003-01-01
The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effective described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field nominally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1) D Dirac's equation is derived. (author)
N=1,2 supergravities in 2+1 dimensions as Chern-Simons theories
International Nuclear Information System (INIS)
Li Miao.
1988-12-01
In this letter we report the results on the explanation of the Lagrangians of 2+1 supergravities as graded Chern-Simons terms, which are derived from inspiration of Witten's recent work on exact solvability of 2+1 Einstein gravity. Further implications will be considered elsewhere. (author). 8 refs
Finite-size effect of the dyonic giant magnons in N=6 super Chern-Simons theory
International Nuclear Information System (INIS)
Ahn, Changrim; Bozhilov, P.
2009-01-01
We consider finite-size effects for the dyonic giant magnon of the type IIA string theory on AdS 4 xCP 3 by applying the Luescher μ-term formula which is derived from a recently proposed S matrix for the N=6 super Chern-Simons theory. We compute explicitly the effect for the case of a symmetric configuration where the two external bound states, each of A and B particles, have the same momentum p and spin J 2 . We compare this with the classical string theory result which we computed by reducing it to the Neumann-Rosochatius system. The two results match perfectly.
International Nuclear Information System (INIS)
Huang Yongchang; Huo Qiuhong
2008-01-01
Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-Abelian Chern-Simons topological term in 2+1 dimensions. We use consistency of Coulomb gauge condition to naturally deduce a new gauge condition. Furthermore, we obtain the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum is the sum of the orbital angular momentum and spin angular momentum of the non-Abelian gauge field. Finally, we obtain the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and A 0 s (x) charge
Boundary effects in 2 + 1 dimensional Maxwell-Chern-Simons theory
International Nuclear Information System (INIS)
Ferrer, E.J.; Incera, V. de la.
1996-09-01
The boundary effects in the screening of an applied magnetic field in a finite temperature 2 + 1 dimensional model of charged fermions minimally coupled to Maxwell and Chern-Simons fields are investigated. It is found that in a sample with only one boundary -a half-plane- a total Meissner effect takes place, while in a sample with two boundaries -an infinite strip- the external magnetic field partially penetrates the material. (author). 17 refs
International Nuclear Information System (INIS)
Rey, Soo-Jong; Suyama, Takao; Yamaguchi, Satoshi
2009-01-01
We study Wilson loop operators in three-dimensional, N = 6 superconformal Chern-Simons theory dual to IIA superstring theory on AdS 4 x CP 3 . Novelty of Wilson loop operators in this theory is that, for a given contour, there are two linear combinations of Wilson loop transforming oppositely under time-reversal transformation. We show that one combination is holographically dual to IIA fundamental string, while orthogonal combination is set to zero. We gather supporting evidences from detailed comparative study of generalized time-reversal transformations in both D2-brane worldvolume and ABJM theories. We then classify supersymmetric Wilson loops and find at most 1/6 supersymmetry. We next study Wilson loop expectation value in planar perturbation theory. For circular Wilson loop, we find features remarkably parallel to circular Wilson loop in N = 4 super Yang-Mills theory in four dimensions. First, all odd loop diagrams vanish identically and even loops contribute nontrivial contributions. Second, quantum corrected gauge and scalar propagators take the same form as those of N = 4 super Yang-Mills theory. Combining these results, we propose that expectation value of circular Wilson loop is given by Wilson loop expectation value in pure Chern-Simons theory times zero-dimensional Gaussian matrix model whose variance is specified by an interpolating function of 't Hooft coupling. We suggest the function interpolates smoothly between weak and strong coupling regime, offering new test ground of the AdS/CFT correspondence.
Holography in Lovelock Chern-Simons AdS gravity
Cvetković, Branislav; Miskovic, Olivera; Simić, Dejan
2017-08-01
We analyze holographic field theory dual to Lovelock Chern-Simons anti-de Sitter (AdS) gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute 1-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level.
Holographic Chern-Simons defects
International Nuclear Information System (INIS)
Fujita, Mitsutoshi; Melby-Thompson, Charles M.; Meyer, René; Sugimoto, Shigeki
2016-01-01
We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7 branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for 2-dimensional QCD.
U(1) x SU(2) Chern-Simons gauge theory of underdoped cuprate superconductors
International Nuclear Information System (INIS)
Marchetti, P.A.; Su Zhao-Bin; Yu Lu
1998-05-01
The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied to the 2-D t-J model in the limit t>>J, to study the normal state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average - a coexisting flux phase and s+id-like RVB state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field V, the holon field is a fermion and the spinon field is a hard-core boson. Within this approximation we show that the B field produces a π flux phase for the holons, converting them into Dirac-like fermions, while the V field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero doping limit. The nonlinear σ-model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long range AF order in reference compounds. Moreover, we derive a low-energy effective action in terms of spinons holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi liquid theory with a Fermi surface consisting of 4 ''half-pockets'' centered at (+-π/2,+-π/2) and one reproduces the results for the electron spectral function obtained in the mean field approximation, in agreement with the photoemission data on underdoped cuprates. The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalisation effects due to gauge fluctuations give rise to non-Fermi liquid behaviour for the composite electron, in certain temperature range showing the linear in T resistivity. This formalism provides a new interpretation of the spin gap in the underdoped superconductors
Dynamics of magnetic fields in Maxwell, Yang-Mills and Chern-Simons theories on the torus
International Nuclear Information System (INIS)
Burgess, M.; McLachlan, A.; Toms, D.J.
1992-01-01
The problem of uniform magnetic fields passing perpendicularly through a 2-torus, Abelian and Non-Abelian, is considered. Focus is on dynamical effects of non-integrable phases on the torus at non zero B and from magnetic fields themselves in the vacuum. The spectrum is computed and is shown to be always independent of the non-integrable phases on the torus. It is concluded that a Chern-Simons term will always be induced by radiative corrections to fermions on the torus when B ≠ 0. The special case of an electromagnetically uncharged anyon gas in noted and shown to be a system whose spectrum can depend on the non-integrable phases in the two torus directions, subject to a consistency requirement. In three and four dimensions, dynamical symmetry breaking of non-Abelian fields and associated condensate formation is possible by radiative corrections. The classification on non-Abelian magnetic fields in terms of ''flux integers'' is discussed, and a method for obtaining such integers for an arbitrary gauge algebra is presented. This provides a rigorous generalisation of Hooft's su (2) classification. 72 refs., 5 figs
Anyons, spin, and statistics in (2+1)-dimensional U(1)-scalar Chern-Simons gauge field theory
International Nuclear Information System (INIS)
Graziano, E.; Rothe, K.D.
1994-01-01
We present a detailed analysis of the quantum field theory of a Chern-Simons field coupled minimally to massive charged bosonic matter. This analysis is carried out in the Coulomb and covariant gauges. Some aspects concerning the transformation law of the fields under Poincare transformations are clarified. Emphasis is placed on gauge-invariant operators. The order and disorder operators are constructed from their dual algebra. The order operator is shown to obey anyonic statistics. The correlator of the disorder operator is computed in the large boson-mass limit, and the corresponding cluster properties are discussed. In the absence of a symmetry-breaking Higgs potential, there is no evidence for the ground state being anyonic
Maxwell-Chern-Simons Casimir effect. II. Circular boundary conditions
International Nuclear Information System (INIS)
Milton, K.A.; Ng, Y.J.
1992-01-01
In odd-dimensional spaces, gauge invariance permits a Chern-Simons mass term for the gauge fields in addition to the usual Maxwell-Yang-Mills kinetic energy term. We study the Casimir effect in such a (2+1)-dimensional Abelian theory. The case of parallel conducting lines was considered by us in a previous paper. Here we discuss the Casimir effect for a circle and examine the effect of finite temperature. The Casimir stress is found to be attractive at both low and high temperatures
International Nuclear Information System (INIS)
Teh, R.
1989-07-01
Vortex-like and string-like solutions of 2+1 Dim. SU(2) YM theory with the Chern-Simons term are discussed. Two ansatze are constructed which yield respectively analytic Bessel function solutions and elliptic function solutions. The Bessel function solutions are vortex-like and tend to the same vacuum state as the Ginzburg-Landau vortex solution at large ρ. The Jacobi elliptic function solutions are string-like, have finite energy and magnetic flux concentrated along a line in the x 1 - x 2 plane. (author). 18 refs
The Chern-Simons diffusion rate in improved holographic QCD
Gürsoy, U.; Iatrakis, I.; Kiritsis, E.; Nitti, F.; O’Bannon, A.
2013-01-01
In (3 + 1)-dimensional SU(N c) Yang-Mills (YM) theory, the Chern-Simons diffusion rate, ΓCS, is determined by the zero-momentum, zero-frequency limit of the retarded two-point function of the CP-odd operator tr [F ∧ F ], with F the YM field strength. The Chern-Simons diffusion rate is a crucial
Superfiled formulation of Chern-Simons supersymmetry
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.
1989-03-01
We discuss an extra supersymmetry present in the covariantly quantized Chern-Simons action within the superfield formalism. By introducing scalar superfields we show how the component transformations are naturally reproduced from the superfield transformation. When the superspace is extended to include an additional odd coordinate for the BRST symmetry, the entire theory is described by a single odd scalar superfield. The implications of this supersymmetry for the renormalized theory are also discussed. (author). 9 refs
Maxwell-Chern-Simons Casimir effect
International Nuclear Information System (INIS)
Milton, K.A.; Ng, Y.J.
1990-01-01
The topology of (2+1)-dimensional space permits the construction of quantum electrodynamics with the usual Maxwell action augmented by a gauge-invariant, but P- and T-violating, Chern-Simons mass term. We discuss the Casimir effect between parallel lines in such a theory. The effect of finite temperature is also considered. In principle, our results provide a way to measure the topological mass of the photon
Remarks on Chern-Simons Invariants
Cattaneo, Alberto S.; Mnëv, Pavel
2010-02-01
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.
Ye, Fei; Marchetti, P. A.; Su, Z. B.; Yu, L.
2017-09-01
The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality. Dedicated to the memory of Mario Tonin.
Chern-Simons terms and cocycles in physics and mathematics
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.
1984-12-01
Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)
Chern-Simons gravity in four dimensions
International Nuclear Information System (INIS)
Morales, Ivan; Neves, Bruno; Piguet, Olivier; Oporto, Zui
2017-01-01
Five-dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to general relativity with cosmological constant. We consider the zero modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and ΛCDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions. (orig.)
Chern-Simons gravity in four dimensions
Energy Technology Data Exchange (ETDEWEB)
Morales, Ivan; Neves, Bruno; Piguet, Olivier [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Vicosa, MG (Brazil); Oporto, Zui [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Vicosa, MG (Brazil); Universidad Mayor de San Andres, Carrera de Fisica, La Paz (Bolivia, Plurinational State of)
2017-02-15
Five-dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to general relativity with cosmological constant. We consider the zero modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and ΛCDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions. (orig.)
''Topological'' (Chern-Simons) quantum mechanics
International Nuclear Information System (INIS)
Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.
1990-01-01
We construct quantum-mechanical models that are analogs of three-dimensional, topologically massive as well as Chern-Simons gauge-field theories, and we study the phase-space reductive limiting procedure that takes the former to the latter. The zero-point spectra of operators behave discontinuously in the limit, as a consequence of a nonperturbative quantum-mechanical anomaly. The nature of the limit for wave functions depends on the representation, but is always such that normalization is preserved
Even-dimensional topological gravity from Chern-Simons gravity
International Nuclear Information System (INIS)
Merino, N.; Perez, A.; Salgado, P.
2009-01-01
It is shown that the topological action for gravity in 2n-dimensions can be obtained from the (2n+1)-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field φ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).
Yang-Mills-Chern-Simons supergravity
International Nuclear Information System (INIS)
Lue, H; Pope, C N; Sezgin, E
2004-01-01
N = (1, 0) supergravity in six dimensions admits AdS 3 x S 3 as a vacuum solution. We extend our recent results presented in Lue et al (2002 Preprint hep-th/0212323), by obtaining the complete N = 4 Yang-Mills-Chern-Simons supergravity in D = 3, up to quartic fermion terms, by S 3 group manifold reduction of the six-dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalization, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3, R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can be obtained by a consistent reduction of string theory or M-theory and that admits AdS 3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N = (1, 0) supergravity in D = 6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited
Equivalence of several Chern-Simons matter models
International Nuclear Information System (INIS)
Chen, W.; Itoi, C.
1994-01-01
Chern-Simons (CS) coupling characterizes not only statistics, but also spin and scaling dimension of matter fields. We demonstrate spin transmutation in relativistic CS matter theory, and moreover show equivalence of several models. We study the CS vector model in some detail, which provides a consistent check to the assertion of the equivalence
Gauge fixing of Chern-Simons N-extended supergravity
Energy Technology Data Exchange (ETDEWEB)
Ney, W G [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Centro Federal de Educacao Tecnologica (CEFET), Campos dos Goytacazes, RJ (Brazil); Piguet, O [Universidade Federal do Espirito Santo (UFES), ES 29000-001, Vitoria (Brazil); Spalenza, W [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2004-08-01
We treat N-extended supergravity in 2+1 space-time dimensions as a Yang-Mills gauge field with Chern-Simons action associated to the N-extended Poincare supergroup. We fix the gauge of this theory within the Batalin-Vilkovisky scheme. (orig.)
Gauge fixing of Chern-Simons N-extended supergravity
International Nuclear Information System (INIS)
Ney, W.G.; Piguet, O.; Spalenza, W.
2004-01-01
We treat N-extended supergravity in 2+1 space-time dimensions as a Yang-Mills gauge field with Chern-Simons action associated to the N-extended Poincare supergroup. We fix the gauge of this theory within the Batalin-Vilkovisky scheme. (orig.)
International Nuclear Information System (INIS)
Teh, R.
1993-06-01
We pointed out that there exists a critical frequency of oscillation for the vortex-like solution above which the system switches to the fields of an alternating current inside a solenoid. We also show the existence a non-abelian gauge for which the fields can alternate periodically in space between the abelian fields and another abelian (or non-abelian) field pointing in a different isospin space direction. The solution discussed here are real, zero-action Minkowski space configurations. (author). 18 refs
International Nuclear Information System (INIS)
Menezes, G.; Svaiter, N.F.
2006-04-01
We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)
Absence of higher order corrections to noncommutative Chern-Simons coupling
International Nuclear Information System (INIS)
Das, Ashok; Sheikh-Jabbari, M.M.
2001-03-01
We analyze the structure of noncommutative pure Chern-Simons theory systematically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not renormalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. (author)
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.
Garoufalidis, S; Garoufalidis, Stavros; Marino, Marcos
2006-01-01
The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold $M$ can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simons matrix integral for Seifert spheres and the trivial connection.
Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics
International Nuclear Information System (INIS)
Sanchez Madrigal, S; Raya, A; Hofmann, C P
2011-01-01
We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.
Chern-Simons matrix models and unoriented strings
International Nuclear Information System (INIS)
Halmagyi, Nick; Yasnov, Vadim
2004-01-01
For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F 1 (S) ±{1/4}({δF 0 (S)}/{δS}). Motivated by the fact that this relationship does not hold for Chern-Simons theory on S 3 , we calculate the sub-leading free energy in the matrix model for this theory, which is a Gaussian matrix model with Haar measure on the group SO/Sp. We derive a quantum loop equation for this matrix model and then find that F 1 is an integral of the leading order resolvent over the spectral curve. We explicitly calculate this integral for quadratic potential and find agreement with previous studies of SO/Sp Chern-Simons theory. (author)
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-02
We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.
Accelerated FRW solutions in Chern-Simons gravity
International Nuclear Information System (INIS)
Cataldo, Mauricio; Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio; Campo, Sergio del; Quinzacara, Cristian C.
2014-01-01
We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when α a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy-momentum tensor for the field h a , a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (α > 0) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time. (orig.)
Instantons, fermions and Chern-Simons terms
International Nuclear Information System (INIS)
Collie, Benjamin; Tong, David
2008-01-01
In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.
International Nuclear Information System (INIS)
Weitsman, J.; Harvard Univ., Cambridge, MA
1991-01-01
We study the quantization of the moduli space of flat connections on a surface of genus one, using the real polarization of this space. The quantum wave functions in this formalism are exponential functions supported along the integral fibres of the polarization. The space of wave functions obtained in this way is isomorphic to a space of theta functions. We use our construction to cunstruct part of what may be a topological field theory in genus one, and to compute the associated invariants of some three manifolds. These computations agree with those of Witten, but the invariants are expressed as sums of quantities computed at a discrete set of connections with curvature concentrated on a link in the three manifold. A similar prescription is used to produce knot invariants. (orig.)
Composite Chern-Simons gauge boson in anyon gas
International Nuclear Information System (INIS)
Nguyen Van Hieu; Nguyen Hung Son.
1990-08-01
It was shown that in a free anyon gas there exists a composite vector gauge field with the effective action containing a Chern-Simons term. The momentum dependence of the energy of the composite boson was found. The mixing between Chern-Simons boson and photon gives rise to the appearance of new quasiparticles - Chern-Simons polaritons. The dispersion equations of Chern-Simons polaritons were derived. (author). 14 refs
Extended charged events and Chern-Simons couplings
International Nuclear Information System (INIS)
Bunster, Claudio; Gomberoff, Andres; Henneaux, Marc
2011-01-01
In three spacetime dimensions, the world volume of a magnetic source is a single point, a magnetically charged event. It has been shown long ago that in three-dimensional spacetime, the Chern-Simons coupling is quantized, because the magnetic event emits an electric charge which must be quantized according to the standard Dirac rule. Recently, the concept of dynamical extended charged events has been introduced, and it has been argued that they should play as central a role as that played by particles or ordinary branes. In this article, we show that in the presence of a Chern-Simons coupling, a magnetically charged extended event emits an extended object, which geometrically is just like a Dirac string, but it is observable, obeys equations of motion, and may be electrically charged. We write a complete action principle which accounts for this effect. The action involves two Chern-Simons terms, one integrated over spacetime and the other integrated over the world volume of the submanifold that is the union of the Dirac world sheet and the history of the emitted physical object. By demanding that the total charge emitted by a composite extended magnetic event be quantized according to Dirac's rule, we find a quantization condition for the Chern-Simons coupling. For a 1-form electric potential in D=2n+1 spacetime dimensions, the composite event is formed by n elementary extended magnetic events separated in time such that the product of their transverse spaces, together with the time axis, is the entire spacetime. We show that the emitted electric charge is given by the integral of the (n-1)-th exterior power of the electromagnetic field strength over the last elementary event, or, equivalently, over an appropriate closed surface. The extension to more general p-form potentials and higher dimensions is also discussed. For the case D=11, p=3, our result for the quantization of the Chern-Simons coupling was obtained previously in the context of M theory, an agreement
Light-front dynamics of Chern-Simons systems
International Nuclear Information System (INIS)
Srivastava, P.P.
1994-10-01
The Chern-Simons theory coupled to complex scalars is quantized on the light-front in the local light-cone gauge by constructing the self-consistent Hamiltonian theory. It is shown that no inconsistency arises on using two local gauge-fixing conditions in the Dirac procedure. The light-front Hamiltonian turns out to be simple and the framework may be useful to construct renormalized field theory of particles with fractional statistics (anyons). The theory is shown to be relativistic and the extra term in the transformation of the matter field under space rotations, interpreted in previous works as anomaly, is argued to be gauge artefact. (author). 20 refs
Dirac matrices for Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Solitons and bubbles in models with Chern-Simons term
International Nuclear Information System (INIS)
Masperi, L.
1992-07-01
It is shown that a gauge theory for complex scalar field with up to sextic self-interactions and a Chern-Simons term in 2 + 1 dimensions has solitons which may become bubbles of the stable broken-symmetry phase in a medium of the symmetric one producing the first-order phase transition. In the non-relativistic limit scale invariance prevents the determination of an optimal bubble size. Possible extensions to 3 + 1 dimensions of bubbles of string type are indicated. (author). 8 refs
Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction
International Nuclear Information System (INIS)
Wu, Y.
1984-01-01
Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved
Dimensional reduction of U(1) x SU(2) Chern-Simons bosonization: Application to the t - J model
International Nuclear Information System (INIS)
Marchetti, P.A.
1996-09-01
We perform a dimensional reduction of the U(1) x SU(2) Chern-Simons bosonization and apply it to the t - J model, relevant for high T c superconductors. This procedure yields a decomposition of the electron field into a product of two ''semionic'' fields, i.e. fields obeying Abelian braid statistics with statistics parameter θ = 1/4, one carrying the charge and the other the spin degrees of freedom. A mean field theory is then shown to reproduce correctly the large distance behaviour of the correlation functions of the 1D t - J model at >> J. This result shows that to capture the essential physical properties of the model one needs a specific ''semionic'' form of spin-charge separation. (author). 31 refs
Ghosh, K. J. B.; Klinkhamer, F. R.
2018-01-01
We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3 ×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U (1) gauge fields Aμ (x) which depend on all four spacetime coordinates (including the coordinate x4 ∈S1 of the compact dimension) and have vanishing components A4 (x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.
The Chern-Simons Current in Systems of DNA-RNA Transcriptions
Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin; Saridakis, Emmanuel N.
2018-04-01
A Chern-Simons current, coming from ghost and anti-ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases $A, T, C, G, U$. After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti-codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern-Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T-cell receptor gene by using a gene tensor correlation network related to the Chern-Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern-Simons current.
The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold
Directory of Open Access Journals (Sweden)
J. A. Helayël-Neto
2017-01-01
Full Text Available It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.
Dynamical generation of non-abelian gauge group via the improved perturbation theory
International Nuclear Information System (INIS)
Kuroki, Tsunehide
2008-01-01
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua. (author)
Abelian tensor hierarchy in 4D, N=1 superspace
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel
2016-01-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Abelian tensor hierarchy in 4D, N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843 (United States)
2016-03-09
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
η-INVARIANT AND CHERN-SIMONS CURRENT
Institute of Scientific and Technical Information of China (English)
ZHANG WEIPING
2005-01-01
The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the aualytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles,and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.
Initial value formulation of dynamical Chern-Simons gravity
Delsate, Térence; Hilditch, David; Witek, Helvi
2015-01-01
We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.
All Chern-Simons invariants of 4D, N=1 gauged superform hierarchies
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch [George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843-4242 (United States); Randall, Stephen [Department of Physics, University of California,Berkeley, CA 94720-7300 (United States); Robbins, Daniel [Department of Physics, University at Albany,Albany, NY 12222 (United States)
2017-04-19
We give a geometric description of supersymmetric gravity/(non-)abelian p-form hierarchies in superspaces with 4D, N=1 super-Poincaré invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, N=1 graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/BF-type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of p-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF-type and cubic Chern-Simons actions. As an application, we compute the quartic invariant ∼AdAdAdA+… relevant, for example, to seven-dimensional supergravity compactifications.
Holographic entanglement for Chern-Simons terms
International Nuclear Information System (INIS)
Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng
2017-01-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS 2k+1 . This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS 7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Holographic entanglement for Chern-Simons terms
Energy Technology Data Exchange (ETDEWEB)
Azeyanagi, Tatsuo [Département de Physique, Ecole Normale Supérieure, CNRS,24 rue Lhomond, 75005 Paris (France); Loganayagam, R. [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Ng, Gim Seng [Department of Physics, McGill University,Montréal, QC H3A 2T8 (Canada)
2017-02-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS{sub 2k+1}. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS{sub 7} and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Holographic entanglement for Chern-Simons terms
Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng
2017-02-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS2 k+1. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong's derivation applied to the corresponding anomaly polynomial. In lower dimensions ( k = 1 , 2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k ≥ 3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Relativistic particles coupled to Chern-Simons term-revisited
International Nuclear Information System (INIS)
Chakraborty, B.
1995-01-01
The author considers the model of N relativistic spinless particles coupled to an abelian Chern-Simons term. Rewriting the action in a time reparamaterized form by introducing an arbitary parameter, parameterizing the world line of the particles, the author makes a classical constraint Hamiltonian analysis of the model. Subsequent to gauge fixing by equating the arbitrary parameter with the time the author identifies the Hamiltonian of the system, which agrees with the Hamiltonian obtained by using Banerjee's method of fixing the arbitrary Langrange multiplier by using equations of motion. The author exhibits the Poincare invariance of the model, at the classical level, by constructing spacetime generators using either the canonical or symmetric definition of the energy-momentum tensor. A detailed comparison of the expressions of angular momentum obtained by both methods show that both agree up to a boundary term. In presence of rotationally symmetric vortex configuration this term can be interpreted as an anomalous angular momentum term. The author also heuristically discusses the effect of gauge fixing on the transformation properties. 13 refs
Scattering amplitude and bosonization duality in general Chern-Simons vector models
Yokoyama, Shuichi
2016-09-01
We present the exact large N calculus of four point functions in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine the two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, an unusual crossing relation and a non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to the Chern-Simons theory interacting with free fermions.
Papapetrou energy-momentum tensor for Chern-Simons modified gravity
International Nuclear Information System (INIS)
Guarrera, David; Hariton, A. J.
2007-01-01
We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom, and Friedmann-Robertson-Walker solutions. To our knowledge this is the first confirmation that the Reissner-Nordstrom and Friedmann-Robertson-Walker metrics are solutions of the modified theory
A Chern-Simons gauge-fixed Lagrangian in a 'non-canonical' BRST approach
International Nuclear Information System (INIS)
Constantinescu, R; Ionescu, C
2009-01-01
This paper presents a possible path which starts from the extended BRST Hamiltonian formalism and ends with a covariant Lagrangian action, using the equivalence between the two formalisms. The approach allows a simple account of the form of the master equation and offers a natural identification of some 'non-canonical' operators and variables. These are the main items which solve the major difficulty of the extended BRST Lagrangian formalism, i.e., the gauge-fixing problem. The algorithm we propose applies to a non-Abelian Chern-Simons model coupled with Dirac fields
Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity
International Nuclear Information System (INIS)
Amarilla, Leonardo; Eiroa, Ernesto F.; Giribet, Gaston
2010-01-01
The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first-class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.
Induced Chern-Simons term in lattice QCD at finite temperature
International Nuclear Information System (INIS)
Borisenko, O.A.; Petrov, V.K.; Zinovjev, G.M.
1995-01-01
The general conditions for the Chern-Simons action to be induced as a non-universal contribution of fermionic determinant are formulated in finite-temperature lattice QCD. The dependence of the corresponding coefficient in the action on non-universal parameters (chemical potentials, vacuum features, etc.) is explored. Special attention is paid to the role of A 0 -condensate if it is available in this theory. ((orig.))
First law of black ring thermodynamics in higher dimensional Chern-Simons gravity
International Nuclear Information System (INIS)
Rogatko, Marek
2007-01-01
The physical process version and the equilibrium state version of the first law of black ring thermodynamics in n-dimensional Einstein gravity with Chern-Simons term were derived. This theory constitutes the simplest generalization of the five-dimensional one admitting a stationary black ring solution. The equilibrium state version of the first law of black ring mechanics was achieved by choosing any cross section of the event horizon to the future of the bifurcation surface
Confinement in Maxwell-Chern-Simons planar quantum electrodynamics and the 1/N approximation
International Nuclear Information System (INIS)
Hofmann, Christoph P.; Raya, Alfredo; Madrigal, Saul Sanchez
2010-01-01
We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first-order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient θ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening - characteristic of the 1/N approximation - is observed in the entire (N,θ)-plane through the local and global properties of the vector part of the fermion propagator.
Dense Chern-Simons matter with fermions at large N
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael; Goykhman, Mikhail; Son, Dam T. [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics,The University of Chicago, 5620 S. Ellis Av., Chicago, IL, 60637 (United States)
2016-04-18
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the ’t Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.
Dense Chern-Simons matter with fermions at large N
International Nuclear Information System (INIS)
Geracie, Michael; Goykhman, Mikhail; Son, Dam T.
2016-01-01
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the ’t Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.
Dense Chern-Simons matter with fermions at large N
Geracie, Michael; Goykhman, Mikhail; Son, Dam T.
2016-04-01
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the 't Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.
Nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model
International Nuclear Information System (INIS)
Han, Jongmin; Jang, Jaeduk
2005-01-01
In this paper we prove the existence of the radially symmetric nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model. We also verify the Chern-Simons limit for those solutions
The Maxwell-Chern-Simons gravity, and its cosmological implications
Energy Technology Data Exchange (ETDEWEB)
Haghani, Zahra; Shahidi, Shahab [Damghan University, School of Physics, Damghan (Iran, Islamic Republic of); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom)
2017-08-15
We consider the cosmological implications of a gravitational theory containing two vector fields coupled via a generalized Chern-Simons term. One of the vector fields is the usual Maxwell field, while the other is a constrained vector field with constant norm included in the action via a Lagrange multiplier. The theory admits a de Sitter type solution, with healthy cosmological perturbations. We also show that there are seven degrees of freedom that propagate on top of de Sitter space-time, consisting of two tensor polarizations, four degrees of freedom related to the two vector fields, and a scalar degree of freedom that makes one of the vector fields massive. We investigate the cosmological evolution of Bianchi type I space-time, by assuming that the matter content of the Universe can be described by the stiff and dust. The cosmological evolution of the Bianchi type I Universe strongly depends on the initial conditions of the physical quantities, as well as on the model parameters. The mean anisotropy parameter, and the deceleration parameter, are also studied, and we show that independently of the matter equation of state the cosmological evolution of the Bianchi type I Universe always ends in an isotropic de Sitter type phase. (orig.)
International Nuclear Information System (INIS)
Ogilvie, M.C.
1999-01-01
Analytic methods for Abelian projection are developed. A number of results are obtained related to string tension measurements. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The methods used emphasize that the projected theory is derived from the underlying non-Abelian theory rather than vice versa. In general, the choice of subgroup used for projection is not very important, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements. Two other issues, Casimir scaling and the conflict between projection and critical universality, are also discussed. copyright 1999 The American Physical Society
Qiang, Li-E.; Xu, Peng
2015-08-01
Having great accuracy in the range and range rate measurements, the GRACE mission and the planed GRACE follow on mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the satellite-to-satellite tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of cm for each free flight of these SST missions, here is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale of the non-dynamical Chern-Simons gravity could be constrained to be larger than eV. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that eV is expected.
Large N Chern-Simons with massive fundamental fermions — A model with no bound states
International Nuclear Information System (INIS)
Frishman, Yitzhak; Sonnenschein, Jacob
2014-01-01
In a previous paper http://dx.doi.org/10.1007/JHEP12(2013)091, we analyzed the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory in three dimensions at level K. It was done in the large N, large K limits where λ=(N/K) was kept fixed. Among other results, we showed there that there are no high mass “quark anti-quark" bound states. Here we show that there are no bound states at all.
Bound states in the (2+1)D scalar electrodynamics with Chern-Simons term
International Nuclear Information System (INIS)
Gomes, M.O.C.; Malacarne, L.C.
1994-01-01
This work studies the existence of bound states for the 3-dimensions scalar electrodynamics, with the Chern-Simons. Quantum field theory is used for calculation of the M fi scattering matrices, in the non-relativistic approximation. The field propagators responsible for the interaction in the scattering processes have been calculated, and scattering matrices have been constructed. After obtaining the scattering matrix, the cross section in the quantum field theory has been compared with the quantum mechanic cross section in the Born approximation, allowing to obtain the form of the potential responsible for the interactions in the scattering processes. The possibility of bound states are analyzed by using the Schroedinger equation
Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.
Yagi, Kent; Yunes, Nicolás; Tanaka, Takahiro
2012-12-21
Dynamical Chern-Simons gravity cannot be strongly constrained with current experiments because it reduces to general relativity in the weak-field limit. This theory, however, introduces modifications in the nonlinear, dynamical regime, and thus it could be greatly constrained with gravitational waves from the late inspiral of black-hole binaries. We complete the first self-consistent calculation of such gravitational waves in this theory. For favorable spin orientations, advanced ground-based detectors may improve existing solar system constraints by 6 orders of magnitude.
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
International Nuclear Information System (INIS)
Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L.
2015-01-01
We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability. (orig.)
Once more about the topologically massive gauge theory
International Nuclear Information System (INIS)
Kogan, Ya.I.
1989-01-01
The general properties of the three-dimensional gauge theory with the topological mass is discussed namely the long-range interaction of the Aharonov-Bohm type. It is argued that Chern-Simons gauge theories must be considered as the infrared limit of the topologically massive theories. The analogy between the Landau problem of a charged particle in a magnetic field and quantization of this gauge theory is considered, as well as the quantization condition for the Abelian Chern-Simons term. 38 refs.; 5 figs
From Lorentz-Chern-Simons to Massive Gravity in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Pino, Simón del [Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso,Av. Universidad 330, Curauma, Valparaíso (Chile); Giribet, Gaston [Physique Théorique et Mathématique, Université Libre de Bruxelles andInternational Solvay Institutes,Campus Plaine C.P. 231, Bruxelles, B-1050 (Belgium); Departamento de Física, Universidad de Buenos Aires and IFIBA-CONICET,Ciudad Universitaria, Pabellón I, Buenos Aires, 1428 (Argentina); Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso,Av. Universidad 330, Curauma, Valparaíso (Chile); Toloza, Adolfo [Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso,Av. Universidad 330, Curauma, Valparaíso (Chile); Centro de Estudios Científicos CECs,Arturo Prat 514, Valdivia (Chile); Zanelli, Jorge [Centro de Estudios Científicos CECs,Arturo Prat 514, Valdivia (Chile)
2015-06-17
We propose a generalization of Chiral Gravity, which follows from considering a Chern-Simons action for the spin connection with anti-symmetric contorsion. The theory corresponds to Topologically Massive Gravity at the chiral point non-minimally coupled to an additional scalar mode that gathers the torsion degree of freedom. In this setup, the effective cosmological constant (the inverse of the curvature radius of maximally symmetric solutions) is either negative or zero, and it enters as an integration constant associated to the value of the contorsion at infinity. We explain how this is not in conflict with the Zamolodchikov’s c-theorem holding in the dual boundary theory. In fact, we conjecture that the theory formulated about three-dimensional Anti-de Sitter space is dual to a two-dimensional conformal field theory whose right- and left-moving central charges are given by c{sub R}=24k and c{sub L}=0, respectively, being k the level of the Chern-Simons action. We study the classical theory both at the linear and non-linear level. In particular, we show how Chiral Gravity is included as a special sector. In addition, the theory has other sectors, which we explore; we exhibit analytic exact solutions that are not solutions of Topologically Massive Gravity (and, consequently, neither of General Relativity) and still satisfy Brown-Henneaux asymptotically AdS{sub 3} boundary conditions.
Research program in elementary particle theory
International Nuclear Information System (INIS)
Balachandran, A.P.; Rosenzweig, C.; Schechter, J.; Wali, K.C.
1992-01-01
In this paper we give a brief account of the work of the group during the past year. The topics covered here include (1) Effective Lagrangians and Solitons; (2) Chern-Simons and Conformal Field Theories; (3) Spin and Statistics; (4) The Standard Model and Beyond; (5) Non-Abelian Monopoles; (6) The Inflationary Universe; (7) The Hubbard Model, and (8) Miscellaneous
N = 1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time
International Nuclear Information System (INIS)
Andrade, M.A. de; Cima, O.M. Del; Colatto, L.P.
1995-06-01
In this letter, we present the Parkes-Siegel formulation for the massive Abelian N=1 super-QED 2+2 coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from (2+2) to (1+2) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the π3 QED 1+2 coupled to a Chern-Simons term naturally comes out. (author). 15 refs
Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.
2018-05-01
The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab of finite thickness is studied by using the consistent hydrodynamic theory. The latter includes viscous, anomalous, and vortical effects, as well as accounts for dynamical electromagnetism. The energy and momentum separations between the Weyl nodes are taken into account via the topological Chern-Simons contributions in the electric current and charge densities in Maxwell's equations. When an external electric field is applied parallel to the slab, it is found that the electron fluid velocity has a nonuniform profile determined by the viscosity and the no-slip boundary conditions. Most remarkably, the fluid velocity field develops a nonzero component across the slab that gradually dissipates when approaching the surfaces. This abnormal component of the flow arises due to the anomalous Hall voltage induced by the topological Chern-Simons current. Another signature feature of the hydrodynamics in Weyl semimetals is a strong modification of the anomalous Hall current along the slab in the direction perpendicular to the applied electric field. Additionally, it is found that the topological current induces an electric potential difference between the surfaces of the slab that is strongly affected by the hydrodynamic flow.
Hassaine, Mokhtar
2016-01-01
This book grew out of a set of lecture notes on gravitational Chern–Simons (CS) theories developed over the past decade for several schools and different audiences including graduate students and researchers.CS theories are gauge-invariant theories that can include gravity consistently. They are only defined in odd dimensions and represent a very special class of theories in the Lovelock family. Lovelock gravitation theories are the natural extensions of General Relativity for dimensions greater than four that yield second-order field equations for the metric. These theories also admit local supersymmetric extensions where supersymmetry is an off-shell symmetry of the action, as in a standard gauge theory.Apart from the arguments of mathematical elegance and beauty, the gravitational CS actions are exceptionally endowed with physical attributes that suggest the viability of a quantum interpretation. CS theories are gauge-invariant, scale-invariant and background independent; they have no dimensional couplin...
Multi-cut solutions in Chern-Simons matrix models
Morita, Takeshi; Sugiyama, Kento
2018-04-01
We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.
Chern-Simons induced spin factors in noncovariant gauges
International Nuclear Information System (INIS)
Tanaka, I.
1993-01-01
We study Chern-Simons induced spin factors in noncovariant metric-independent gauges, such as the axial gauge and the Coulomb gauge. These spin factors are defined without loop splitting. We find that they are equal to integers and have particular geometrical meanings. In the axial gauge, this integer is the writhe number of a link diagram defined by the projection of a loop to the time direction. In the Coulomb gauge, it is suggested that this integer is also the writhe number of a link diagram, defined by the projection of a loop to a spatial plane
d=3 Chern-Simons action, supergravity and quantization
International Nuclear Information System (INIS)
Dayi, O.F.
1989-01-01
An interpretation of three-dimensional simple supergravity as a pure Chern-Simons gauge action is shown to be valid up to the one loop level. Canonical quantization of this system does not lead to an explicit definition of the physical Hilbert space. Hence another formulation of the N = 1 three-dimensional supergravity is introduced. In this formalism an explicit definition of the physical Hilbert space is possible, but still one has to solve the problems of showing that there exists a global set of coordinates and of defining the inner product. (author). 10 refs
Deformed N = 8 supergravity from IIA strings and its Chern-Simons duals
Energy Technology Data Exchange (ETDEWEB)
Guarino, Adolfo [Nikhef Theory Group, Amsterdam (Netherlands); Jafferis, Daniel L. [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA (United States); Varela, Oscar [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA (United States); Centre de Physique Theorique, Ecole Polytechnique, CNRS UMR 7644, Palaiseau (France)
2016-04-15
Do electric/magnetic deformations of N = 8 supergravity enjoy a string/M-theory origin, or are they just a fourdimensional artefact? We address this question for the gauging of a group closely related to SO(8): its contraction ISO(7). We argue that the deformed ISO(7) supergravity arises from consistent truncation of massive IIA supergravity on S{sup 6}, and its electric/magnetic deformation parameter descends directly from the Romans mass. The critical points of the supergravity uplift to AdS{sub 4} massive type IIA vacua and the corresponding CFT{sub 3} duals are identified as super-Chern-Simons-matter theories with gauge group SU(N) and level k given also by the Romans mass. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity
International Nuclear Information System (INIS)
Meusburger, C; Schroers, B J
2003-01-01
In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms
Framing anomaly in the effective theory of the fractional quantum Hall effect.
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo
2015-01-09
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators
Alekseev, Anton; Naef, Florian; Xu, Xiaomeng; Zhu, Chenchang
2018-03-01
Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern-Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as p= where F is the curvature 2-form and is an invariant scalar product on the corresponding Lie algebra g. The descent for p gives rise to an element ω =ω _3+ω _2+ω _1+ω _0 of mixed degree. The 3-form part ω _3 is the Chern-Simons form. The 2-form part ω _2 is known as the Wess-Zumino action in physics. The 1-form component ω _1 is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components ω _1 and ω _0. Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara-Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara-Vergne equation F is mapped to ω _1=C(F). Furthermore, the component ω _0 is related to the associator Φ corresponding to F. It is surprising that while F and Φ satisfy the highly nonlinear twist and pentagon equations, the elements ω _1 and ω _0 solve the linear descent equation.
Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
International Nuclear Information System (INIS)
Tierz, Miguel
2016-01-01
We solve for finite N the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N f fundamental and N f anti-fundamental chiral multiplets of R-charge 1/2 and of mass m, by identifying it with an average of inverse characteristic polynomials in a Stieltjes-Wigert ensemble. This requires the computation of the Cauchy transform of the Stieltjes-Wigert polynomials, which we carry out, finding a relationship with Mordell integrals, and hence with previous analytical results on the matrix model. The semiclassical limit of the model is expressed, for arbitrary N f , in terms of a single Hermite polynomial. This result also holds for more general matter content, involving matrix models with double-sine functions.
Surface theorem for the Chern-Simons axion coupling
DEFF Research Database (Denmark)
Olsen, Thomas; Taherinejad, Maryam; Vanderbilt, David
2017-01-01
The Chern-Simons axion coupling of a bulk insulator is only defined modulo a quantum of e2/h. The quantized part of the coupling is uniquely defined for a bounded insulating sample, but it depends on the specific surface termination.Working in a slab geometry and representing the valence bands...... in terms of hybridWannier functions, we show how to determine that quantized part from the excess Chern number of the hybridWannier sheets located near the surface of the slab. The procedure is illustrated for a tight-binding model consisting of coupled quantum anomalous Hall layers. By slowly modulating...... the model parameters it is possible to transfer one unit of Chern number from the bottom to the top surface over the course of a cyclic evolution of the bulk Hamiltonian, changing the surface anomalous Hall conductivity by a quantum of conductance e2/h. When the evolution of the surface Hamiltonian is also...
Static solutions in Einstein-Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Crisóstomo, J.; Gomez, F.; Mella, P.; Quinzacara, C.; Salgado, P., E-mail: jcrisostomo@udec.cl, E-mail: fernagomez@udec.cl, E-mail: patriciomella@udec.cl, E-mail: cristian.cortesq@uss.cl, E-mail: pasalgad@udec.cl [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile)
2016-06-01
In this paper we study static solutions with more general symmetries than the spherical symmetry of the five-dimensional Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field h{sup a} with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with h{sup a}. It is found that exist (i) a negative tangential pressure zone around low-mass distributions (μ < μ{sub 1}) when the coupling constant α is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies μ < μ{sub 2}; (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field h{sup a} plays the role of a cosmological constant.
Finite action for Chern-Simons Ads gravity
Energy Technology Data Exchange (ETDEWEB)
Mora, P.; Olea, R.; Troncoso, R.; Zanelli, J. E-mail: jz@cecs.cl
2004-06-01
A finite principle for Chern-Simons AdS gravity is presented. The construction is carried out in detail first in five dimensions, where the bulk action is given by a particular combination of the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term; and is then generalized for arbitrary odd dimensions. The boundary term needed to render the action finite is singled out demanding the action to attain an extremum for an appropriate set of boundary conditions. The boundary term is a local function of the fields at the boundary and is sufficient to render the action finite for asymptotically AdS solutions, without requiring background fields. It is shown that the Euclidean continuation of the action correctly describes black hole thermodynamics in the canonical ensemble. Additionally, background independent conserved charges associated with the asymptotic symmetries can be written as surface integrals by direct application of Noether's theorem. (author)
Ricci dark energy in Chern-Simons modified gravity
Energy Technology Data Exchange (ETDEWEB)
Silva, J.G.; Santos, A.F. [Universidade Federal de Mato Grosso (UFMT), Campo Grande, MT (Brazil)
2013-07-01
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρ{sub x} ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
Ricci dark energy in Chern-Simons modified gravity
International Nuclear Information System (INIS)
Silva, J.G.; Santos, A.F.
2013-01-01
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρ x ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge
Directory of Open Access Journals (Sweden)
Nikolaos Bournaveas
2009-09-01
Full Text Available We prove local well-posedness for the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge with initial data of low regularity. Our result improves earlier results by Huh [10, 11].
BPS-kink and more global solutions of the Chern-Simons (super)gravity term
International Nuclear Information System (INIS)
Grumiller, D.
2004-01-01
We study the supersymmetry of the Kaluza-Klein reduced gravitational Chern-Simons term in two dimensions and propose supergravity transformations that allow for some supersymmetry of the kink solution. (author)
Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity
Energy Technology Data Exchange (ETDEWEB)
Barnich, Glenn [Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Giribet, Gastón [Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Leston, Mauricio [Instituto de Astronomía y Física del Espacio IAFE-CONICET, Ciudad Universitaria, Pabellón IAFE, C.C. 67 Suc. 28, 1428 Buenos Aires (Argentina)
2015-07-15
We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity.
Electron-electron attractive interaction in Maxwell-Chern-Simons QED3 at zero temperature
International Nuclear Information System (INIS)
Belich, H.; Ferreira Junior, M.M.; Helayel-Neto, J.A.; Ferreira Junior, M.M.
2001-04-01
One discusses the issue of low-energy electron-electron bound states in the Maxwell-Chern-Simons model coupled to QED 3 with spontaneous breaking of a local U(1)-symmetry. The scattering potential, in the non-relativistic limit, steaming from the electron-electron Moeller scattering, mediated by the Maxwell-Chern-Simons-Proca gauge field and the Higgs scalar, might be attractive by fine-tuning properly the physical parameters of the model. (author)
Zero-modes of non-Abelian solitons in three-dimensional gauge theories
International Nuclear Information System (INIS)
Eto, Minoru; Gudnason, Sven Bjarke
2011-01-01
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d = 2 + 1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We find that the zero-modes of the topological solitons are governed by the moduli matrix H 0 only and those of the non-topological solitons are governed by both H 0 and the gauge invariant field Ω. We prove local uniqueness of the master equation in the YM case and finally compare all results between the CS and YM theories.
(Non-)Abelian Kramers-Wannier duality and topological field theory
Severa, Pavol
2002-01-01
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for higher-dimensional cases. In this form they lead to simple TFTs with boundary coloured in two colours. The statistical models live on the boundary of these TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie T-duality) suggest a non-abelian generalization in the 2dcase, with abelian groups replaced by quantum groups. Amazingly, the TFT formulation solves the problem without computation: quantum groups appear in pictures, independently of the classical motivation. Connection with Chern-Simons theory appears at the symplectic level, and also in the pictures of the Drinfeld double: Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the double, are included in these TFTs. All this suggests nice phenomena in higher dimensions.
High-temperature response functions and the non-Abelian Kubo formula
International Nuclear Information System (INIS)
Jackiw, R.; Nair, V.P.
1993-01-01
We describe the relationship between time-ordered and retarded response functions in a plasma. We obtain an expression, including the proper iε prescription, for the induced current due to hard thermal loops in a non-Abelian theory, thus giving the non-Abelian generalization of the Kubo formula. The result is closely related to the eikonal for a Chern-Simons theory and is relevant for a guage-invariant description of Landau damping in the quark-gluon plasma at high temperature
Quest for Casimir repulsion between Chern-Simons surfaces
Fialkovsky, Ignat; Khusnutdinov, Nail; Vassilevich, Dmitri
2018-04-01
In this paper we critically reconsider the Casimir repulsion between surfaces that carry the Chern-Simons interaction (corresponding to the Hall-type conductivity). We present a derivation of the Lifshitz formula valid for arbitrary planar geometries and discuss its properties. This analysis allows us to resolve some contradictions in the previous literature. We compute the Casimir energy for two surfaces that have constant longitudinal and Hall conductivities. The repulsion is possible only if both surfaces have Hall conductivities of the same sign. However, there is a critical value of the longitudinal conductivity above which the repulsion disappears. We also consider a model where both parity odd and parity even terms in the conductivity are produced by the polarization tensor of surface modes. In contrast to the previous publications [L. Chen and S.-L. Wan, Phys. Rev. B 84, 075149 (2011), 10.1103/PhysRevB.84.075149; Phys. Rev. B 85, 115102 (2012), 10.1103/PhysRevB.85.115102], we include the parity anomaly term. This term ensures that the conductivities vanish for infinitely massive surface modes. We find that at least for a single mode, regardless of the sign and value of its mass, there is no Casimir repulsion.
The geometry and physics of Abelian gauge groups in F-theory
Energy Technology Data Exchange (ETDEWEB)
Keitel, Jan
2015-07-14
In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.
The geometry and physics of Abelian gauge groups in F-theory
International Nuclear Information System (INIS)
Keitel, Jan
2015-01-01
In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Recently, the Banados-Teitelboim-Zanelli (BTZ) black hole in the presence of the gravitational Chern-Simons term has been studied, and it is found that the usual thermodynamic quantities, like the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such that the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of a vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative corrections of the gravitational Chern-Simons term. This provides a nontrivial check of the AdS/CFT correspondence, in the presence of higher-derivative terms in the gravity action
Effective Chern-Simons actions of particles coupled to 3D gravity
Trześniewski, Tomasz
2018-03-01
Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincaré group, integrating out the gravitational degrees of freedom it is possible to obtain the effective action for particle dynamics. We review the known results, both for single and multiple particles, and attempt to extend this approach to the (anti-)de Sitter group, using the factorizations of isometry groups into the double product of the Lorentz group and AN (2) group. On the other hand, for the de Sitter group one can also perform a contraction to the semidirect product of AN (2) and the translation group. The corresponding effective action curiously describes a Carrollian particle with the AN (2) momentum space. We derive this contraction in a more rigorous manner and further explore its properties, including a generalization to the multiparticle case.
Inducing the μ and the Bμ term by the radion and the 5d Chern-Simons term
International Nuclear Information System (INIS)
Hebecker, A.; March-Russell, J.; Ziegler, R.
2009-01-01
In 5-dimensional models with gauge-Higgs unification, the F-term vacuum expectation value of the radion provides, in close analogy to the Giudice-Masiero mechanism, a natural source for the μ and Bμ term. Both the leading order gauge theory lagrangian and the supersymmetric Chern-Simons term contain couplings to the radion superfield which can be used for this purpose. We analyse the basic features of this mechanism for μ term generation and provide an explicit example, based on a variation of the SU(6) gauge-Higgs unification model of Burdman and Nomura. This construction contains all the relevant features used in our generic analysis. More generally, we expect our mechanism to be relevant to many of the recently discussed orbifold GUT models derived from heterotic string theory. This provides an interesting way of testing high-scale physics via Higgs mass patterns accessible at the LHC.
Chern-Simons forms and four-dimensional N=1 superspace geometry
International Nuclear Information System (INIS)
Girardi, G.; Grimm, R.
1986-12-01
The complete superspace geometry for Yang-Mills, chiral U(1) and Lorentz Chern-Simons forms is constructed. The analysis is completely off-shell and covers the cases of minimal, new minimal and 16-16 supergravity. Supersymmetry is guaranteed by construction. Invariant superfield actions are proposed
Entropy for gravitational Chern-Simons terms by squashed cone method
International Nuclear Information System (INIS)
Guo, Wu-Zhong; Miao, Rong-Xin
2016-01-01
In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D there is no anomaly of entropy. But the original squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation dΩ_4_n_−_1=tr(R"2"n). We notice that the entropy of tr(R"2"n) is a total derivative locally, i.e. S=ds_C_S. We propose to identify s_C_S with the entropy of gravitational Chern-Simons terms Ω_4_n_−_1. In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term tr(R"2"n) and the Euler density, is a topological invariant on the entangling surface.
Electron-electron attractive interaction in Maxwell-Chern-Simons QED{sub 3} at zero temperature
Energy Technology Data Exchange (ETDEWEB)
Belich, H.; Ferreira Junior, M.M.; Helayel-Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: belich@cbpf.br; manojr@cbpf.br; helayel@gft.ucp.br; Ferreira Junior, M.M. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: delcima@gft.ucp.br
2001-04-01
One discusses the issue of low-energy electron-electron bound states in the Maxwell-Chern-Simons model coupled to QED{sub 3} with spontaneous breaking of a local U(1)-symmetry. The scattering potential, in the non-relativistic limit, steaming from the electron-electron Moeller scattering, mediated by the Maxwell-Chern-Simons-Proca gauge field and the Higgs scalar, might be attractive by fine-tuning properly the physical parameters of the model. (author)
Dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model
Energy Technology Data Exchange (ETDEWEB)
Belich, H. Jr.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); E-mails: belich@cbpf.br; helayel@cbpf.br; Ferreira, M.M. Jr. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); Maranhao Univ., Sao Luiz, MA (Brazil). Dept. de Fisica]. E-mail: manojr@cbpf.br; Orlando, M.T.D. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); Espirito Santo Univ., Vitoria, ES (Brazil). Dept. de Fisica e Quimica; E-mail: orlando@cce.ufes.br
2003-01-01
Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional to D = 1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, {nu}{sup {mu}}. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of {nu}{sup {mu}} . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitary of the gauge sector is assured without any restriction , while the scalar sector is unitary only in the space-like case. (author)
Dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model
International Nuclear Information System (INIS)
Belich, H. Jr.; Helayel Neto, J.A.; Ferreira, M.M. Jr.; Maranhao Univ., Sao Luiz, MA; Orlando, M.T.D.; Espirito Santo Univ., Vitoria, ES
2003-01-01
Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional to D = 1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, ν μ . In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of ν μ . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitary of the gauge sector is assured without any restriction , while the scalar sector is unitary only in the space-like case. (author)
Vortex dynamics in self-dual Chern-Simons-Higgs systems
International Nuclear Information System (INIS)
Kim, Y.; Lee, K.
1994-01-01
We consider vortex dynamics in self-dual Chern-Simons-Higgs systems. We show that the naive Aharonov-Bohm phase is the inverse of the statistical phase expected from the vortex spin, and that the self-dual configurations of vortices are degenerate in energy but not in angular momentum. We also use the path integral formalism to derive the dual formulation of Chern-Simons-Higgs systems in which vortices appear as charged particles. We argue that in addition to the electromagnetic interaction, there is an additional interaction between vortices, the so-called Magnus force, and that these forces can be put together into a single ''dual electromagnetic'' interaction. This dual electromagnetic interaction leads to the right statistical phase. We also derive and study the effective action for slowly moving vortices, which contains terms both linear and quadratic in the vortex velocity. We show that vortices can be bounded to each other by the Magnus force
Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
International Nuclear Information System (INIS)
Olmo, Mariano A. del; Plyushchay, Mikhail S.
2006-01-01
The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern-Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons
Possible daily and seasonal variations in quantum interference induced by Chern-Simons gravity.
Okawara, Hiroki; Yamada, Kei; Asada, Hideki
2012-12-07
Possible effects of Chern-Simons (CS) gravity on a quantum interferometer turn out to be dependent on the latitude and direction of the interferometer on Earth in orbital motion around the Sun. Daily and seasonal variations in phase shifts are predicted with an estimate of the size of the effects, wherefore neutron interferometry with ~5 m arm length and ~10(-4) phase measurement accuracy would place a bound on a CS parameter comparable to the Gravity Probe B satellite.
Field redefinitions and Chern-Simons terms in the heterotic string
International Nuclear Information System (INIS)
Bern, Z.; Shimada, T.
1987-07-01
Field redefinitions in the low energy effective action of the heterotic string are discussed. A field redefinition is constructed which generates the local counterterm that transforms the Lorentz into the gravitational form of the anomaly. We also discuss the field redefinition which torsionizes the Lorentz Chern-Simons term and its relation to an amplitude matching study of the compatibility of torsion with the Gauss-Bonnet combination. (orig.)
N=2-Maxwell-Chern-Simons model with anomalous magnetic moment coupling via dimensional reduction
International Nuclear Information System (INIS)
Christiansen, H.R.; Cunha, M.S.; Helayel Neto, Jose A.; Manssur, L.R.U; Nogueira, A.L.M.A.
1998-02-01
An N=1-supersymmetric version of the Cremmer-Scherk-Kalb-Ramond model with non-minimal coupling to matter is built up both in terms of superfields and in a component field formalism. By adopting a dimensional reduction procedure, the N=2-D=3 counterpart of the model comes out, with two main features: a genuine (diagonal) Chern-Simons term and an anomalous magnetic moment coupling between matter and the gauge potential. (author)
Jejjala, Vishnumohan
2002-01-01
makes falsifiable predictions about TeV scale physics. Susskind has proposed that the fractional quantum Hall system can be realized through an Abelian Chern-Simons theory with a Moyal product. Susskind's Chern-Simons field is a hydrodynamical quantity. Lopez and Fradkin have an alternate Chern-Simons description couched in terms of a statistical gauge field. We show that this statistical Chern-Simons theory also possesses a non-commutative structure and develop the dictionary between the two Chern-Simons pictures.
On the role of the Chern-Simons action for the description of the QHE
International Nuclear Information System (INIS)
Cabo, A.; Oliva, D.
1990-05-01
The role of the Chern-Simons action in the description of the quantum Hall effects is stressed. The 2D-electromagnetic picture of Widom and Srivastava is shown to be valid in a superlattice of 2D-electron gases. A Meissner-like effect appears in such systems. In them, the difference between the external and the integer filling factor fields is exponentially screened by the surface (edge) currents. Also, effective Maxwell equations for one sheet or a superlattice are obtained. (author). 21 refs
Abelian 2-form gauge theory: special features
International Nuclear Information System (INIS)
Malik, R P
2003-01-01
It is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two (1 + 1)-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is not an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the topological 2D free Abelian (and self-interacting non-Abelian) gauge theories
Abelian dominance in Einstein’s theory
International Nuclear Information System (INIS)
Cho, Y M; Oh, S H; Kim, Sang-Woo
2012-01-01
We conjecture the Abelian dominance in Einstein’s theory, that is, the Abelian part of the theory plays the central role in the dynamics. Treating Einstein’s theory as a gauge theory of the Lorentz group, we show that Einstein’s theory can be decomposed into the restricted part made up of the restricted connection which has the full Lorentz gauge invariance and the valence part made up of the valence connection which plays the role of gravitational source of the restricted gravity. In this decomposition, the role of the metric g μν is replaced by a four-index metric tensor g μν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇ α g μν = 0 of the connection is replaced by the gauge and generally covariant condition D μ g μν = 0. We show that there are two different Abelian decompositions, the light-like (or null) decomposition and the non-light-like (or non-null) decomposition, because the Lorentz group has two maximal Abelian subgroups. The decomposition shows the existence of the restricted gravity which has the full general invariance but is much simpler than Einstein’s theory. Moreover, it tells us that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-1 field. This establishes the Abelian dominance in Einstein’s theory. (paper)
Linearized fermion-gravitation system in a (2+1)-dimensional space-time with Chern-Simons data
International Nuclear Information System (INIS)
Mello, E.R.B. de.
1990-01-01
The fermion-graviton system at linearized level in a (2+1)-dimensional space-time with the gravitational Chern-Simons term is studied. In this approximation it is shown that this system presents anomalous rotational properties and spin, in analogy with the gauge field-matter system. (A.C.A.S.) [pt
Elements of theory of abelian groups
International Nuclear Information System (INIS)
Lebedenko, V.M.
1977-01-01
Some methods and results of studies on the abelian group theory being an important branch of modern algebra are presented. Some examples of the application of the abelian groups in physics are given. A primary information on commutative groups is presented. The concepts of a group, a subgroup, homomorphism, an order of element are given; those of torsion, torsion-free and mixed groups are considered, as well as the concepts of direct and full direct sums. The concepts of a free group and defining relations, of linear dependence and a rank are given. The main classes of abelian groups and subgroup types are described. Some classical results on the abelian group theory are presented, its modern state is described, the links with other regions of algebra are presented
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
Maxwell-Chern-Simons vortices in a CPT-odd Lorentz-violating Higgs electrodynamics
International Nuclear Information System (INIS)
Casana, R.; Ferreira, M.M.; Hora, E. da; Neves, A.B.F.
2014-01-01
We study BPS vortices in a CPT-odd and Lorentz-violating Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating parameter induces a pronounced behavior at origin (for the magnetic/electric fields and energy density) which is absent in the MCSH vortices. For some combination of the Lorentz-violating coefficients there always exists a sufficiently large winding number n 0 such that for all vertical stroke n vertical stroke ≥ vertical stroke n 0 vertical stroke the magnetic field flips sign, yielding two well-defined regions with opposite magnetic flux. However, the total magnetic flux remains quantized and proportional to the winding number. (orig.)
Quantum field theory in 2+1 dimensions
International Nuclear Information System (INIS)
Marino, E.C.
1998-01-01
An introductory review is made of many outstanding features of Quantum Field Theory formulated in three-dimensional spacetime. These include topological properties, the Huygens Principle, the Coulomb potential, topological excitations like vortices and skyrmions, dynamical mass generation, fractional spin and statistics, duality nd bosonization. Theories including the Maxwell-Chern-Simons, Abelian Higgs and C P 1 -Nonlinear Sigma Model are used to illustrate the different features. Applications to High-T c Superconductivity and to the Quantum Hall Effect are also presented. (author)
Restricted gravity: Abelian projection of Einstein's theory
International Nuclear Information System (INIS)
Cho, Y.M.
2013-01-01
Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection Γμ into the restricted connection made of the potential of the maximal Abelian subgroup H of Lorentz group G and the valence connection made of G/H part of the potential which transforms covariantly under Lorentz gauge transformation. With this we show that Einstein's theory can be decomposed into the restricted gravity made of the restricted connection which has the full Lorentz gauge invariance which has the valence connection as gravitational source. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory,
Holography in three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
The holographic description of the three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy-momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the conventional Hawking temperature, and it is found that the usual Gibbons-Hawking entropy is modified. It is remarked that, due to the gravitational Chern-Simons term, (a) the results go beyond the analytic continuation from AdS, (b) the maximum-mass/N-bound conjecture may be violated and (c) the three-dimensional cosmology is chiral. A statistical mechanical computation of the entropy, from a Cardy-like formula for a dual CFT at the asymptotic boundary, is discussed. Some remarks on the technical differences in the Chern-Simons energy-momentum tensor, from the literature, are also made
A Relation Between Topological Quantum Field Theory and the Kodama State
Oda, Ichiro
2003-01-01
We study a relation between topological quantum field theory and the Kodama (Chern-Simons) state. It is shown that the Kodama (Chern-Simons) state describes a topological state with unbroken diffeomorphism invariance in Yang-Mills theory and Einstein's general relativity in four dimensions. We give a clear explanation of "why" such a topological state exists.
Thin accretion disk signatures in dynamical Chern-Simons-modified gravity
International Nuclear Information System (INIS)
Harko, Tiberiu; Kovacs, Zoltan; Lobo, Francisco S N
2010-01-01
A promising extension of general relativity is Chern-Simons (CS)-modified gravity, in which the Einstein-Hilbert action is modified by adding a parity-violating CS term, which couples to gravity via a scalar field. In this work, we consider the interesting, yet relatively unexplored, dynamical formulation of CS-modified gravity, where the CS coupling field is treated as a dynamical field, endowed with its own stress-energy tensor and evolution equation. We consider the possibility of observationally testing dynamical CS-modified gravity by using the accretion disk properties around slowly rotating black holes. The energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and compared to the standard general relativistic Kerr solution. It is shown that the Kerr black hole provides a more efficient engine for the transformation of the energy of the accreting mass into radiation than their slowly rotating counterparts in CS-modified gravity. Specific signatures appear in the electromagnetic spectrum, thus leading to the possibility of directly testing CS-modified gravity by using astrophysical observations of the emission spectra from accretion disks.
The Chern-Simons current in time series of knots and links in proteins
Capozziello, Salvatore; Pincak, Richard
2018-06-01
A superspace model of knots and links for DNA time series data is proposed to take into account the feedback loop from docking to undocking state of protein-protein interactions. In particular, the direction of interactions between the 8 hidden states of DNA is considered. It is a E8 ×E8 unified spin model where the genotype, from active and inactive side of DNA time data series, can be considered for any living organism. The mathematical model is borrowed from loop-quantum gravity and adapted to biology. It is used to derive equations for gene expression describing transitions from ground to excited states, and for the 8 coupling states between geneon and anti-geneon transposon and retrotransposon in trash DNA. Specifically, we adopt a modified Grothendieck cohomology and a modified Khovanov cohomology for biology. The result is a Chern-Simons current in (8 + 3) extradimensions of a given unoriented supermanifold with ghost fields of protein structures. The 8 dimensions come from the 8 hidden states of spinor field of genetic code. The extradimensions come from the 3 types of principle fiber bundle in the secondary protein.
Cosmological Analysis of Dynamical Chern-Simons Modified Gravity via Dark Energy Scenario
Directory of Open Access Journals (Sweden)
Abdul Jawad
2015-01-01
Full Text Available The purpose of this paper is to study the cosmological evolution of the universe in the framework of dynamical Chern-Simons modified gravity. We take pilgrim dark energy model with Hubble and event horizons in interacting scenario with cold dark matter. For this scenario, we discuss cosmological parameters such as Hubble and equation of state and cosmological plane like ωϑ-ωϑ′ and squared speed of sound. It is found that Hubble parameter approaches the ranges 75-0.5+0.5 (for u=2 and (74, 74.30 (for u=1,-1,-2 for Hubble horizon pilgrim dark energy. It implies the ranges 74.80-0.005+0.005 (for u=2 and (73.4, 74 (for u=-2 for event horizon pilgrim dark energy. The equation of state parameter provides consistent ranges with different observational schemes. Also, ωϑ-ωϑ′ planes lie in the range (ωϑ=-1.13-0.25+0.24,ωϑ′<1.32. The squared speed of sound shows stability for all present models in the present scenario. We would like to mention here that our results of various cosmological parameters show consistency with different observational data like Planck, WP, BAO, H0, SNLS, and WMAP.
Non-Abelian Gauge Theory in the Lorentz Violating Background
Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais
2018-03-01
In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.
Quantum field theory I foundations and Abelian and non-Abelian gauge theories
Manoukian, Edouard B
2016-01-01
This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman’s well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Pa...
Abelian gauge symmetries in F-theory and dual theories
Song, Peng
In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by
A new gauge for supersymmetric abelian gauge theories
International Nuclear Information System (INIS)
Smith, A.W.; Barcelos Neto, J.
1984-01-01
A new gauge for supersymmetric abelian gauge theories is presented. It is shown that this new gauge allows us to obtain terms which usually come as radiative corrections to the supersymmetric abelian gauge theories when one uses the Wess-Zumino gauge. (Author) [pt
Topological charge in non-abelian lattice gauge theory
International Nuclear Information System (INIS)
Lisboa, P.
1983-01-01
We report on a numerical calculation of topological charge densities in non-abelian gauge theory with gauge groups SU(2) and SU(3). The group manifold is represented by a discrete subset thereof which lies outside its finite subgroups. The results shed light on the usefulness of these representations in Monte Carlo evaluations of non-abelian lattice gauge theory. (orig.)
Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system
Lim, Zhuo Min
2018-02-01
We consider the initial-value problem for the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in Rt × Rx2 with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in Hs for s ⩾ 1, and the solution map satisfies a local-in-time weak Lipschitz bound. By energy conservation, we also obtain a global regularity result. The key is to retain the non-perturbative part of the derivative nonlinearity in the principal operator, and exploit the dispersive properties of the resulting paradifferential-type principal operator using adapted Up and Vp spaces.
Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons QED3?
International Nuclear Information System (INIS)
Belich, Humberto; Helayeel-Neto, Jose Abdalla; Ferreira Junior, Manoel Messias
2000-01-01
Full text follows: We show that low-energy electron-electron bound states appear in the Maxwell-Chern-Simons (MCS) planar QED. In spite of the repulsive interaction mediated by the MCS gauge field, a net attractive interaction stems due to the Higgs mechanism through an Yukawa-type interaction. The spontaneous breaking of a local U(1)-symmetry is realized by a γ 6 -type potential. We conclude, by using the Schroedinger equation associated to the net attractive scattering potential, that electron-electron bound states arise in the model. Therefore, the Higgs mechanism overcomes the difficulties found out by Girotti et al. (Phys. Rev. Lett. 69 (1992) 2623) in searching for bound states in the MCS planar QED. (author)
Energy Technology Data Exchange (ETDEWEB)
Bartolo, Nicola; Orlando, Giorgio, E-mail: nicola.bartolo@pd.infn.it, E-mail: giorgio.orlando@phd.unipd.it [Dipartimento di Fisica e Astronomia ' ' G. Galilei' , Università degli Studi di Padova, via Marzolo 8, 35131, Padova (Italy)
2017-07-01
Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f (φ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass M {sub CS}. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra ( γ γ ζ ) for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f (φ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.
Anomaly cancellation condition in abelian lattice gauge theories
International Nuclear Information System (INIS)
Suzuki, Hiroshi
1999-11-01
We analyze the general solution of the Wess-Zumino consistency condition in abelian lattice gauge theories, without taking the classical continuum limit. We find that, if the anomaly density is a local pseudo-scalar field on the lattice, the non-trivial anomaly is always proportional to the anomaly coefficient in the continuum theory. The possible extension of this result to non-abelian theories is briefly discussed. (author)
Geometric symmetries and topological terms in F-theory and field theory
Energy Technology Data Exchange (ETDEWEB)
Kapfer, Andreas
2016-08-25
In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory. The first part treats settings of supersymmetry breaking in five dimensions. We focus on an N=4 to N=2 breaking in gauged supergravity. For certain classes of embedding tensors we can analyze the theory around the vacuum to a great extent. Importantly, one-loop corrections to Chern-Simons terms are generically induced which are independent of the supersymmetry-breaking scale. We investigate concrete examples of consistent truncations of supergravity and M-theory which show this N=4 to N=2 breaking pattern in five dimensions. In particular, we analyze necessary conditions for these consistent truncations to be used as effective theories for phenomenology by demanding consistency of the scale-independent corrections to Chern-Simons couplings. The second part is devoted to the study of anomalies and large gauge transformations in circle-reduced gauge theories and F-theory. We consider four- and six-dimensional matter-coupled gauge theories on the circle and classify all large gauge transformations that preserve the boundary conditions of the matter fields. Enforcing that they act consistently on one-loop Chern-Simons couplings in three and five dimensions explicitly yields all higher-dimensional gauge anomaly cancelation conditions. In the context of F-theory compactifications we identify the classified large gauge transformations along the circle with arithmetic structures on elliptically fibered Calabi-Yau manifolds via the dual M-theory setting. Integer Abelian large gauge transformations correspond to free basis shifts in the Mordell-Weil lattice of rational sections while special fractional non-Abelian large gauge transformations are matched to torsional shifts in the Mordell-Weil group. For integer non-Abelian large gauge transformations we
Directory of Open Access Journals (Sweden)
Gattringer Christof
2018-01-01
Full Text Available We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes, or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles. Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2 principal chiral model with chemical potential coupled to two of the Noether charges, SU(2 lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.
Gattringer, Christof; Göschl, Daniel; Marchis, Carlotta
2018-03-01
We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.
Local observables in non-Abelian gauge theories
International Nuclear Information System (INIS)
Sharatchandra, H.S.
1981-09-01
Labelling of the physical states of a non-Abelian gauge theory on a lattice in terms of local observables in considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter field is also included. The non-local variables required when space is multiply-connected, are specified. Non-Abelian version of the Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail. (orig.)
Vortex structure in abelian-projected lattice gauge theory
International Nuclear Information System (INIS)
Ambjoern, J.; Giedt, J.; Greensite, J.
2000-01-01
We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice has at most a global Z 2 symmetry in the confined phase, rather than the global U(1) symmetry that might be expected in a dual superconductor or monopole Coulomb gas picture. Implications for monopole and center vortex theories of confinement are discussed
Solving topological field theories on mapping tori
International Nuclear Information System (INIS)
Blau, M.; Jermyn, I.; Thompson, G.
1996-05-01
Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1 modul 1) model of Rozansky and Saleur on Σ x S 1 , both directly and using equivalent two-dimensional theories. We also derive the partition function on a certain non-abelian generalization of the U(1 modul 1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two- dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold. (author). 20 refs
Dual potentials in non-Abelian gauge theories
International Nuclear Information System (INIS)
Caticha, A.
1988-01-01
Motivated by the possibility that confinement and superconductivity are similar phenomena, dual potentials are introduced into Yang-Mills theory in two different ways. Both are extensions of Zwanziger's two-potential formalism for Abelian charges and monopoles to the non-Abelian case. In the first approach the dual potentials carry a color index and there is a rather simple, although nonlocal, dual-variable formulation. In the second approach dual variables are introduced into the so-called Abelian projection of the SU(2) Yang-Mills theory. An interesting feature is that the quartic contact interactions are absent and there is a special gauge choice for which the theory takes on a ''purely electromagnetic'' form. More important, however, is the appearance of an additional Abelian magnetic gauge symmetry the dynamical breaking of which may be associated with confinement
The Hawking effect in abelian gauge theories
International Nuclear Information System (INIS)
Stephens, C.R.
1989-01-01
In an effort to compare and contrast gravity with other field theories an investigation is made into whether the Hawking effect is a peculiarly gravitational phenomenon. It is found that the effect exists for a particular background abelian gauge field configuration, as well as certain background gravitational field configurations. Specifically, pair production in a uniform electric field is shown to admit a thermal interpretation. In an effort to find out just what is singular about gravity it is found that the Hawking temperature characteristic of a particular gravitational field configuration is independent of the properties of the quantum fields propagating theorem, in direct contrast to the gauge field case. This implies that if the one loop approximation is to be valid the electric field must be ''cold'' relative to the energy scales set by the quantum fields. In gravity, however, because of the existence of a fundamental scale, the Planck length, the gravitational field can be ''hot'' or ''cold'' and a one loop approximation still remain valid. copyright 1989 Academic Press, Inc
On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories
International Nuclear Information System (INIS)
Meggiolaro, Enrico
2005-01-01
The high-energy elastic scattering amplitude of two colour-singlet qq-bar pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with Nc colours, but stopping to the order O(g4) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections
Erratum: Erratum to: "A higher-spin Chern-Simons theory of anyons"
Boulanger, N.; Sundell, P.; Valenzuela, M.
2017-09-01
In the published version there is an error in the affiliation (the word "Andre's" with accent) of the author Per Sundell. The present form in this erratum is the correct (should be the word "Andres" without accent). The affiliation under the symbol " b" should read: Departamento de Ciencias Físicas, Universidad Andres Bello, Santiago, Chile
Some aspects of non-Abelian gauge theories
International Nuclear Information System (INIS)
Tyburski, L.J.
1976-01-01
Two aspects of the theory of non-Abelian gauge fields are considered. In the first part, the fermion-fermion scattering amplitude is calculated for a non-Abelian gauge theory with SU(N) gauge symmetry in the limit of high energy with fixed momentum transfer through sixth order in the coupling constant. Only the leading logarithmic terms in each order of perturbation theory are kept. To avoid the infrared problem, the Higgs mechanism is invoked to give masses to the vector bosons of the theory. It is found that the scattering amplitude exponentiates to a Regge form. This result is qualitatively different from an earlier published calculation. In the second part of the thesis, we consider fermion-fermion scattering in a non-Abelian gauge theory with massless vector bosons, and demonstrate that for physically measurable cross sections the infrared divergences of the theory cancel out to lowest nontrivial order
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
Nonequilibrium formulation of abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Zoeller, Thorsten
2013-09-01
This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at
High-energy behavior of non-Abelian gauge theories
International Nuclear Information System (INIS)
Nieh, H.T.; Yao, Y.
1976-01-01
This paper is a detailed account of a study in perturbation theory of the high-energy behavior of non-Abelian gauge theories. The fermion-fermion scattering amplitude is calculated up to sixth order in the coupling constant in the high-energy limit s → infinity with fixed t, in the approximation of keeping only the leading logarithmic terms. Results indicate that the high-energy behavior of non-Abelian gauge theories are complicated, and quite different from the known behaviors of other field theories studied so far
Non-Abelian gauge theory of fields associated with dyons
International Nuclear Information System (INIS)
Rajput, B.S.; Kumar, S.R.
1983-01-01
A suitable Lorentz invariant non-Abelian gauge theory of the fields associated with dyons has been constructed to describe the dual dynamics between colour isocharges and topological charges. It has been shown that the generalized particle current is gauge covariant and not conserved in non-Abelian theory. It has also been shown that in this theory the unphysical string variables and unphysical charged fields are not needed and that any extra constraint to maintain the dual symmetry of field equation and Lagrangian is also not needed. (author)
Comments on Dirac-like monopole, Maxwell and Maxwell-Chern-Simons electrodynamics in D=(2+1)
Energy Technology Data Exchange (ETDEWEB)
Moura-Melo, Winder A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: winder@cbpf.br; Helayel Neto, J.A. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: helayel@cbpf.br
2000-05-01
Classical Maxwell and Maxwell-Chern-Simons Electrodynamics in (2+1) D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved. Conceptual and technical difficulties arise, however, for accelerated charges. The propagation of electromagnetic signals is also studied and their reverberation is worked out and discussed. Furthermore, we show that a Dirac-like monopole yields a (static) tangential electric field. We also discuss some classical and quantum consequences of the field created by such a monopole when acting upon an usual electric charge. In particular, we show that at large distances, the dynamics of one single charged particle under the action of such a potential and a constant (external) magnetic field as well, reduces to that of one central harmonic oscillator, presenting, however, an interesting angular sector which admits energy-eigenvalues. For example, the quantisation of these eigenvalues yields a Dirac-like condition on the product of the charges. Moreover, such eigenvalues are shown to feel (and respond) to discrete shift of the angle variable. We also raise the question on the possibility of the formation pf bound states in this system. (author)
Abelian Chern endash Simons theory. II. A functional integral approach
International Nuclear Information System (INIS)
Manoliu, M.
1998-01-01
Following Witten, [Commun. Math. Phys. 21, 351 endash 399 (1989)] we approach the Abelian quantum Chern endash Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170 endash 206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization. copyright 1998 American Institute of Physics
Problem of colour confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Gribov, V.N.
1978-01-01
The problem of the colour confinement in the non-abelian gauge theories is studied. A more rigorous treatment of the Fadeev-Popov procedure for the quantization of the non-abelian gauge theories is presented. In the improved procedure one has to introduce additional bounds on the region of integration in the functional space of non-abelian fields. The integration is to be performed over the fields with positive-definite Faddeev-Popov determinant. This limitation has little influence on oscillations with high frequencies, but reduces drastically the amplitudes of low-frequency oscillations. This implies, that interaction of two colour charges does not go into infinity at finite distances, rather it is linearly rising with distance
Fermion-dyon dynamics in non-Abelian gauge theory
International Nuclear Information System (INIS)
Pant, P.C.; Pandey, V.P.; Rajput, B.S.
1999-01-01
The study of behaviour of a fermion in the field of non-Abelian dyon has been undertaken in Lagrangian and Hamiltonian formulation. Solving Dirac equation, expression for energy Eigen value has been obtained and the Hamiltonian of this system has been shown to involve spin as well as contribution of massive fields associated with these particles. By introducing suitable spinors, the Pauli equation for a dyon moving in the field of fermion has been solved in non-Abelian gauge gauge theory and it is shown that introduction of massive fields perceptibly modifies the energy Eigen value and Eigen function of bound states of the system. (author)
The chiral bosonization in non-Abelian gauge theories
International Nuclear Information System (INIS)
Andrianov, A.A.; Novozhilov, Y.
1985-01-01
The chiral bosonization in non-Abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, the QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour Skyrmion-boson with the baryon number 2/3. (author)
Onset of dynamical chaos in topologically massive gauge theories
International Nuclear Information System (INIS)
Giansanti, A.; Simic, P.D.
1988-01-01
The onset of dynamical chaos is studied numerically in (2+1)-dimensional non-Abelian field theory with the Chern-Simons topological term. In the limit of strong fields, slowly varying in space (spatially homogeneous fields), this theory is an analog to a system of three charged particles moving in a plane in an orthogonal magnetic field and under the influence of a quartic potential. The ''phase transition'' (order chaos) is observed within a narrow energy range. The threshold of the transition depends on the sign of the angular momentum of the field reflecting parity violation in the underlying field theory. The transition region is investigated in some detail and the hyperfine structure of order-chaos-order-... transitions is observed suggesting the necessity of probabilistic description
Abelian scalar theory at large global charge
Energy Technology Data Exchange (ETDEWEB)
Loukas, Orestis [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern (Switzerland)
2017-09-15
We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global U(1) charge in an arbitrary number of dimensions. The ground state vertical stroke v right angle is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation we systematically analyze the quantum fluctuations around vertical stroke v right angle in order to derive an effective action for the Goldstone mode, which becomes perturbatively meaningful when the charge is large. In this regime we explicitly show, by computing the first few loop corrections, that the whole construction is stable against quantum effects, in the sense that any higher derivative couplings to Goldstone's tree-level action are suppressed by appropriate powers of the large charge. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Black string first order flow in N=2, d=5 abelian gauged supergravity
Energy Technology Data Exchange (ETDEWEB)
Klemm, Dietmar; Petri, Nicolò; Rabbiosi, Marco [Dipartimento di Fisica, Università di Milano andINFN, Sezione di Milano, Via Celoria 16, I-20133 Milano (Italy)
2017-01-25
We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N=2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.
Anomaly cancelation in field theory and F-theory on a circle
International Nuclear Information System (INIS)
Grimm, Thomas W.; Kapfer, Andreas
2016-01-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
Construction of non-Abelian gauge theories on noncommutative spaces
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin
2001-01-01
We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)
Construction of non-Abelian gauge theories on noncommutative spaces
Energy Technology Data Exchange (ETDEWEB)
Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)
2001-06-01
We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)
I-Love-Q relations for neutron stars in dynamical Chern Simons gravity
Gupta, Toral; Majumder, Barun; Yagi, Kent; Yunes, Nicolás
2018-01-01
Neutron stars are ideal to probe, not only nuclear physics, but also strong-field gravity. Approximate universal relations insensitive to the star’s internal structure exist among certain observables and are useful in testing general relativity, as they project out the uncertainties in the equation of state. One such set of universal relations between the moment of inertia (I), the tidal Love number and the quadrupole moment (Q) has been studied both in general relativity and in modified theories. In this paper, we study the relations in dynamical Chern–Simons gravity, a well-motivated, parity-violating effective field theory, extending previous work in various ways. First, we study how projected constraints on the theory using the I-Love relation depend on the measurement accuracy of I with radio observations and that of the Love number with gravitational-wave observations. Provided these quantities can be measured with future observations, we find that the latter could place bounds on dynamical Chern–Simons gravity that are six orders of magnitude stronger than current bounds. Second, we study the I–Q and Q-Love relations in this theory by constructing slowly-rotating neutron star solutions to quadratic order in spin. We find that the approximate universality continues to hold in dynamical Chern–Simons gravity, and in fact, it becomes stronger than in general relativity, although its existence depends on the normalization of the dimensional coupling constant of the theory. Finally, we study the variation of the eccentricity of isodensity contours inside a star and its relation to the degree of universality. We find that, in most cases, the eccentricity variation is smaller in dynamical Chern–Simons gravity than in general relativity, providing further support to the idea that the approximate self-similarity of isodensity contours is responsible for universality.
Free Abelian 2-form gauge theory: BRST approach
International Nuclear Information System (INIS)
Malik, R.P.
2008-01-01
We discuss various symmetry properties of the Lagrangian density of a four- (3+1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition, which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of our present theory are found to be absolutely anticommuting in nature. For the present 2-form theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of physicality criteria, where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of the BRST formalism, from the constraint analysis. (orig.)
$N=2^∗$ (non-)Abelian theory in the $\\Omega$ background from string theory
Samsonyan, Marine; Antoniadis, Ignatios
2018-01-01
We present a D-brane realisation of the Abelian and non-Abelian N = 2 ∗ theory both in five and four dimensions. We compute topological amplitudes in string theory for Ω deformed spacetime first with one and then with two parameters. In the field theory limit we recover the perturbative partition function of the deformed N = 2 ∗ theory in agreement with the existing literature.
Renormalization of an abelian gauge theory in stochastic quantization
International Nuclear Information System (INIS)
Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.
1987-01-01
The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)
Non-Abelian duality in N = 4 supersymmetric gauge theories
International Nuclear Information System (INIS)
Dorey, Nicholas; Fraser, Christophe; Hollowood, Timithy J.; Kneipp, Marco A.C.
1996-03-01
A semi-classical check of the Goddard-Nuyts-Olive (GNO) generalized duality conjecture for gauge theories with adjoint Higgs fields is performed for the case where the unbroken gauge group is non-Abelian. The monopole solutions of the theory transform under the non-Abelian part of the unbroken global symmetry and the associated component of the moduli space is a Lie group coset space. The well-known problems in introducing collective coordinates for these degrees-of-freedom are solved by considering suitable multi monopole configurations in which the long-range non-Abelian fields cancel. In the context of an N = 4 supersymmetric gauge theory, the multiplicity of BPS saturated states is given by the number of ground-states of a supersymmetric quantum mechanics on the compact internal moduli space. The resulting degeneracy is expressed as the Euler character of the coset space. In all cases the number of states is consistent with the dimensions of the multiplets of the unbroken dual gauge group, and hence the results provide strong support for the GNO conjecture. (author). 39 refs
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
The non-Abelian gauge theory of matrix big bangs
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
SU(2) gauge theory in the maximally Abelian gauge without monopoles
International Nuclear Information System (INIS)
Shmakov, S.Yu.; Zadorozhnyj, A.M.
1995-01-01
We present an algorithm for simulation of SU(2) lattice gauge theory under the maximally Abelian (MA) gauge and first numerical results for the theory without Abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual Abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected. 12 refs., 1 tab
Higgs phase in non-Abelian gauge theories
International Nuclear Information System (INIS)
Kaymakcalan, O.S.
1981-06-01
A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed, it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase
Topological BF field theory description of topological insulators
International Nuclear Information System (INIS)
Cho, Gil Young; Moore, Joel E.
2011-01-01
Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Soldering formalism in noncommutative field theory: a brief note
International Nuclear Information System (INIS)
Ghosh, Subir
2004-01-01
In this Letter, I develop the soldering formalism in a new domain--the noncommutative planar field theories. The soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present Letter is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance (or the lack of it), in the above soldering process, is revealed in an interesting way
Aspects Topologiques de la Theorie des Champs et leurs Applications
Caenepeel, Didier
This thesis is dedicated to the study of various topological aspects of field theory, and is divided in three parts. In two space dimensions the possibility of fractional statistics can be implemented by adding an appropriate "fictitious" electric charge and magnetic flux to each particle (after which they are known as anyons). Since the statistical interaction is rather difficult to handle, a mean-field approximation is used in order to describe a gas of anyons. We derive a criterion for the validity of this approximation using the inherent feature of parity violation in the scattering of anyons. We use this new method in various examples of anyons and show both analytically and numerically that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons. Chern-Simons theories give an elegant implementation of anyonic properties in field theories, which permits the emergence of new mechanisms for anyon superconductivity. Since it is reasonable to think that superconductivity is a low energy phenomenon, we have been interested in non-relativistic C-S systems. We present the scalar field effective potential for non-relativistic matter coupled to both Abelian and non-Abelian C-S gauge fields. We perform the calculations using functional methods in background fields. Finally, we compute the scalar effective potential in various gauges and treat divergences with various regularization schemes. In three space dimensions, a generalization of Chern-Simons theory may be achieved by introducing an antisymmetric tensor gauge field. We use these theories, called B wedge F theories, to present an alternative to the Higgs mechanism to generate masses for non-Abelian gauge fields. The initial Lagrangian is composed of a fermion with current-current and dipole-dipole type self -interactions minimally coupled to non-Abelian gauge fields. The mass generation occurs upon the fermionic functional
Non-Abelian vortices in N=1* gauge theory
International Nuclear Information System (INIS)
Markov, V.; Marshakov, A.; Yung, A.
2005-01-01
We consider the N=1* supersymmetric SU(2) gauge theory and demonstrate that the Z2 vortices in this theory acquire orientational zero modes, associated with the rotation of magnetic flux inside SU(2) group, and turn into the non-Abelian strings, when the masses of all chiral fields become equal. These non-Abelian strings are not BPS-saturated. We study the effective theory on the string world sheet and show that it is given by two-dimensional non-supersymmetric O(3) sigma model. The confined 't Hooft-Polyakov monopole is seen as a junction of the Z2-string and anti-string, and as a kink in the effective world sheet sigma model. We calculate its mass and show that besides the four-dimensional confinement of monopoles, they are also confined in the two-dimensional theory: the monopoles stick to anti-monopoles to form the meson-like configurations on the strings they are attached to
International Nuclear Information System (INIS)
Battistel, O.A.; Dallabona, G.
2004-01-01
We consider the possible role played by the anomaly cancellation mechanism in the evaluation of the radiatively induced Chern-Simons (CS) term, arising from the Lorentz and CPT non-invariant fermionic sector, of an extended version of QED. We explicit evaluate the most general mathematical structure associated to the AVV triangle amplitude, closely related to the one involved in the CS term evaluation, using for this purposes an alternative calculational strategy to handle divergences in QFT's. We show that the requirement of consistency with the choices made in the construction of the Standard Model's renormalizability, in the evaluation of the AVV Green function, leave no room for a nonvanishing radiatively induced CS term, independently of the regularization prescription or equivalent philosophy adopted, in accordance with what was previously conjectured by other authors. (orig.)
Non-Abelian formulation of a vector-tensor gauge theory with topological coupling
International Nuclear Information System (INIS)
Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.
1995-08-01
We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs
Abelian Toda field theories on the noncommutative plane
Cabrera-Carnero, Iraida
2005-10-01
Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.
Scalar formalism for non-Abelian gauge theory
International Nuclear Information System (INIS)
Hostler, L.C.
1986-01-01
The gauge field theory of an N-dimensional multiplet of spin- 1/2 particles is investigated using the Klein--Gordon-type wave equation ]Pi x (1+isigma) x Pi+m 2 ]Phi = 0, Pi/sub μ/equivalentpartial/partialix/sub μ/-eA/sub μ/, investigated before by a number of authors, to describe the fermions. Here Phi is a 2 x 1 Pauli spinor, and sigma repesents a Lorentz spin tensor whose components sigma/sub μ//sub ν/ are ordinary 2 x 2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. The equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum tau-functions, tau(2,1, xxx 3 xxx)equivalent , where Psi/sub in/ is a Heisenberg operator belonging to a 4N x 1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics
The theory of anyonic superconductivity
International Nuclear Information System (INIS)
Lukken, J.D.; Sonnenschien, J.; Weiss, N.
1991-01-01
Particles in two spatial dimensions with fractional statistics known, generically, as anyons, have been of interest to particle physicists for nearly ten years. A major change in the direction of research occurred when it was discovered that anyons could play a role as quasiparticles in condensed-matter systems. This was originally discovered to be the case in systems exhibiting the Fractional Quantum Hall Effect. The application of anyons to condensed-matter systems received yet another boost when it was discovered by Laughlin that even an ideal gas of anyons was a superfluid and, as a result, a gas of charged anyons would be a superconductor. This led immediately to attempts to explain the superconductivity of high-T c materials which are layered ceramics in terms of anyons. The main challenge was to find a reasonable model for these materials which has quasiparticles obeying anyonic statistics. The goal of this article is to review the theory of anyonic superconductivity and its possible relation to high-T c materials. The emphasis in this review is on field-theoretical methods. In this paper the authors explain what an anyon is and how it can be modeled mathematically. The authors discuss the possible relationship between anyons and high-T c materials. The authors review several of the attempts to obtain anyonic quasiparticles from the Hubbard model which is commonly used to describe these materials. The authors describe the mathematical modeling of anyons in terms of their interaction with an Abelian gauge field with a Chern-Simons term. This description of anyons is used extensively in this article. The authors discuss the possible criteria for superconductivity in anyonic systems with particular emphasis on criteria which would be useful in the Chern-Simons description
Energy Technology Data Exchange (ETDEWEB)
Gattringer, Christof, E-mail: christof.gattringer@uni-graz.at; Marchis, Carlotta, E-mail: carla.marchis@uni-graz.at
2017-03-15
We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over “abelian color cycles” (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).
Non-Abelian gauge field theory in scale relativity
International Nuclear Information System (INIS)
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-01-01
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description
Comment on the Adler-Bardeen theorem in non-Abelian gauge theories
International Nuclear Information System (INIS)
Fujikawa, Kazuo.
1981-09-01
It is pointed out that the constructive proof of the Adler-Bardeen theorem for the chiral and scale (counting identity) anomalies in non-Abelian gauge theories proceeds just as in the spinor electrodynamics, although several interesting features characteristic of non-Abelian theories appear. (author)
Path-integral invariants in abelian Chern–Simons theory
International Nuclear Information System (INIS)
Guadagnini, E.; Thuillier, F.
2014-01-01
We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants
Gauge and integrable theories in loop spaces
International Nuclear Information System (INIS)
Ferreira, L.A.; Luchini, G.
2012-01-01
We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.
Renormalizable Abelian-projected effective gauge theory derived from quantum chromodynamics
International Nuclear Information System (INIS)
Kondo, Kei-ichi; Shinohara, Toru
2001-01-01
We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the β-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory. (author)
Abelian Chern endash Simons theory. I. A topological quantum field theory
International Nuclear Information System (INIS)
Manoliu, M.
1998-01-01
We give a construction of the Abelian Chern endash Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern endash Simons theory [J. Diff. Geom. 33, 787 endash 902 (1991); Topology 32, 509 endash 529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175 endash 186 (1989)]. copyright 1998 American Institute of Physics
Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report
International Nuclear Information System (INIS)
Wadia, Spenta R.
2009-01-01
We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)
Monopole Solutions in Topologically Massive Gauge Theory
International Nuclear Information System (INIS)
Teh, Rosy; Wong, Khai-Ming; Koh, Pin-Wai
2010-01-01
Monopoles in topologically massive SU(2) Yang-Mils-Higgs gauge theory in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by him. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern-Simon term strength and for several fixed values of Higgs field strength.
Topological field theory and surgery on three-manifolds
International Nuclear Information System (INIS)
Guadagnini, E.; Panicucci, S.
1992-01-01
The solution of the SU(2) quantum Chern-Simons field theory defined on a closed, connected and orientable three-manifold is presented. The vacuum expectation values of Wilson line operators, associated with framed links in a generic manifold, are computed in terms of the expectation values of the three-sphere. The method consists of using an operator realization of Dehn surgery. The rules, corresponding to the surgery instructions in the three-sphere, are derived and the three-manifold invariant defined by the Chern-Simons theory is constructed. Several examples are considered and explicit results are reported. (orig.)
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
New results in topological field theory and Abelian gauge theory
International Nuclear Information System (INIS)
Thompson, G.
1995-10-01
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs
New results in topological field theory and Abelian gauge theory
Energy Technology Data Exchange (ETDEWEB)
Thompson, G
1995-10-01
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs.
Phase structure and critical properties of an abelian gauge theory
Energy Technology Data Exchange (ETDEWEB)
Mo, Sjur
2001-12-01
The main new results are presented in the form of three papers at the end of this thesis. The main topic is Monte-Carlo studies of the phase structure and critical properties of the phenomenological Ginzburg-Landau model, i.e. an abelian gauge theory. However, the first paper is totally different and deals with microscopic theory for lattice-fermions in a magnetic field. Paper I is about ''Fermion-pairing on a square lattice in extreme magnetic fields''. We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to ''k-space'', or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C{sub 4{nu}} of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down. Paper II is about the ''Hausdorff dimension of critical fluctuations in abelian gauge theories''. Here we analyze the geometric properties of the line-like critical fluctuations (vortex loops) in the Ginzburg-Landau model in zero magnetic background field. By using a dual description, we obtain scaling relations between exponents of geometric arid thermodynamic nature. In particular we connect the anomalous scaling dimension {eta} of the dual matter field to the Hausdorff or fractal dimension D{sub H} of the critical fluctuations, in the original model
Research program in elementary particle theory
International Nuclear Information System (INIS)
1989-01-01
The Syracuse High Energy Theory group has continued to make significant contributions to many areas. Many novel aspects of Chern-Simons terms and effective Lagrangians were investigated. Various interesting aspects of quantum gravity and string theory were explored. Gauge models of elementary particles were studied in depth. The investigations of QCD at finite temperatures and multiply connected configuration spaces continued. 24 refs
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
Quantum field theory and link invariants
International Nuclear Information System (INIS)
Cotta-Ramusino, P.; Guadagnini, E.; Mintchev, M.; Martellini, M.
1990-01-01
A skein relation for the expectation values of Wilson line operators in three-dimensional SU(N) Chern-Simons gauge theory is derived at first order in the coupling constant. We use a variational method based on the properties of the three-dimensional field theory. The relationship between the above expectation values and the known link invariants is established. (orig.)
International Nuclear Information System (INIS)
Kamiya, Noriaki; Sato, Matsuo
2014-01-01
We define Hermitian (ϵ,δ)-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of the u(N)⊕u(M) and sp(2N)⊕u(1) Hermitian 3-algebras. We apply a *-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit
Plasma instabilities and turbulence in non-Abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Scheffler, Sebastian Herwig Juergen
2010-02-17
Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (
Plasma instabilities and turbulence in non-Abelian gauge theories
International Nuclear Information System (INIS)
Scheffler, Sebastian Herwig Juergen
2010-01-01
Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (< or similar 1 GeV). Essential results can be translated from the gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the quasi
Conformal field theory construction for non-Abelian hierarchy wave functions
Tournois, Yoran; Hermanns, Maria
2017-12-01
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
Moving vortices in noncommutative gauge theory
International Nuclear Information System (INIS)
Horvathy, P.A.; Stichel, P.C.
2004-01-01
Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern-Simons
Energy Technology Data Exchange (ETDEWEB)
Abakumova, V.A.; Kaparulin, D.S.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2018-02-15
Most general third-order 3d linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the 00-components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations. (orig.)
Field-strength formulation of gauge theories. The Hamiltonian approach in the Abelian theory
International Nuclear Information System (INIS)
Mendel, E.; Durand, L.
1984-01-01
We develop a Hamiltonian approach to the field-strength or dual formation of the Abelian gauge theory in which the potential A/sup μ/ is eliminated as a dynamical variable. Our work is based on the covariant gauge x/sup μ/A/sub μ/(x) = 0 which allows a simple elimination of A/sup μ/ in terms of the field strengths F/sup munu/. We obtain complete results for the generating functional for the Green's functions of the theory, Z = Z[f,g], where f and g are nonlocal currents coupled to E and B, and illustrate some unfamiliar aspects of the new formalism
Classical field theory on electrodynamics, non-abelian gauge theories and gravitation
Scheck, Florian
2018-01-01
Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...
Twisted boundary conditions: a non-perturbative probe for pure non-abelian gauge theories
International Nuclear Information System (INIS)
Baal, P. van.
1984-01-01
In this thesis the author describes a pure non-abelian gauge theory on the hypertorus with gauge group SU(N). To test the flux tube picture he has studied the large distance limit of this theory, leading to a large coupling constant. To tackle this problem, he describes two approaches, in both of which twisted boundary conditions play an important role. (Auth.)
Vortices and quark confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Mandelstam, S.
1976-01-01
Non-Abelian vortices of the type proposed by Nielsen and Olesen are discussed. It is shown that the vortices must contain a single unit of quantized flux absorbed by a Dirac monopole at each end. The monopoles satisfy a confinement condition; if quark numbers are assigned to the monopoles, is is found that the model contains a natural explanation of quark confinement. The I-spin variables associated with the non-Abelian gauge field correspond to the colour degree freedom. An alternative model in which (colour) charges and monopoles are interchanged is also suggested. The Higgs field which breaks the degeneracy of the vacuum is replaced by an operator which creates monopoles of the type suggested by 't Hooft. In such a model colour might be confined. The investigations are at a very preliminary stage, but the model appears to offer a natural explanation of confinement without the explicit introduction of monopole fields. (Auth.)
Classical gauge theories on the coadjoint orbits of infinite dimensional groups
International Nuclear Information System (INIS)
Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung
1991-01-01
We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)
Domaratzki, Michael; Rampersad, Narad
2011-01-01
We investigate Abelian primitive words, which are words that are not Abelian powers. We show that unlike classical primitive words, the set of Abelian primitive words is not context-free. We can determine whether a word is Abelian primitive in linear time. Also different from classical primitive words, we find that a word may have more than one Abelian root. We also consider enumeration problems and the relation to the theory of codes. Peer reviewed
International Nuclear Information System (INIS)
Ward, B.F.L.
2006-01-01
We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED-QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and the final state of Hawking radiation. In all cases, the extension of the YFS approach, originally introduced for Abelian gauge theory, to non-Abelian gauge theories, QCD and quantum general relativity, leads to new results and solutions which we briefly summarize
Naked singularities, branes and Chern-Simons couplings: The dark side of the 2+1 black hole
International Nuclear Information System (INIS)
Zanelli, Jorge
2010-01-01
Branes are naked singularities, analogous to linear or planar defects in crystals. Zero-branes in AdS spacetimes are n egative mass black holes , which can be generalized to higher-dimensional branes. When these solutions are endowed with angular momentum, the extremal spinning branes correspond to BPS states. On the other hand, the 2p-branes, spanning a (2p + 1)-dimensional worldsheet, provide a naturally coupling to CS field theories defined on a D-dimensional spacetime, with D > 2p + 1. In this picture, the field that lives in the D-dimensional spacetime, as well as the sources that couple to it are made out of the same stuff -an SO(D - 1,2) connection. The fact that on the brane the AdS group is necessarily broken down to SO(2p, 2), brings in a number of tensor fields that play the role of charged matter living on the brane.
A geometric view on topologically massive gauge theories
International Nuclear Information System (INIS)
Horvathy, P.A.; Nash, C.
1985-01-01
The topologically massive gauge theory of Deser, Jackiw and Templeton is understood from Souriau's Principle of General Covariance. The non-gauge invariant mass term corresponds to a non-trivial class in the first cohomology group of configuration space, generated by the Chern-Simons secondary characteristic class. Quantization requires this class to be integral
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
International Nuclear Information System (INIS)
Agulló, Iván; Borja, Enrique F.; Díaz-Polo, Jacobo
2009-01-01
Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity
Phase structure of lattice gauge theories for non-abelian subgroups of SU(3)
International Nuclear Information System (INIS)
Grosse, H.; Kuehnelt, H.
1981-01-01
The authors study the phase structure of Euclidean lattice gauge theories in four dimensions for certain non-abelian subgroups of SU(3) by using Monte-Carlo simulations and strong coupling expansions. As the order of the group increases a splitting of one phase transition into two is observed. (Auth.)
Constant self-dual Abelian gauge fields and fermions in SU(2) gauge theory
International Nuclear Information System (INIS)
Kay, D.; Parthasarathy, R.; Viswanathan, K.S.
1983-01-01
Fermion one-loop corrections to the effective action in a self-dual Abelian background field are calculated for an SU(2) gauge theory. It is found that these corrections for massless fermions tend to destabilize the vacuum. The quantitative and qualitative features of such corrections for the case of massive fermions are discussed
Recursion rules for scattering amplitudes in non-Abelian gauge theories
International Nuclear Information System (INIS)
Kim, C.; Nair, V.P.
1997-01-01
We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed. copyright 1997 The American Physical Society
Problems of an external field in non-Abelian gauge theory
International Nuclear Information System (INIS)
Gavrilov, S.P.; Gitman, D.M.
1992-01-01
In the Abelian gauge field theory QED the principal problems connected with an external field are the problems of exact keeping of an external field in a perturbation theory and appearing in this case the peculiarities of the theory such as the instability of the vacuum and so on. There is the problem of an external field introduction or its interpretation side by side with this problem in Non-Abelian gauge theory. The solution of both these problems in Non-Abelian theory can be considered by analogy with QED. In the present paper, the authors discuss on the example of the spontaneously broken SU(2) x U(1) electroweak theory both the problems of an external field introduction and the problem of exact keeping of this field in the perturbation theory. The Langrangian of this theory in covariant gauge is chosen in the BRST invariant form. In spite of concrete character of the theory studied, the method can be extended to any gauge theory
A reciprocity formula from abelian BF and Turaev–Viro theories
Directory of Open Access Journals (Sweden)
P. Mathieu
2016-11-01
Full Text Available In this article we show that the use of Deligne–Beilinson cohomology in the context of the U(1 BF theory on a closed 3-manifold M yields a discrete ZN BF theory whose partition function is an abelian TV invariant of M. By comparing the expectation values of the U(1 and ZN holonomies in both BF theories we obtain a reciprocity formula.
Atomic Quantum Simulations of Abelian and non-Abelian Gauge Theories
CERN. Geneva
2014-01-01
Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, in a collaboration of atomic and particle physicists, we have constructed a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum link models which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows investigations of string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods. Similarly, using ultracold alkaline-earth atoms in optical lattices, we have constructed a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum ...
Fermions and vortex solutions in Abelian and non-Abelian gauge theories
International Nuclear Information System (INIS)
de Vega, H.J.
1978-01-01
The interaction of fermions with an extended vortex solution of the Higgs model is investigated. It is found that this interaction has long-range inverse-square tail. It is caused by the coupling of the fermion angular momentum with the vortex gauge field itself. The fermion-vortex bound states present at the threshold and the fermion-vortex scattering are studied. The scattering phase shifts and the Jost functions are obtained for large and small fermion momenta as well as the low-energy cross section which diverges at zero momentum. The quantum field theory in the one-vortex sectors is developed. It is found that, in the presence of fermions, a vortex with an even (odd) number of flux quanta has a half-integer (integer) fermionic number. It follows that a two-quantum vortex is stable. Finally, the stable vortex solution of an SU(2) Higgs model is investigated. The appropriate ansatz for the field is given and radial equations are discussed. It is shown that the interaction of a vortex with any nonsinglet particle has a long-range inverse-square tail
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Delcamp, Clement [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo,200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada); Dittrich, Bianca; Riello, Aldo [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
2016-11-18
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the ‘magnetic centre choice’, as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement entropy can be related to a choice of (squeezed) vacuum state.
Dual computations of non-Abelian Yang-Mills theories on the lattice
International Nuclear Information System (INIS)
Cherrington, J. Wade; Khavkine, Igor; Christensen, J. Daniel
2007-01-01
In the past several decades there have been a number of proposals for computing with dual forms of non-Abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-Abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet nontrivial case in which the gauge group is non-Abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-Abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest
Topics in low-dimensional field theory
International Nuclear Information System (INIS)
Crescimanno, M.J.
1991-01-01
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Scheck, Florian
2018-04-01
Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.
Monte Carlo studies of non-Abelian gauge theories
International Nuclear Information System (INIS)
Creutz, M.
1980-05-01
After some general remarks on the efficiency of various Monte Carlo algorithms for gauge theories, the calculation of the asymptotic freedom scales of SU(2) and SU(3) gauge theories in the absence of quarks was discussed. There are large numerical factors between these scales when defined in terms of the bare coupling of the lattice theory or when defined in terms of the physical force between external sources
Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
International Nuclear Information System (INIS)
Dudal, D.; Verschelde, H.; Sarandy, M.S.
2007-01-01
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension two condensate discussed here, with the non-trivial vacuum energy originating from the condensate 2 μ >, which has attracted much attention in the Landau gauge. (author)
Non-Abelian sigma models from Yang-Mills theory compactified on a circle
Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.
2018-06-01
We consider SU(N) Yang-Mills theory on R 2 , 1 ×S1, where S1 is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on R 2 , 1 whose target space is a 2 (N - 1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU (N) ×SU (N) /ZN. The latter is the direct product of SU(N) and its Langlands dual SU (N) /ZN, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.
Beyond Lovelock gravity: Higher derivative metric theories
Crisostomi, M.; Noui, K.; Charmousis, C.; Langlois, D.
2018-02-01
We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.
International Nuclear Information System (INIS)
Bertrand, Bruno; Govaerts, Jan
2007-01-01
Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the (2+1)-dimensional Maxwell-Chern-Simons and (3+1)-dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However, through an appropriate canonical transformation, a gauge-invariant factorization of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge-invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase-space description of the associated non-dynamical pure TFT. Within canonical quantization, a likewise factorization of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorization scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge-fixing procedure whatsoever
Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories
International Nuclear Information System (INIS)
Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
2000-01-01
The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the 'Chern character' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Luescher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions
Renormalization of non-abelian gauge theories in curved space-time
International Nuclear Information System (INIS)
Freeman, M.D.
1984-01-01
We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe
Spherically symmetric solutions in abelian Kaluza-Klein theories
International Nuclear Information System (INIS)
Angus, I.G.
1986-01-01
We present the most general spherically symmetric solution to the field equations of the truncated five-dimensional Kaluza-Klein theory. We also detail some of the special forms of this solution. With the exception of the Gross-Perry-Sorkin monopole and the Schwarzschild solutions we find that most, and we conjecture all, of the solutions have naked curvature singularities. We then proceed to consider higher-dimensional theories with toroidal compactification and we exhibit a class of nonsingular monopole solutions which are the natural generalization of the Gross-Perry-Sorkin monopole to more than five dimensions. We also present some selected solutions including a solution pertaining to a model with a Ricci-flat, but not curvature-flat, internal manifold. All of these other solutions have naked curvature singularities. (orig.)
Electric-magnetic duality in non-Abelian gauge theories
International Nuclear Information System (INIS)
Mizrachi, L.
1982-03-01
The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase) is performed in the radial gauge (xsub(μ)Asub(μ)sup(a)(x)=0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is 1/g. The theory is self dual in this region, and the effective coupling of the dual Lagrangian is 1/g. Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operator transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self duality holds only for this subset of fields. In the strong coupling region a strong coupling expansion in powers of 1/g is suggested. (author)
International Nuclear Information System (INIS)
Kazama, Y.; Yao, Y.
1982-01-01
In spontaneously broken non-Abelian gauge theories which admit gauge hierarchy at the tree level, we show, to all orders in perturbation theory, that (i) the superheavy particles decouple from the light sector at low energies, (ii) an effective low-energy renormalizable theory emerges together with appropriate counterterms, and (iii) the gauge hierarchy can be consistently maintained in the presence of radiative corrections. These assertions are explicitly demonstrated for O(3) gauge theory with two triplets of Higgs particles in a manner easily applicable to more realistic grand unified theories. Furthermore, as a by-product of our analysis, we obtain a systematic method of computing the parameters of the effective low-energy theory via renormalization-group equations to any desired accuracy
Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
Cvetic, Mirjam; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-01-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required ...
Concerning Gribov vacuum copies in non-abelian gauge theory
International Nuclear Information System (INIS)
Frampton, P.H.; Palmer, W.F.; Pinsky, S.S.
1978-01-01
Construction of gauge field configurations A/sub μ//sup a/(x) in an SU(2) Yang-Mills theory satisfying everywhere F/sub μν//sup a/(x) = 0 is discussed. Using the method of sections, a field related to the zero-size limit of an instanton is presented. The corresponding limit for a multi-instanton solution requires a generalization of the Landau gauge condition. Finally, an alternative method and explicit solution is given for the case of delta/sub μ/A/sub μ//sup a/ = 0
International Nuclear Information System (INIS)
Jing Sicong; Ruan Jie; AH. Dept. of Modern Physics)
1990-01-01
The perturbation theory in coset pure gauge field theory is studied for the first time. By using the Bjorken-johnson-Low technique and calculating the Schwinger term in related commutators, the anomalous Ward identity in Abelian coset pure gauge field theory is derived, which is consistent with the non-perutrbative calculation
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
International Nuclear Information System (INIS)
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-01-01
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined
Perfect Fluid Theory and its Extensions
Jackiw, R.; Nair, V. P.; Pi, S. -Y.; Polychronakos, A. P.
2004-01-01
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).
Origin of Abelian gauge symmetries in heterotic/F-theory duality
International Nuclear Information System (INIS)
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-01-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m)×U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m)×ℤ_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)’s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)’s is found by taking into account a Stückelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.
A string realisation of Ω-deformed Abelian N=2⁎ theory
Directory of Open Access Journals (Sweden)
Carlo Angelantonj
2017-10-01
Full Text Available The N=2⁎ supersymmetric gauge theory is a massive deformation of N=4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-Abelian N=2⁎ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N=2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.
A string realisation of Ω-deformed Abelian N =2* theory
Angelantonj, Carlo; Antoniadis, Ignatios; Samsonyan, Marine
2017-10-01
The N =2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N =2* theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N = 2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.
Some novel features in 2D non-Abelian theory: BRST approach
Srinivas, N.; Kumar, S.; Kureel, B. K.; Malik, R. P.
2017-08-01
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.
Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field
Directory of Open Access Journals (Sweden)
Daniel G. Figueroa
2018-01-01
Full Text Available Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark–gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U(1 gauge sector, a(xFμνF˜μν, reproducing the continuum limit to order O(dxμ2 and obeying the following properties: (i the system is gauge invariant and (ii shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K=FμνF˜μν that admits a lattice total derivative representation K=Δμ+Kμ, reproducing to order O(dxμ2 the continuum expression K=∂μKμ∝E→⋅B→. If we consider a homogeneous field a(x=a(t, the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern–Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking in Abelian gauge theories at finite temperature. When a(x=a(x→,t is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O(dxμ2 accuracy. We discuss an iterative scheme allowing to overcome this difficulty.
International Nuclear Information System (INIS)
Teh, R.
1989-07-01
Here I would like to show a general way of writing the gauge potentials A μ α for which the SU(2) Yang-Mills equations of motion can be simplified and become solvable. A number of exact solutions can be obtained from these simplified equations of motion. (author). 14 refs
Quantum Noether identities for non-local transformations in higher-order derivatives theories
International Nuclear Information System (INIS)
Li, Z.P.; Long, Z.W.
2003-01-01
Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantum canonical Noether identities (NIs) under a local and non-local transformation in phase space have been deduced, respectively. For a singular higher-order Lagrangian, one must use an effective canonical action I eff P in quantum canonical NIs instead of the classical I P in classical canonical NIs. The quantum NIs under a local and non-local transformation in configuration space for a gauge-invariant system with a higher-order Lagrangian have also been derived. The above results hold true whether or not the Jacobian of the transformation is equal to unity or not. It has been pointed out that in certain cases the quantum NIs may be converted to conservation laws at the quantum level. This algorithm to derive the quantum conservation laws is significantly different from the quantum first Noether theorem. The applications of our formulation to the Yang-Mills fields and non-Abelian Chern-Simons (CS) theories with higher-order derivatives are given, and the conserved quantities at the quantum level for local and non-local transformations are found, respectively. (orig.)
Symmetry analysis for anisotropic field theories
International Nuclear Information System (INIS)
Parra, Lorena; Vergara, J. David
2012-01-01
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Superfield approach to topological features of non-Abelian gauge theory
International Nuclear Information System (INIS)
Malik, R.P.
2002-01-01
We discuss some of the key topological aspects of a (1+1)-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of chiral superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy-momentum tensor, topological invariants, etc, by exploiting the on-shell nilpotent BRST and co-BRST symmetries that emerge after the application of (dual) horizontality conditions. We show that the above physically interesting quantities geometrically correspond to the translation of some local (but composite) chiral superfields along one of the two independent Grassmannian directions of a (2+2)-dimensional supermanifold. This translation is generated by the conserved and on-shell nilpotent (co-)BRST charges that are present in the theory. (author)
Critical non-Abelian vortex in four dimensions and little string theory
Shifman, M.; Yung, A.
2017-08-01
As was shown recently, non-Abelian vortex strings supported in four-dimensional N =2 supersymmetric QCD with the U(2) gauge group and Nf=4 quark multiplets (flavors) become critical superstrings. In addition to the translational moduli, non-Abelian strings under consideration carry six orientational and size moduli. Together, they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau noncompact threefold, namely, the conifold. We study closed string states which emerge in four dimensions and identify them with hadrons of four-dimensional N =2 QCD. One massless state was found previously; it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper, we find a number of massive states. To this end, we exploit the approach used in LST little string theory, namely, the equivalence between the critical string on the conifold and noncritical c =1 string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.
Super-Galilei invariant field theories in 2+1 dimensions
International Nuclear Information System (INIS)
Bergman, O.; Thorn, C.B.
1995-01-01
The authors extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. They also study the generalization to matrix valued fields, which are relevant to the formulation of superstring theory as a 1/N c expansion of a field theory. The authors find that in the matrix case, the field theory is much more restricted by the supersymmetry
A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces
International Nuclear Information System (INIS)
Soda, Jiro
1991-02-01
We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Smiseth, Jo
2005-07-01
The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)
Wigner's little group as a gauge generator in linearized gravity theories
International Nuclear Information System (INIS)
Scaria, Tomy; Chakraborty, Biswajit
2002-01-01
We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory
Harz, Julia; Petraki, Kalliopi
2018-01-01
We compute the cross-sections for the radiative capture of non-relativistic particles into bound states, in unbroken perturbative non-Abelian theories. We find that the formation of bound states via emission of a gauge boson can be significant for a variety of dark matter models that feature non-Abelian long-range interactions, including multi-TeV scale WIMPs and dark matter co-annihilating with coloured partners. Our results disagree with previous computations, on the relative sign of the Ab...
On the elimination of infinitesimal Gribov ambiguities in non-Abelian gauge theories
International Nuclear Information System (INIS)
Pereira, Antonio D.; Sobreiro, Rodrigo F.
2013-01-01
An alternative method to account for the Gribov ambiguities in gauge theories is presented. It is shown that, to eliminate Gribov ambiguities, at infinitesimal level, it is required to break the BRST symmetry in a soft manner. This can be done by introducing a suitable extra constraint that eliminates the infinitesimal Gribov copies. It is shown that the present approach is consistent with the well established known cases in the literature, i.e., the Landau and maximal Abelian gauges. The method is valid for gauges depending exclusively on the gauge field and is restricted to classical level. However, occasionally, we deal with quantum aspects of the technique, which are used to improve the results. (orig.)
Kinoshita-Lee-Nauenberg theorem and soft radiation in gauge theories: Abelian case
International Nuclear Information System (INIS)
Akhoury, R.; Sotiropoulos, M.G.; Zakharov, V.I.
1997-01-01
We present a covariant formulation of the Kinoshita-Lee-Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that, when combined with the Low theorem, this leads to a proof of the absence of the 1/Q corrections to inclusive processes (such as the Drell-Yan process). In this paper the Abelian case is discussed to all orders in the coupling. copyright 1997 The American Physical Society
High-energy behaviour in a non-abelian gauge theory. Pt. 2
International Nuclear Information System (INIS)
Bartels, J.
1980-01-01
In this second part of our attempt to construct a unitary high-energy description of a spontaneously broken non-abelian gauge theory we calculate, for the n → m amplitude in the multi-Regge limit, the first corrections beyond the leading logarithmic approximation. The resulting amplitudes come in the form of the reggeon calculus where the number of reggeons in each t-channel is restricted to one or two. We then study the limit where the mass of the vector particle is taken to zero: for the 2 → 2 amplitude show that this limit exists, not only for the approximation of the present paper but also for higher-order corrections. (orig.)
All the Four-Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory
International Nuclear Information System (INIS)
Cvetic, M.; Youm, D.
1995-01-01
We present the explicit form for all the four-dimensional, static, spherically symmetric solutions in (4+n)-d Abelian Kaluza-Klein theory by performing a subset of SO(2,n) transformations corresponding to four SO(1,1) boosts on the Schwarzschild solution, supplemented by SO(n)/SO(n-2) transformations. The solutions are parametrized by the mass M, Taub-NUT charge a, and n electric rvec Q and n magnetic rvec P charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstroem or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while nonsupersymmetric extreme ones have a global space-time of extreme Reissner-Nordstroem black holes. copyright 1995 The American Physical Society
Zk string fluxes and monopole confinement in non-Abelian theories
International Nuclear Information System (INIS)
Kneipp, Marco A.C.; Centro Brasileiro de Pesquisas Fisicas
2002-11-01
Recently we considered N = 2 Super Yang-Mills with a mass breaking term and showed the existence of BPS Z k -string solutions for arbitrary simple gauge groups which are spontaneously broken to non-Abelian residual gauge groups. We also calculated their string tensions exactly. In doing so, we have considered in particular the hyper multiplet in the representation of a diquark condensate. In the present work we shall analyze some of the different phases of the theory and find that the magnetic fluxes of the monopoles and Z k strings of the theory are proportional to one another, allowing for monopole confinement in one of the phase transitions of the theory. Then we will calculate the threshold length for a string to break in a new pair of monopole-anti monopole. We will further show that some of the resulting confining theories can obtained by adding a deformation term to N 2 or N = 4 superconformal theories and, as such, may satisfy a gauge/string correspondence. (author)
Two field formulation of closed string field theory
International Nuclear Information System (INIS)
Bogojevic, A.R.
1990-09-01
A formulation of closed string field theory is presented that is based on a two field action. It represents a generalization of Witten's Chern-Simons formulation of 3d gravity. The action contains only 3 string interactions and no string field truncations, unlike the previous non-polynomial action of Zwiebach. The two field action is found to follow from a purely cubic, background independent action similar to the one for open strings. (orig.)
Fuchs, László
2015-01-01
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah’s seminal work on the undecidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, th...
Anatomy of isolated monopole in Abelian projection od SU(2) lattice gauge theory
Belavin, V A; Veselov, A I
2001-01-01
The structure of the isolated static monopolies in the maximum Abelian projection of the SU(2) gluodynamics on the lattice studied. The standard parametrization of the coupling matrix was used by determining the maximum Abelian projection of the R functional maximization relative to all scale transformations. The monopole radius R approx = 0.06 fm is evaluated
International Nuclear Information System (INIS)
Scheck, Florian
2010-01-01
Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [de
Restoration of the local gauge symmetry and color confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Hata, Hiroyuki
1982-01-01
Restoration of the local gauge symmetry and its connection to color confinement is investigated in non-Abelian gauge theories with covariant gauge fixing. We consider the Noether current J sub(μ,#betta#)sup(a) of the local gauge transformation with transformation functions #betta#sup(b)(x) linear in x sub(μ); #betta#sup(b)(x) = delta sup(ab)x sub(#betta#). This current is conserved only in the physical subspace of the state vector space and in perturbation theory contains a massless pole communicating to the gauge field. We define the local gauge symmetry restoration as the disappearance of this massless ''Goldstone'' pole from J sub(μ,#betta#)sup(a). The restoration condition is obtained and it coincides exactly with the color confinement criterion proposed earlier by Kugo and Ojima. Quarks and other colored particles are shown to be confined in the local gauge symmetry restored phase by using the Ward identities of J sub(μ,#betta#)sup(a). (author)
High energy instanton induced processes in electroweak theory
International Nuclear Information System (INIS)
McLerran, L.
1992-01-01
It is well known that in electroweak theory, baryon plus lepton number is conserved by the classical equations of motion. This is of course consistent with the lack of experimental observation of such processes. It is a little less well known that when quantum corrections are included in electroweak theory, baryon plus lepton number is not conserved. This was first discovered as a consequence of the Adler-Bardeen-Bell-Jackiw triangle anomaly. It is perhaps most easily understood as a consequence of vacuum degeneracy, fermion energy level crossing and filling of the negative energy Dirac sea upon second quantization. To understand how baryon plus lepton number is not conserved upon second quantization, consider the situation shown in the energy of the system is shown as a function of a parameter which characterizes the gauge fields, the Chern-Simons charge. The Chern-Simons charge is a function only of the gauge fields, and the B + L change is equal to the change in Chern-Simons charge, ΔQ B+L = ΔQ CS
Srinivas, N.; Malik, R. P.
2017-11-01
We derive the off-shell nilpotent symmetries of the two (1 + 1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parametrized by the superspace coordinates ZM = (xμ,𝜃,𝜃¯) where xμ (with μ = 0, 1) are the bosonic coordinates and a pair of Grassmannian variables (𝜃,𝜃¯) obey the relationships: 𝜃2 = 𝜃¯2 = 0, 𝜃𝜃¯ + 𝜃¯𝜃 = 0. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.
Chauhan, B.; Kumar, S.; Malik, R. P.
2018-02-01
We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the (D,1)-dimensional (anti-) chiral super-submanifolds (of the general (D,2)-dimensional supermanifold) where only the (anti-)chiral super expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism.
Medium generated gap in gravity and a 3D gauge theory
Gabadadze, Gregory; Older, Daniel
2018-05-01
It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in d =D +1 spacetime dimensions, and for a solid in D =2 spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of D =2 spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory, and motivated by this we recast the massive theory of gravity in AdS3 as a massive Chern-Simons gauge theory with an unusual mass term. We find that in the flat space limit the Chern-Simons theory has a novel gauge invariance that mixes the kinetic and mass terms, and enables the massive theory with a noncompact internal group to be free of ghosts and tachyons.
A note on the fate of the Landau–Yang theorem in non-Abelian gauge theories
Directory of Open Access Journals (Sweden)
Matteo Cacciari
2016-02-01
Full Text Available Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N Yang–Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
A note on the fate of the Landau–Yang theorem in non-Abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Cacciari, Matteo [Université Paris Diderot, F-75013 Paris (France); Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005 Paris (France); CNRS, UMR 7589, LPTHE, F-75005 Paris (France); CERN, PH-TH, CH-1211 Geneva 23 (Switzerland); Del Debbio, Luigi [Higgs Centre for Theoretical Physics, School of Physics & Astronomy, University of Edinburgh, Edinburgh EH9 3FD (United Kingdom); CERN, PH-TH, CH-1211 Geneva 23 (Switzerland); Espinosa, José R. [ICREA, Institució Catalana de Recerca i Estudis Avançats, Barcelona (Spain); IFAE, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); Polosa, Antonio D., E-mail: antonio.polosa@roma1.infn.it [Dipartimento di Fisica and INFN, ‘Sapienza’ Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma (Italy); Testa, Massimo [Dipartimento di Fisica and INFN, ‘Sapienza’ Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma (Italy)
2016-02-10
Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N) Yang–Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
Universal character and large N factorization in topological gauge/string theory
International Nuclear Information System (INIS)
Kanno, Hiroaki
2006-01-01
We establish a formula of the large N factorization of the modular S-matrix for the coupled representations in U(N) Chern-Simons theory. The formula was proposed by Aganagic, Neitzke and Vafa, based on computations involving the conifold transition. We present a more rigorous proof that relies on the universal character for rational representations and an expression of the modular S-matrix in terms of the specialization of characters
International Nuclear Information System (INIS)
Mansouri, F.; Suranyi, P.; Wijewardhana, L.C.R.
1992-10-01
Dynamics of 2+1 dimensional gravity is analyzed by coupling matter to Chern Simons Witten action in two ways and obtaining the exact gravity Hamiltonian for each case. 't Hoot's Hamiltonian is obtained as an approximation. The notion of space-time emerges in the very end as a broken phase of the gauge theory. We have studied the patterns of discrete and continuous symmetry breaking in 2+1 dimensional field theories. We formulate our analysis in terms of effective composite scalar field theories. Point-like sources in the Chern-Simons theory of gravity in 2+1 dimensions are described by their Poincare' charges. We have obtained exact solutions of the constraints of Chern-Simons theory with an arbitrary number of isolated point sources in relative motion. We then showed how the space-time metric is constructed. A reorganized perturbation expansion with a propagator of soft infrared behavior has been used to study the critical behavior of the mass gap. The condition of relativistic covariance fixes the form of the soft propagator. Approximants to the correlation critical exponent were obtained in two loop order for the two and three dimensional theories. We proposed a new model of QED exhibiting two phases and a Majorana mass spectrum of single particle states. The model has a new source of coupling constant renormalization which opposes screening and suggests the model may confine. Assuming that the bound states of e + e - essentially obey a Majorana spectrum, we obtained a consistent fit of the GSI peaks as well as predicting new peaks and their spin assignments
International Nuclear Information System (INIS)
Dudal, D.; Verschelde, H.; Gracey, J.A.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P.; Sarandy, M.S.
2004-01-01
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate μ 2 >, which has attracted much attention in the Landau gauge
Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru
2015-05-01
The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark
Moduli space of Chern-Simons gravity
International Nuclear Information System (INIS)
Soda, Jiro; Yamanaka, Yuki
1990-09-01
Conformally invariant (2+1)-dimensional gravity, Chern-Shimons gravity, is studied. Its solution space, moduli space, is investigated using the linearization method. The dimension of moduli space is determined as 18g - 18 for g > 1,6 for g = 1 and 0 for g = 0. We discuss the geometrical meaning of our investigation. (author)
Anomalous commutator of gauge group generators in a non-Abelian chiral theory
International Nuclear Information System (INIS)
Jo, S.
1985-01-01
This paper discusses commutators among non-Abelian fermion currents that are calculated using the BJL limit. It is observed that the gauge dependence of the fermion current with fixed canonical variables should be different from the covariant seagull in order to have correct anomalous commutators
International Nuclear Information System (INIS)
Tanimura, Shogo
1992-01-01
R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs
Two-loop ghost-antighost condensation for SU(2) Yang-Mills theories in the maximal abelian gauge
International Nuclear Information System (INIS)
Fazio, A.R.
2004-01-01
In the framework of the formalism of Cornwall et.al. for composite operators I study the ghost-antighost condensation in SU(2) Yang-Mills theories quantized in the Maximal Abelian Gauge and derive analytically a condensating effective potential at two ghost loops. I find that in this approximation the one-loop pairing ghost-antighost is not destroyed and no mass is generated if the ansatz for the propagator suggested by the tree level Hubbard-Stratonovich transformations is used
An introduction to topological Yang-Mills theory
International Nuclear Information System (INIS)
Baal, P. van; Rijksuniversiteit Utrecht
1990-01-01
In these lecture notes I give a ''historical'' introduction to topological gauge theories. My main aim is to clearly explain the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory. I show how this Hamiltonian arises from Witten's formulation of Morse theory as applied by Floer to the infinite dimensional space of gauge connections, with the Chern-Simons functional as the appriopriate Morse function(al). I therefore discuss the De Rham cohomology, Hodge theory, Morse theory, Floer homology, Witten's construction of the Lagrangian for topological gauge theory, the subsequent BRST formulation of topological quantum field theory and finally Witten's construction of the Donaldson polynomials. (author)
Scattering theory of space-time non-commutative abelian gauge field theory
International Nuclear Information System (INIS)
Rim, Chaiho; Yee, Jaehyung
2005-01-01
The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.
Euclidean D-branes and higher-dimensional gauge theory
International Nuclear Information System (INIS)
Acharya, B.S.; Figueroa-O'Farrill, J.M.; Spence, B.; O'Loughlin, M.
1997-07-01
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane-that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory-is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N T =2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G 2 holonomy. (author). 22 refs, 3 tabs
Non-abelian action of D0-branes from Matrix theory in the longitudinal 5-brane background
International Nuclear Information System (INIS)
Asano, Masako; Sekino, Yasuhiro
2002-01-01
We study one-loop effective action of Berkooz-Douglas Matrix theory and obtain non-abelian action of D0-branes in the background field produced by longitudinal 5-branes. Since these 5-branes do not have D0-brane charge and are not present in BFSS Matrix theory, our analysis provides an independent test for the coupling of D-branes to general weak backgrounds proposed by Taylor and Van Raamsdonk from the analysis of the BFSS model. The proposed couplings appear in the Berkooz-Douglas effective action precisely as expected, which suggests the consistency of the two matrix models. We also point out the existence of the terms which are not given by the symmetrized trace prescription in the Matrix theory effective action
International Nuclear Information System (INIS)
Khoze, V.V.
1991-06-01
The semiclassical evaluation of the functional integral on non-Abelian gauge theories is generalized by means of the so-called valley method. The physically very important example of the valley, the instanton-anti-instanton field configuration, is discussed in details and its contributions to the physical quantities for zero-temperature and for thermal field theories are investigated. The high-energy behaviour of the total cross-section σ Δ F for electroweak fermion number violating two particles collisions is studied using the optical theorem approach. The calculation is done at energies below the sphaleron mass (E<10TeV) where it leads to the most complete result for σ Δ F known to date. Some estimations and a qualitative physical picture are discussed for energies above the sphaleron mass for the confinement and Higgs phases of the gauge theory. The effects of instanton-anti-instanton interactions are also studied in thermal QCD. (au)
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1989-01-01
In this paper, we generalize our earlier discussion of renormalization of the energy-momentum tensor in scalar QED to that in non-Abelian gauge theories involving scalar fields. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be derived from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/)
Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory
International Nuclear Information System (INIS)
Chernicoff, Mariano; Garcia, J. Antonio; Gueijosa, Alberto
2011-01-01
We study the dynamics of a 'composite' or 'dressed' quark in strongly-coupled large-N c N=4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a Lorentz covariant formula for its rate of radiation.
Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory
Chernicoff, Mariano; Garcia, J. Antonio; Guijosa, Alberto
2010-01-01
We study a `dressed' or `composite' quark in strongly-coupled N=4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding quantum non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a...
Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory
Chernicoff, Mariano; García, J. Antonio; Güijosa, Alberto
2011-09-01
We study the dynamics of a 'composite` or 'dressed` quark in strongly-coupled large-Nc N=4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a Lorentz covariant formula for its rate of radiation.
Analytical results for Abelian projection
International Nuclear Information System (INIS)
Ogilivie, Michael C.
1999-01-01
Analytic methods for Abelian projection are developed, and a number of results related to string tension measurements are obtained. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The subgroup used for projection need only contain the center of the gauge group, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements
Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories
Ferreira, L. A.; Miramontes, J. Luis; Guillén, Joaquín Sánchez
1995-02-01
We consider the Hamiltonian reduction of the "two-loop" Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra G. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of G, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.
International Nuclear Information System (INIS)
Wadia, S.R.
1979-01-01
A detailed formulation of the quantum theory of non-abelian gauge fields is presented in the Schroedinger picture. It is applied to the semiclassical quantization of the t'Hoft-Polyakov monopole, with special attention paid to the treatment of boundary conditions and local and global gauge symmetry. The perturbation expansion is then discussed with the aid of standard collective co-ordinates. In the Prasad-Sommerfield limit, all the eigenfunctions of the fluctuation equation are presented, the ground-state wave function is constructed in terms of gauge and translation invariant co-ordinates, and its total angular momentum is computed to be zero. Aspects of instanton phenomena are then examined in the Schroedinger picture; the role of euclidean time is elucidated. The precise relation between boundary conditions, choice of gauge, and the corresponding picture of the semiclassical vacuum is demonstrated
Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio
2010-08-01
It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.
International Nuclear Information System (INIS)
Hart, C.F.
1981-01-01
A gauge invariant effective action which generalizes the usual background field method is applied to quantum non-Abelian gauge theories. The gauge properties of the theory as well as its equivalence to the conventional theory are presented. Solutions to the new effective field equations are found to be physical and it is shown how S-matrix elements may be computed in terms of this new effective action. Feynman rules are given and the renormalization theory is discussed using minimal subtraction and dimensional regularization. The resulting computation of counterterms is found to be simpler than that of the usual method. A complete two-loop calculation of the β function for pure Yang-Mills theory is given as a specific example of this approach
Differential and integral forms in supergauge theories and supergravity
International Nuclear Information System (INIS)
Zupnik, B.M.; Pak, D.G.
1989-01-01
D = 3, 4, N = 1 supergauge theories and D = 3, N = 1 supergravity are considered in the superfield formalism by using differential and integral forms. A special map of the space of differential forms into the space of integral forms is proposed. By means of this map we find the superfield Chern-Simons terms in D = 3, N = 1 Yang-Mills theory and supergravity. The integral forms corresponding to superfield invariants of D = 4, N = 1 supergauge theory have also been constructed. (Author)
A Kallosh theorem for BF-type topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Gibbs, R.; Mokhtari, S.
1991-01-01
A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the 'no Vilkovisky-DeWitt' gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed. (orig.)
A Kallosh theorem for BF-type topological field theory
Energy Technology Data Exchange (ETDEWEB)
Birmingham, D. (Theory Div., CERN, Geneva (Switzerland)); Gibbs, R.; Mokhtari, S. (Physics Dept., Louisiana Tech. Univ., Ruston, LA (United States))
1991-12-12
A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the 'no Vilkovisky-DeWitt' gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed. (orig.).
K-decompositions and 3d gauge theories
Energy Technology Data Exchange (ETDEWEB)
Dimofte, Tudor [Institute for Advanced Study, Einstein Dr., Princeton, NJ 08540 (United States); UniversityC. Davis, Dept. of Mathematics and Center for Quantum Mathematics and Physics,Davis, CA 95616 (United States); Gabella, Maxime [Institute for Advanced Study, Einstein Dr., Princeton, NJ 08540 (United States); Institut de Physique Théorique, CEA/Saclay, 91191 Gif-sur-Yvette (France); Goncharov, Alexander B. [Yale University Mathematics Dept., New Haven, CT 06520 (United States)
2016-11-24
This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K,ℂ)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space L{sub K}(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of L{sub K}(M) as a Lagrangian subvariety in the symplectic moduli space X{sub K}{sup un}(∂M) of framed flat connections on the boundary — and more so, as a “K{sub 2}-Lagrangian,” meaning that the K{sub 2}-avatar of the symplectic form restricts to zero. We construct an open part of L{sub K}(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K,ℂ)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of L{sub K}(M) is K{sub 2}-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that L{sub K}(M) is K{sub 2}-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K{sub 2}-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N=2 superconformal field theories T{sub K}[M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K=2. Just as for K=2, the theories T{sub K}[M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2–3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N{sub f}=1
Quantization conditions and functional equations in ABJ(M) theories
International Nuclear Information System (INIS)
Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki
2014-12-01
The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same Chern-Simons coupling.
Supergravity and Yang-Mills theories as generalized topological fields with constraints
International Nuclear Information System (INIS)
Ling Yi; Tung Rohsuan; Guo Hanying
2004-01-01
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand
Introduction to Abelian varieties
Murty, V Kumar
1993-01-01
The book represents an introduction to the theory of abelian varieties with a view to arithmetic. The aim is to introduce some of the basics of the theory as well as some recent arithmetic applications to graduate students and researchers in other fields. The first part contains proofs of the Abel-Jacobi theorem, Riemann's relations and the Lefschetz theorem on projective embeddings over the complex numbers in the spirit of S. Lang's book Introduction to algebraic and abelian functions. Then the Jacobians of Fermat curves as well as some modular curves are discussed. Finally, as an application, Faltings' proof of the Mordell conjecture and its intermediate steps, the Tate conjecture and the Shafarevich conjecture, are sketched. - H. Lange for MathSciNet.
Alexeev, Valery; Clemens, C Herbert; Beauville, Arnaud
2008-01-01
This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes. In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors, of compactified Jacobians of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties.
On the duality in CPT-even Lorentz-breaking theories
Energy Technology Data Exchange (ETDEWEB)
Scarpelli, A.P.B. [Departamento de Policia Federal, Sao Paulo (Brazil); Ribeiro, R.F.; Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica (Brazil)
2015-07-15
We generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is shown using the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical. (orig.)
A general solution of the BV-master equation and BRST field theories
International Nuclear Information System (INIS)
Dayi, O.F.
1993-05-01
For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization. (author). 17 refs
On the duality in CPT-even Lorentz-breaking theories
International Nuclear Information System (INIS)
Scarpelli, A.P.B.; Ribeiro, R.F.; Nascimento, J.R.; Petrov, A.Yu.
2015-01-01
We generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is shown using the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical. (orig.)
International Nuclear Information System (INIS)
Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, R.
2006-01-01
We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z g Z A 1/2 =1, relating the renormalization factors of the gauge coupling constant Z g and of the diagonal gluon field Z A , still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field
Energy Technology Data Exchange (ETDEWEB)
Yokoyama, Kan-ichi; Kubo, Reijiro
1974-12-01
The framework of the Nakanishi-Lautrup formalism should be enlarged by introducing a scalar dipole ghost field B(x), which is called gauge on field, together with its pair field. By taking free Lagrangian density, Free-field equations can be described. The vacuum is defined by using a neutral vector field U..mu..(x). The state-vector space is generated by the adjoining conjugates of U..mu..sup((+))(x), and auxiliary fields B(x), B/sub 1/(x) and B/sub 2/(x), which were introduced in the form of the Lagrangian density. The physical states can be defined by the supplementary conditions of the form B/sub 1/sup((+))(x) 1 phys>=B/sub 2/sup((+))(x) 1 phys>=0. It is seen that all the field equations and all the commutators are kept form-invariant, and that the gauge parameter ..cap alpha.. is transformed into ..cap alpha..' given by ..cap alpha..'=..cap alpha..+lambda, with epsilon unchanged. The Lagrangian density is specified only by the gauge invariant parameter epsilon. The gauge structure of theory has universal meaning over whole Abelian-gauge field. C-number gauge transformation and the gauge structure in the presence of interaction are also discussed.
Adler's theorem in finite massless QED and possible extensions to non-Abelian gauge theories. II
International Nuclear Information System (INIS)
Bernstein, J.
1975-01-01
The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (Auth.)
Abelian versus non-abelian Higgs model in three dimensions
International Nuclear Information System (INIS)
Buchmueller, W.; Philipsen, O.
1995-04-01
We study the phase structure of the abelian Higgs model in three dimensions based on perturbation theory and a set of gauge independent gap equations for Higgs boson and vector boson masses. Contrary to the non-abelian Higgs model, the vector boson mass vanishes in the symmetric phase. In the Higgs phase the gap equations yield masses consistent with perturbation theory. The phase transition is first-order for small values of the scalar self-coupling λ, where the employed loop expansion is applicable. (orig.)
Theory of the disordered ν =5/2 quantum thermal Hall state: Emergent symmetry and phase diagram
Lian, Biao; Wang, Juven
2018-04-01
Fractional quantum Hall (FQH) system at Landau level filling fraction ν =5 /2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σx y=5 e2/2 h . Thermal Hall conductances of the Pf and APf states are quantized at κx y=7 /2 and κx y=3 /2 , respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν =5 /2 FQH state is κx y=5 /2 . It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κx y=5 /2 phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ1, which is lowered to an emergent U (1 )×U (1) symmetry at energy scales between Λ1 and a higher value Λ2, and is finally lowered to the composite fermion parity symmetry Z2F above Λ2. Based on the emergent symmetries, we propose a phase diagram of the disordered ν =5 /2 FQH system and show that a κx y=5 /2 phase arises at disorder energy scales Λ >Λ1 . Furthermore, we show the gapped double-semion sector of ND compact domain walls contributes nonlocal topological degeneracy 2ND-1, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological 1 +1 D domain walls (two-surface defects) applicable to any 2 +1 D non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various ν =5 /2 FQH states in terms of fermionic version of U (1) ±8 Chern-Simons theory ×Z8 -class TQFTs.
Adler's theorem in finite massless QED and possible extensions to non- Abelian gauge theories II
Bernstein, J
1975-01-01
For pt.I see ibid., vol.B95, p.461 (1975). The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger (1962) for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (7 refs).
High-energy behaviour in a non-abelian gauge theory. Pt. 3
International Nuclear Information System (INIS)
Bartels, J.
1991-07-01
The high energy limit (Regge limit) of a spontaneously broken SU(2) gauge theory is studied beyond the leading-lns approximation. Calculations are based upon the analytic structure of scattering amplitudes in generalized Regge limits, and the resulting amplitudes satisfy reggeon unitarity in the t-channel as well as unitarity in the s-channel. The calculations lead to a systematic construction of a reggeon field theory. (orig.)
Topological Field Theory of Time-Reversal Invariant Insulators
Energy Technology Data Exchange (ETDEWEB)
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory
International Nuclear Information System (INIS)
Uensal, Mithat
2008-01-01
We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial S 1 xR 3 . The absence of thermal fluctuations, and the fact that quantum fluctuations favor the vacuum with unbroken center symmetry in a weakly coupled regime, renders the interesting dynamics of these theories analytically calculable. Confinement and the generation of the mass gap in the gluonic sector are shown analytically. In this regime, theory exhibits confinement without continuous chiral-symmetry breaking. However, a flavor singlet chiral condensate (which breaks a discrete chiral symmetry) persists at arbitrarily small S 1 . Under certain reasonable assumptions, we show that the theory exhibits a zero temperature chiral phase transition in the absence of any change in spatial center symmetry realizations
An off-shell formulation of N=4 supersymmetric Yang-Mills theory in twistor harmonic superspace
International Nuclear Information System (INIS)
Sokatchev, E.
1989-01-01
Twistor-like harmonic variables which parametrize the coset space SO(1, 4)/SO(1, 2)xSO(2) are introduced. With their help the on-shell constraints for N=4, d=5 supersymmetric Yang-Mills theory are rewritten as conditions for flatness in the harmonic directions of superspace. A Chern-Simons off-shell action leading to those equations is proposed. There are indications that the off-shell theory might be finite, despite the fact that the on-shell one seems non-renormalizable. (orig.)
SUSY non-Abelian gauge models: exact beta function from one loop of perturbation theory
International Nuclear Information System (INIS)
Shifman, M.A.; Vajnshtejn, A.I.; Zakharov, V.I.
1985-01-01
The method for calculating the exact β function (to all orders in the coupling constant) proposed earlier in supersymmetric electrodynamics is extended. The starting point is the observation that the low-energy effective action is exhausted by one loop provided that the theory is regularized supersymmetrically both in the ultraviolet and infrared domains in four dimensions. The Pouli-Villars method of the ultraviolet regularization is used. Two methods for the infrared regularization are considered. The first one - quantization in a box with a finite volume L 3 - is universally applicable to anygauge theory. The second method is based on the effective Higgs mechanism for mass generation and requires the presence of certain matter superfields in the lagrangian. Within this method the necessary condition is the existence of flat directions, so called valeys, along which the vacuum energy vanishes. The theory is quantized near epsilon non-vanishing value of the scalar field from the bottom of the valley. After calculating the one-loop effective action one and the same exact expression is obtained for the β function within the both approaches, and it also coincides with our earlier result extracted from instanton calculus. A few remarks on the problem of anomalies in SUSY gauge theories are presented
Point-splitting analysis of commutator anomalies in non-abelian chiral gauge theories
International Nuclear Information System (INIS)
Ghosh, S.; Banerjee, R.
1988-01-01
A gauge covariant point-splitting regularisation is employed to calculate different anomalous commutators in four dimensional chiral gauge theories. For an external gauge field the fixed time anomalous commutator of the gauge group generators is seen to violate the Jacobi identity. The cohomological prediction can be confirmed provided the electric fields do not commute. Other commutators like the current-current and current-electric field are consistent with the Bjorken-Johnson-Low (BJL) derivation. (orig.)
International Nuclear Information System (INIS)
Mansouri, F.; Suranyi, P.; Wijewardhana, L.C.R.; Witten, L.
1990-10-01
A 2+1 dimensional deSitter Chern-Simons theory has been constructed and shown to be consistent. Wilson loop variables have been computed and shown to close under Poisson bracket operation for N = 2 Poincare supergravity. It has also been shown that there are two equivalent pictures of describing two particle scattering in 2+1 dimensional gravity theory, which are related by multivalued gauge transformations. We have generalized the Jackiw-Johnson sumrule, relating Goldstone boson decay constants to the dynamical masses of fermions, to an arbitrary symmetry group. We have analyzed dynamical parity breaking in 2+1 dimensional 4-fermi theories. Finally, we have found the partition function for a system of free parabosons and parafermions of order two. 53 refs
International Nuclear Information System (INIS)
Mansouri, F.; Suranyi, P; Wijewardhana, L.C.R.
1991-10-01
In the test particle approximation, the scattering amplitude for two-particle scattering in (2+1)-dimensional Chern-Simons-Witten gravity and supergravity was computed and compared to the corresponding metric solutions. The formalism was then extended to the exact gauge theoretic treatment of the two-particle scattering problem and compared to 't Hooft's results from the metric approach. We have studied dynamical symmetry breaking in 2+1 dimensional field theories. We have analyzed strong Extended Technicolor (ETC) models where the ETC coupling is close to a critical value. There are effective scalar fields in each of the theories. We have worked our how such scalar particles can be produced and how they decay. The φ 4 field theory was investigated in the Schrodinger representation. The critical behavior was extracted in an arbitrary number of dimensions in second order of a systematic truncation approximation. The correlation exponent agrees with known values within a few percent
Non-abelian gauge bosons in the compactified bosonic membrane theory
International Nuclear Information System (INIS)
Kubo, J.
1988-01-01
We consider the bosonic membrane compactified on a torus. The membrane motion is stabilized by a topologically non-trivial background. We find that, in the narrow membrane limit, the mass formula to O(ℎ) reduces to exactly the same form as that of the compactified closed bosonic string theory, and we obtain (almost) massless vector bosons in the adjoint representation of a simply laced Lie group in D=27. This is only dimension at which the graviton and gauge bosons may coexist in that background. (orig.)
Field theory approach to quantum hall effect
International Nuclear Information System (INIS)
Cabo, A.; Chaichian, M.
1990-07-01
The Fradkin's formulation of statistical field theory is applied to the Coulomb interacting electron gas in a magnetic field. The electrons are confined to a plane in normal 3D-space and also interact with the physical 3D-electromagnetic field. The magnetic translation group (MTG) Ward identities are derived. Using them it is shown that the exact electron propagator is diagonalized in the basis of the wave functions of the free electron in a magnetic field whenever the MTG is unbroken. The general tensor structure of the polarization operator is obtained and used to show that the Chern-Simons action always describes the Hall effect properties of the system. A general proof of the Streda formula for the Hall conductivity is presented. It follows that the coefficient of the Chern-Simons terms in the long-wavelength approximation is exactly given by this relation. Such a formula, expressing the Hall conductivity as a simple derivative, in combination with diagonal form of the full propagator allows to obtain a simple expressions for the filling factor and the Hall conductivity. Indeed, these results, after assuming that the chemical potential lies in a gap of the density of states, lead to the conclusion that the Hall conductivity is given without corrections by σ xy = νe 2 /h where ν is the filling factor. In addition it follows that the filling factor is independent of the magnetic field if the chemical potential remains in the gap. (author). 21 ref, 1 fig
Renormalization of topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.; Thompson, G.
1988-11-01
One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs
A further pathology of the Coulomb gauge in non-Abelian Yang-Mills theories
International Nuclear Information System (INIS)
Ademollo, M.; Napolitano, E.; Sciuto, S.
1978-01-01
In the first part the vacuum structure of SU(2) Yang-Mills theories in the Coulomb gauge is discussed. It is proved that the only transverse pure gauge field Asub(μ)(x) = U -1 deltasub(μ)U with U(x) → (as r→infinity) const., is the trivial one Asub(μ)(x) equivalent to 0; the features of other possible vacua with U(x) → (as r→infinity) U(theta, pli) are studied. In the second part, regular Euclidean configurations that connect a vacuum state at x 4 = -infinity to another at x 4 = +infinity are discussed. It is proved, always working in the Coulomb gauge, that the perturbative vacuum Asub(μ)(x) equivalent to 0 cannot tunnel into any other one and that regular configurations with non-vanishing Pontryagin number q cannot affect such a vacuum. Moreover, strong arguments are given to show that many-instanton configurations (mod(q)>=2) cannot be expressed at all in the Coulomb gauge, that is by a regular field Asub(μ) satisfying the transversality condition deltasub(i)Asub(i) (x, x 4 ) = 0. (Auth.)
International Nuclear Information System (INIS)
Ma Zhongshui; Su Zhaobin.
1992-09-01
By applying the Dirac quantization method, we build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system and show that the constraint can be transmuted from hierarchy to hierarchy. For a finite system, we derive that the action for each hierarchy can be split into two parts: a surface part provides the action for the edge excitations while the remaining part is precisely the bulk action for the next hierarchy. An the action for the edge could be decoupled from the bulk only at the hierarchy filling. (author). 16 refs
Critical properties of effective gauge theories for novel quantum fluids
Energy Technology Data Exchange (ETDEWEB)
Smoergrav, Eivind
2005-07-01
Critical properties of U(1) symmetric gauge theories are studied in 2+1 dimensions, analytically through duality transformations and numerically through Monte Carlo simulations. Physical applications range from quantum phase transitions in two dimensional insulating materials to superfluid and superconducting properties of light atoms such as hydrogen under extreme pressure. A novel finite size scaling method, utilizing the third moment M{sub 3} of the action, is developed. Finite size scaling analysis of M{sub 3} yields the ratio (1 + alpha)/ny and 1/ny separately, so that critical exponents alpha and ny can be obtained independently without invoking hyperscaling. This thesis contains eight research papers and an introductory part covering some basic concepts and techniques. Paper 1: The novel M{sub 3} method is introduced and employed together with Monte Carlo simulations to study the compact Abelian Higgs model in the adjoint representation with q = 2. Paper 2: We study phase transitions in the compact Abelian Higgs model for fundamental charge q = 2; 3; 4; 5. Various other models are studied to benchmark the M{sub 3} method. Paper 3: This is a proceeding paper based on a talk given by F. S. Nogueira at the Aachen EPS HEP 2003 conference. A review of the results from Paper 1 and Paper 2 on the compact Abelian Higgs model together with some results on q = 1 obtained by F. S. Nogueira, H. Kleinert, and A. Sudboe is given. Paper 4: The effect of a Chern-Simons (CS) term in the phase structure of two Abelian gauge theories is studied. Paper 5: We study the critical properties of the N-component Ginzburg-Landau theory. Paper 6: We consider the vortices in the 2-component Ginzburg-Landau model in a finite but low magnetic field. The ground state is a lattice of co centered vortices in both order parameters. We find two novel phase transitions. i) A 'vortex sub-lattice melting' transition where vortices in the field with lowest phase stiffness (&apos
Noncompact symmetries in string theory
International Nuclear Information System (INIS)
Maharana, J.; Schwarz, J.H.
1993-01-01
Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by noncompact groups modded out by their maximal compact subgroups and discrete duality groups. Then it was found that many other moduli spaces have analogous descriptions. More recently, noncompact group symmetries have turned up in effective actions used to study string cosmology and other classical configurations. This paper explores these noncompact groups in the case of toroidal compactification both from the viewpoint of low-energy effective field theory, using the method of dimensional reduction, and from the viewpoint of the string theory world-sheet. The conclusion is that all these symmetries are intimately related. In particular, we find that Chern-Simons terms in the three-form field strength H μνρ play a crucial role. (orig.)
Light-front quantization of field theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.
Light-front quantization of field theory
International Nuclear Information System (INIS)
Srivastava, Prem P.
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs
On the infinite-dimensional spin-2 symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Hohm, O.; Hamburg Univ.
2005-11-01
We consider the couplings of an infinite number of spin-2 fields to gravity appearing in Kaluza-Klein theories. They are constructed as the broken phase of a massless theory possessing an infinite-dimensional spin-2 symmetry. Focusing on a circle compactification of four-dimensional gravity we show that the resulting gravity/spin-2 system in D=3 has in its unbroken phase an interpretation as a Chern-Simons theory of the Kac-Moody algebra iso(1,2) associated to the Poincare group and also fits into the geometrical framework of algebra-valued differential geometry developed by Wald. Assigning all degrees of freedom to scalar fields, the matter couplings in the unbroken phase are determined, and it is shown that their global symmetry algebra contains the Virasoro algebra together with an enhancement of the Ehlers group SL(2,R) to its affine extension. The broken phase is then constructed by gauging a subgroup of the global symmetries. It is shown that metric, spin-2 fields and Kaluza-Klein vectors combine into a Chern-Simons theory for an extended algebra, in which the affine Poincare subalgebra acquires a central extension. (orig.)
Effective field theory and integrability in two-dimensional Mott transition
International Nuclear Information System (INIS)
Bottesi, Federico L.; Zemba, Guillermo R.
2011-01-01
Highlights: → Mott transition in 2d lattice fermion model. → 3D integrability out of 2D. → Effective field theory for Mott transition in 2d. → Double Chern-Simons. → d-Density waves. - Abstract: We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a quantum group symmetry as a consequence of a recently found solution of the Zamolodchikov tetrahedron equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U q (sl(2)-circumflex)xU q (sl(2)-circumflex), with deformation parameter q = -1. Based on this result, the low-energy effective field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k = 1 (with the standard normalization). By further employing the effective filed theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Non-planar ABJ theory and parity
International Nuclear Information System (INIS)
Caputa, Pawel; Kristjansen, Charlotte; Zoubos, Konstantinos
2009-01-01
While the ABJ Chern-Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this Letter we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance. For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account.
Non-planar ABJ Theory and Parity
DEFF Research Database (Denmark)
Caputa, Pawel; Kristjansen, Charlotte; Zoubos, Konstantinos
2009-01-01
we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance......While the ABJ Chern-Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this letter....... For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account....
International Nuclear Information System (INIS)
Verlinde, Herman; Wang, L-T; Yavin, Itay; Wijnholt, Martijn
2008-01-01
We exhibit a simple and robust mechanism for bulk mediation of supersymmetry breaking between hidden and visible sectors localized on geometrically separated D-branes in type II string theory. The mediation proceeds via RR p-forms that couple via linear Chern-Simons terms to the abelian vector bosons on the branes. From a 4-d low energy perspective, the mechanism reduces to U(1) mediation
Presheaves of symmetric tensor categories and nets of C*-algebras
Vasselli, Ezio
2012-01-01
Motivated by algebraic quantum field theory, we study presheaves of symmetric tensor categories defined over the base of a space, intended as a spacetime. Any section of a presheaf (that is, any "superselection sector", in the applications that we have in mind) defines a holonomy representation whose triviality is measured by Cheeger-Chern-Simons characteristic classes, and a non-abelian unitary cocycle defining a Lie group gerbe. We show that, given an embedding in a presheaf of full subcate...
Modifications of Einstein's theory of gravity at large distances
2015-01-01
In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edite...
Wang, Juven C.; Wen, Xiao-Gang
2015-01-01
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.
Theory of orbital magnetoelectric response
International Nuclear Information System (INIS)
Malashevich, Andrei; Souza, Ivo; Coh, Sinisa; Vanderbilt, David
2010-01-01
We extend the recently developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric (ME) response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing one to calculate the ME response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear ME tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the 'Chern-Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, 'Kubo' terms, involve the first-order change in the orbitals and give isotropic as well as anisotropic contributions to the response. In ordinary ME insulators all terms are generally present, while in strong Z 2 topological insulators only the Chern-Simons term is allowed, and is quantized. In order to validate the theory, we have calculated under periodic boundary conditions the linear ME susceptibility for a 3D tight-binding model of an ordinary ME insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples.
Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory
International Nuclear Information System (INIS)
Balatsky, A.
1991-01-01
In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-1/2 semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-1/2 semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to Su(2) κ=1 Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of ''spin rigidity'' of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacenmants. We argue that topological structure of Su(2) κ=1 Chern-Simons theory unambiguously dictates semion statistics of spinons. 19 refs
Instantons in Lifshitz field theories
Energy Technology Data Exchange (ETDEWEB)
Fujimori, Toshiaki; Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2015-10-05
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for “the superpotential” defining “the detailed balance condition”. The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.
Energy Technology Data Exchange (ETDEWEB)
Alday, Luis F.; Genolini, Pietro Benetti; Bullimore, Mathew; Loon, Mark van [Mathematical Institute, University of Oxford, Andrew Wiles Building,Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom)
2017-04-28
We explore aspects of the correspondence between Seifert 3-manifolds and 3d N=2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N=2 theories constructed from boundary conditions and interfaces in a 4d N=2{sup ∗} theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-’t Hooft loops in the 4d N=2{sup ∗} theory. In the presence of a mass parameter for the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.
International Nuclear Information System (INIS)
Dudal, David; Verschelde, Henri; Rodino Lemes, Vitor Emanuel; Sarandy, Marcelo S.; Sorella, Silvio Paolo; Picariello, Marco
2002-01-01
The existence of a SL(2;R) symmetry is discussed in SU(N) Yang-Mills in the maximal abelian gauge. This symmetry, also present in the Landau and Curci-Ferrari gauge, ensures the absence of tachyons in the maximal abelian gauge. In all these gauges, SL(2;R) turns out to be dynamically broken by ghost condensates. (author)
The gravitational sector of 2d (0,2) F-theory vacua
Energy Technology Data Exchange (ETDEWEB)
Lawrie, Craig [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, Heidelberg, 69120 (Germany); Schäfer-Nameki, Sakura [Mathematical Institute, University of Oxford,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, Heidelberg, 69120 (Germany)
2017-05-19
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S{sup 1} reduction of the dual F-theory.
The gravitational sector of 2d (0,2) F-theory vacua
International Nuclear Information System (INIS)
Lawrie, Craig; Schäfer-Nameki, Sakura; Weigand, Timo
2017-01-01
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S 1 reduction of the dual F-theory.
Energy Technology Data Exchange (ETDEWEB)
Capri, M.A.L.; Fiorentini, D.; Sorella, S.P. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Pereira, A.D. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); UFF - Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)
2017-08-15
In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hepth]), Pereira et al. (arXiv:1605.09747 [hep-th]), the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement. (orig.)
Capri, M. A. L.; Fiorentini, D.; Pereira, A. D.; Sorella, S. P.
2017-08-01
In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hep-th]), Pereira et al. (arXiv:1605.09747 [hep-th]),the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.
Buividovich, P. V.; Davody, A.
2017-12-01
We develop numerical tools for diagrammatic Monte Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First, we note that the path integral measure of such theories contributes a bare mass term in the effective action which is proportional to the bare coupling constant. This mass term renders the perturbative expansion infrared-finite and allows us to study it directly in the large-N and infinite-volume limits using the diagrammatic Monte Carlo approach. On the exactly solvable example of a large-N O (N ) sigma model in D =2 dimensions we show that this infrared-finite weak-coupling expansion contains, in addition to powers of bare coupling, also powers of its logarithm, reminiscent of resummed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. We numerically demonstrate the convergence of these double series to the manifestly nonperturbative dynamical mass gap. We then develop a diagrammatic Monte Carlo algorithm for sampling planar diagrams in the large-N matrix field theory, and apply it to study this infrared-finite weak-coupling expansion for large-N U (N ) ×U (N ) nonlinear sigma model (principal chiral model) in D =2 . We sample up to 12 leading orders of the weak-coupling expansion, which is the practical limit set by the increasingly strong sign problem at high orders. Comparing diagrammatic Monte Carlo with conventional Monte Carlo simulations extrapolated to infinite N , we find a good agreement for the energy density as well as for the critical temperature of the "deconfinement" transition. Finally, we comment on the applicability of our approach to planar QCD at zero and finite density.
Instanton bound states in ABJM theory
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.
Ghost free dual vector theories in 2+1 dimensions
International Nuclear Information System (INIS)
Dalmazi, Denis
2006-01-01
We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach
Matrix effective theories of the fractional quantum Hall effect
International Nuclear Information System (INIS)
Cappelli, Andrea; Rodriguez, Ivan D
2009-01-01
The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain 'composite fermion' excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum Hall effect, where the composite-fermion construction naturally follows from gauge invariance. The matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the Laughlin and Jain hierarchical states. The matrix theory possesses a physical limit for commuting matrices that could be reachable while staying in the same phase.
International Nuclear Information System (INIS)
Phillips, S.
1985-01-01
The mathematical problem of inverting the operator Δ x μν ≡ g μν g αβ δ x α δ x β -δ x μ δ x ν , as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article. Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, Δ x μν L ν (x) J μ (x), can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one. Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action
Chiral and parity anomalies at finite temperature and density
International Nuclear Information System (INIS)
Sisakyan, A.N.; Shevchenko, O.Yu.; Solganik, S.B.
1997-01-01
Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern-Simons term. By using different methods it is shown that μ 2 =m 2 is the crucial point for Chern-Simons term at zero temperature. So when μ 2 2 , μ influence disappears and we get the usual Chern-Simons term. On the other hand, when μ 2 >m 2 , the Chern-Simons term vanishes because of nonzero density of background fermions. It occurs that the chiral anomaly doesn't depend on density and temperature. The connection between parity anomalous Chern-Simons term and chiral anomaly is generalized on finite density. These results hold in any dimension both in Abelian and in non-Abelian cases
Topologically massive gauge theories and their dual factorized gauge-invariant formulation
International Nuclear Information System (INIS)
Bertrand, Bruno; Govaerts, Jan
2007-01-01
There exists a well-known duality between the Maxwell-Chern-Simons theory and the 'self-dual' massive model in (2 + 1) dimensions. This dual description may be extended to topologically massive gauge theories (TMGT) for forms of arbitrary rank and in any dimension. This communication introduces the construction of this type of duality through a reparametrization of the 'master' theory action. The dual action thereby obtained preserves the full gauge symmetry structure of the original theory. Furthermore, the dual action is factorized into a propagating sector of massive gauge-invariant variables and a decoupled sector of gauge-variant variables defining a pure topological field theory. Combining the results obtained within the Lagrangian and Hamiltonian formulations, a completed structure for a gauge-invariant dual factorization of TMGT is thus achieved. (fast track communication)
International Nuclear Information System (INIS)
Knight, D.W.
1976-01-01
Reasons are given for studying the form factor and a method for constructing all believed-to-be leading form factor diagrams in a certain class of non-Abelian gauge theories (NAGT's) in typical kinematic limits. The possibility that the form factor ''exponentiates'' in NAGT's (as it does in QED) is discussed. A method is given for constructing all 1CI planar diagrams (this is, all 1PI diagrams except those which separate upon cutting at a vertex) directly from one's heat--that is, without the need to refer to tables, et cetera. It is noted that the material is believed to be essentially completely original, that is, the technique for constructing all 1CI planar diagrams in an iterative fashion is completely new. Of course, one can construct them in an essentially random fashion, but this technique is slow and extremely error prone compared with the iterative technique given. The idea of associating an elastic resonance with a complex pole in the analytic scattering amplitude, T(E), is discussed. Calculations of the pole position and the residue of the Δ 33 resonance are given, along with an analysis of experimentally induced error in the pole position
Gravitational catalysis of merons in Einstein-Yang-Mills theory
Canfora, Fabrizio; Oh, Seung Hun; Salgado-Rebolledo, Patricio
2017-10-01
We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter λ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing λ to be different from its usual value of 1 /2 . In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".
Non-Abelian bubbles in microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Ramírez, Pedro F. [Instituto de Física Teórica UAM/CSIC,C/ Nicolás Cabrera, 13-15, C.University Cantoblanco, E-28049 Madrid (Spain); Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers bâtiment 774, F-91191 Gif-sur-Yvette (France)
2016-11-24
We find the first smooth bubbling microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of N=1, d=5 Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.
Building Abelian Functions with Generalised Baker-Hirota Operators
Directory of Open Access Journals (Sweden)
Matthew England
2012-06-01
Full Text Available We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus.
Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
Directory of Open Access Journals (Sweden)
Matthew England
2010-03-01
Full Text Available We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.
Instanton effects in ABJM theory from Fermi gas approach
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2012-11-19
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1, 2, 3, 4, 6 up to N=44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.
Vacuum static compactified wormholes in eight-dimensional Lovelock theory
International Nuclear Information System (INIS)
Canfora, Fabrizio; Giacomini, Alex
2008-01-01
In this paper, new exact solutions in eight-dimensional Lovelock theory will be presented. These solutions are the vacuum static wormhole, the black hole, and generalized Bertotti-Robinson space-times with nontrivial torsion. All of the solutions have a cross product structure of the type M 5 xΣ 3 , where M 5 is a five-dimensional manifold and Σ 3 a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the 'navigableness' of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as 'geometrical filter': A very large torsion may 'increase the traversability' for scalars while acting as a 'polarizator' on spinning particles. This may have interesting phenomenological consequences.
Theory of activated transport in bilayer quantum Hall systems.
Roostaei, B; Mullen, K J; Fertig, H A; Simon, S H
2008-07-25
We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.
Three-dimensional spin-3 theories based on general kinematical algebras
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Grumiller, Daniel; Prohazka, Stefan [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); Rosseel, Jan [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland); Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria)
2017-01-25
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible Inönü-Wigner contraction procedures of the kinematical algebra of spin-3 theory in three dimensional (anti-) de Sitter space-time. We demonstrate how to construct associated actions of Chern-Simons type, directly in the ultra-relativistic case and by suitable algebraic extensions in the non-relativistic case. We show how to give these kinematical algebras an infinite-dimensional lift by imposing suitable boundary conditions in a theory we call “Carroll Gravity”, whose asymptotic symmetry algebra turns out to be an infinite-dimensional extension of the Carroll algebra.
Complexity growth in massive gravity theories, the effects of chirality, and more
Ghodrati, Mahdis
2017-11-01
To study the effect of parity violation on the rate of complexity growth, by using "complexity=action " conjecture, we find the complexity growth rates in different solutions of the chiral theory of topologically massive gravity (TMG) and parity-preserving theory of new massive gravity (NMG). Using the results, one can see that decreasing the parameter μ , which increases the effect of the Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped conformal field theories in the tensor network renormalization picture.
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
-orbit coupling (Rashba and Dresselhaus couplings), familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating phenomena such as the quantum spin Hall effect, three-dimensional topological insulators, topological superconductors and superfluids of various kinds. One also expects here the appearance of excitations in a form of topological edge states that can support robust transport, or entangled Majorana fermions in the case of topological superconductors or superfluids. Again, while many kinds of topological insulators have been realized in condensed matter systems, a controlled way of creating them in AMO systems and studying quantum phase transitions between various kinds of them is obviously very appealing and challenging. The various systems listed so far correspond to static gauge fields, which are externally imposed by the experimentalists. Even more fascinating is the possibility of generating synthetically dynamical gauge fields, i.e. gauge fields that evolve in time according to an interacting gauge theory, e.g., a full lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far, most of the theoretical proposals concern the simulation of Abelian gauge theories, however, several groups have recently proposed extensions to the non-Abelian scenarios. The scope of the present focused issue of Journal of Physics B is to cover all of these developments, with particular emphasis on the non-Abelian gauge fields. The 14 papers in this issue include contributions from the leading theory groups working in this field; we believe that this collection will provide the reference set for quantum simulations of gauge fields. Although the special issue contains exclusively theoretical proposals and studies, it should be stressed that
Tallarita, Gianni; Peterson, Adam
2018-04-01
We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.
Stringy origin of non-Abelian discrete flavor symmetries
International Nuclear Information System (INIS)
Kobayashi, Tatsuo; Nilles, Hans Peter; Ploeger, Felix; Raby, Stuart; Ratz, Michael
2007-01-01
We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D 4 and Δ(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Abelian flavor symmetries
Mesons from (non) Abelian T-dual backgrounds
Energy Technology Data Exchange (ETDEWEB)
Itsios, Georgios [Instituto de Física Teórica, UNESP-Universidade Estadual Paulista, R. Dr. Bento T. Ferraz 271, Bl. II, Sao Paulo 01140-070, SP (Brazil); Department of Physics, University of Oviedo,Avda. Calvo Sotelo 18, 33007 Oviedo (Spain); Núñez, Carlos [Department of Physics, Swansea University,Swansea SA2 8PP (United Kingdom); Zoakos, Dimitrios [Centro de Física do Porto, Universidade do Porto,Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2017-01-03
In this work we study mesonic excitations in a Quantum Field Theory dual to the non Abelian T-dual of AdS{sub 5}×S{sup 5}, using a D6 brane probe on the Sfetsos-Thompson background. Before and after the duality, we observe interesting differences between the spectra and interpret them. The spectrum of masses and the interactions between mesonic excitations teach valuable lessons about the character of non-Abelian T-duality and its implications for Holography. The case of Abelian T-duality is also studied.
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Superconformal quantum field theories in string. Gauge theory dualities
International Nuclear Information System (INIS)
Wiegandt, Konstantin
2012-01-01
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Non-Abelian strings and axions
International Nuclear Information System (INIS)
Gorsky, A.; Shifman, M.; Yung, A.
2006-01-01
We address two distinct but related issues: (i) the impact of (two-dimensional) axions in a two-dimensional theory known to model confinement, the CP(N-1) model; (ii) bulk axions in four-dimensional Yang-Mills theory supporting non-Abelian strings. In the first case n, n kinks play the role of 'quarks'. They are known to be confined. We show that introduction of axions leads to deconfinement (at very large distances). This is akin to the phenomenon of wall liberation in four-dimensional Yang-Mills theory. In the second case we demonstrate that the bulk axion does not liberate confined (anti)monopoles, in contradistinction with the two-dimensional model. A novel physical effect which we observe is the axion radiation caused by monopole-antimonopole pairs attached to the non-Abelian strings
Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles
International Nuclear Information System (INIS)
Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru
2009-01-01
The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.
Non-abelian bosonization in two-dimensional condensed matter physics
International Nuclear Information System (INIS)
Froehlich, J.; Kerler, T.; Marchetti, P.A.
1992-01-01
We derive mathematical identities proving that some systems of interacting, non-relativistic fermions of spin or 'isospin' S=1/2, 3/3, 5/2, ... confined to a plane (e.g. a heterojuncture) can be described in terms of a complex boson of spin or isospin S coupled to statistical U(1) and SU(2) gauge fields. In a Feynman path integral formulation, the U(1) gauge field has a Chern-Simons action with coupling constant k=2/(2l+1), l=0, 1, 2, ..., while the SU(2) gauge field has a Chern-Simons action with level 2S. Generalization to internal symmetry groups other than SU(2) are sketched, and applications of our formalism to an analysis of excitations with braid statistics in incompressible quantum fluids and of holons and spinons in the t-J model are discussed. (orig.)
Metrically universal abelian groups
Czech Academy of Sciences Publication Activity Database
Doucha, Michal
2017-01-01
Roč. 369, č. 8 (2017), s. 5981-5998 ISSN 0002-9947 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : Abelian group Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.426, year: 2016 http://www.ams.org/journals/tran/2017-369-08/S0002-9947-2017-07059-8/
F-theory and 2d (0,2) theories
Energy Technology Data Exchange (ETDEWEB)
Schäfer-Nameki, Sakura [Department of Mathematics, King’s College London, The Strand, London WC2R 2LS (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, 69120 Heidelberg (Germany)
2016-05-11
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.
Non Abelian T-duality in Gauged Linear Sigma Models
Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto
2018-04-01
Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.
Exploring Lovelock theory moduli space for Schrödinger solutions
Jatkar, Dileep P.; Kundu, Nilay
2016-09-01
We look for Schrödinger solutions in Lovelock gravity in D > 4. We span the entire parameter space and determine parametric relations under which the Schrödinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schrödinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schrödinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.
Stability of infinite derivative Abelian Higgs models
Ghoshal, Anish; Mazumdar, Anupam; Okada, Nobuchika; Villalba, Desmond
2018-04-01
Motivated by the stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability; the Yukawa coupling between the scalar and the fermion, the gauge coupling, and the self interaction of the Higgs yields exponentially suppressed running at high energies, showing that such class of theory never suffers from vacuum instability. We briefly discuss its implications for the early Universe cosmology.
Non-Abelian Kubo formula and the multiple time-scale method
International Nuclear Information System (INIS)
Zhang, X.; Li, J.
1996-01-01
The non-Abelian Kubo formula is derived from the kinetic theory. That expression is compared with the one obtained using the eikonal for a Chern endash Simons theory. The multiple time-scale method is used to study the non-Abelian Kubo formula, and the damping rate for longitudinal color waves is computed. copyright 1996 Academic Press, Inc
International Nuclear Information System (INIS)
Moore, G.; Seiberg, N.
1989-01-01
All known rational conformal field theories may be obtained from (2+1)-dimensional Chern-Simons gauge theories by appropriate choice of gauge group. We conjecture that all rational field theories are classified by groups via (2+1)-dimensional Chern-Simons gauge theories. (orig.)
Perturbative analysis of non-Abelian Aharonov-Bohm scattering
International Nuclear Information System (INIS)
Bak, D.; Bergman, O.
1995-01-01
We perform a perturbative analysis of the non-Abelian Aharonov-Bohm problem to one loop in the framework of a local field theory, and show the necessity of contact interactions for renormalizability of perturbation theory. Moreover at critical values of the contact interaction strength the theory is finite and preserves classical conformal invariance
First and second order vortex dynamics
International Nuclear Information System (INIS)
Kim, Yoonbai; Lee, Kimyeong
2002-01-01
The low energy dynamics of vortices in self-dual Abelian Higgs theory in (2+1)-dimensional spacetime is of second order in vortex velocity and characterized by the moduli space metric. When the Chern-Simons term with a small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provide an additional check of the first and second order terms by studying the angular momentum in field theory
A simple remark on three dimensional gauge theories
International Nuclear Information System (INIS)
Lemes, V.E.R.; Linhares de Jesus, C.; Sasaki, C.A.G.; Sorella, S.P.; Vilar, L.C.Q.; Ventura, O.S.
1997-08-01
Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is proved. (author)