Maxwell-Chern-Simons theory and an ambiguity in Chern-Simons perturbation theory
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Leblanc, M.; Thomaz, M.T. (Center for Theoretical Physics, Lab. for Nuclear Science, Dept. of Physics, Massachusetts Inst. of Technology, Cambridge, MA (United States))
1992-05-14
We calculate the one-loop effective potential for a matter scalar field in the N=2 supersymmetric Maxwell-Chern-Simons model. It is found that the degeneracy of the classical potential is not lifted by radiative corrections. We show that reduction to the effective potential for the Chern-Simons theory as a limit from the Maxwell-Chern-Simons theory gives rise at one loop to an expression that differs from the result obtained solely within Chern-Simons theory. (orig.).
Chern-Simons Theory on Supermanifolds
Grassi, Pietro Antonio
2016-01-01
We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N=1 D=3 super-Chern-Simons theory.
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...... using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three...
W∞ Algebras from Noncommutative Chern Simons Theory
Pinzul, A.; Stern, A.
We examine Chern Simons theory written on a noncommutative plane with a "hole", and show that the algebra of observables is a nonlinear deformation of the w∞ algebra. The deformation depends on the level (the coefficient in the Chern Simons action), and the noncommutativity parameter, which were identified, respectively, with the inverse filling fraction (minus one) and the inverse density in a recent description of the fractional quantum Hall effect. We remark on the quantization of our algebra. The results are sensitive to the choice of ordering in the Gauss law.
Perturbative Chern-Simons theory revisited
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
We reconsider perturbative Chern-Simons theory on a closed and oriented three-manifold with a choice of contact structure following C. Beasley and E. Witten. Closed three manifolds that admit a Sasakian structure are explicitly computed to first order in perturbation in terms of their Seifert dat...
Self-dual Chern-Simons theories
Dunne, Gerald
1995-01-01
Self-dual Chern-Simons theories form a new class of self-dual gauge theories and provide a field theoretical formulation of anyonic excitations in planar (i.e., two-space-dimensional) systems. Much of the recent attention of these theories is due to the surprising and novel ways in which they differ from the standard Maxwell, or Yang-Mills, gauge theories. These Chern-Simons theories are particular to planar systems and have therefore received added research impetus from recent experimental and theoretical breakthroughs in actual planar condensed-matter systems, such as the quantum Hall effect. This book gives a pedagogical introduction to the basic properties of the "self-dual" Chern-Simons theories, concluding with an overview of more advanced results and an extensive bibliography. Such models possess Bogomol'nyi energy bounds, topological charges, vortex solutions, and supersymmetric extensions, features which are familiar from other well-known self-dual systems such as instantons, monopoles, and vortices....
Gauge dependence in Chern-Simons theory
Dilkes, F A; McKeon, D G C; Sherry, T N
1996-01-01
We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (\\alpha) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form (\\alpha / \\sqrt{p^2}) \\epsilon _{\\mu \\lambda \
Maxwell Chern Simons Theory in a Geometric Representation
Leal, L C
2001-01-01
We quantize the Maxwell Chern Simons theory in a geometric representation that generalizes the Abelian Loop Representation of Maxwell theory. We find that in the physical sector, the model can be seen as the theory of a massles scalar field with a topological interaction that enforces the wave functional to be multivalued. This feature allows to relate the Maxwell Chern Simons theory with the quantum mechanics of particles interacting through a Chern Simons field
W-Infinity Algebras from Noncommutative Chern-Simons Theory
Pinzul, A N
2003-01-01
We examine Chern-Simons theory written on a noncommutative plane with a `hole', and show that the algebra of observables is a nonlinear deformation of the $w_\\infty$ algebra. The deformation depends on the level (the coefficient in the Chern-Simons action), which was identified recently with the inverse filling fraction in the fractional quantum Hall effect.
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...
Kinetic derivation of generalized phase space Chern-Simons theory
Hayata, Tomoya
2016-01-01
We study a kinetic theory in $2d$ phase space when all abelian Berry curvatures are nonzero. We derive the complete form of the Poisson brackets, and calculate transports induced by Berry curvatures. Then we construct the low-energy effective theory to reproduce the transports. Such an effective theory is given by the Chern-Simons theory in $1+2d$ dimensions. Some implications of the Chern-Simons theory are also discussed.
Perturbative expansion of Chern-Simons theory
SAWON, Justin
2005-01-01
An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of an analogous finite-dimensional integral, we discuss this case in detail.
Level/rank Duality and Chern-Simons-Matter Theories
Hsin, Po-Shen
2016-01-01
We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin$_c$ connections and the metric). The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields. In order for the duality to be valid we must add finite counterterms depending on these background fields. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.
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.
Chern-Simons theory in SIM(1) superspace
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Vohanka, Jiri [Masaryk University, Department of Theoretical Physics and Astrophysics, Brno (Czech Republic); Faizal, Mir [University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada)
2015-12-15
In this paper,wewill analyze a three-dimensional supersymmetric Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern-Simons theory with N = 1 supersymmetry will break down to N = 1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern-Simons action using SIM(1) projections ofN = 1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern-Simons action using these SIM(1) superfields. Furthermore, we will analyze the gauge symmetry of this Chern-Simons theory. This is the first time that a Chern-Simons theory with N = 1/2 supersymmetry will be constructed on a manifold without a boundary. (orig.)
Frobenius-Chern-Simons gauge theory
Bonezzi, Roberto; Sezgin, Ergin; Sundell, Per
2016-01-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as...
Frobenius-Chern-Simons gauge theory
Bonezzi, Roberto; Boulanger, Nicolas; Sezgin, Ergin; Sundell, Per
2017-02-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H , we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an {{{Z}}2} -graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in (arXiv:1505.04957) as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the {{{Z}}2} -grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H\\otimes F . We give a new model of this type based on a twisting of {C}≤ft[{{{Z}}2}× {{{Z}}4}\\right] , which leads to self-dual complexified gauge fields on AdS 4. If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of {C}[{{({{{Z}}2})}3}] that yields the original model, and the Clifford algebra C{{\\ell}2n} which provides an FCS formulation of the bosonic Konstein-Vasiliev model with gauge algebra hu≤ft({{4}n-1},0\\right) .
String theory duals of Lifshitz-Chern-Simons gauge theories
Balasubramanian, Koushik
2011-01-01
We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern-Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic dictionary, we identify the bulk fields that are dual to these deformations. The geometry describing the groundstate of the non-Abelian LCS gauge theory realized here ends smoothly in the infrared region. This is a signal for confinement in the dual field theory, suggesting that non-Abelian Lifshitz gauge theories can indeed flow to strongly-coupled confining theories.
Abelian Chern-Simons theory, Stokes' Theorem, and generalized connections
Sahlmannn, Hanno
2010-01-01
Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes' Theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions. The abelian theory considered in the present article is test case for our method. It can also be applied to the non-abelian theory. Results for that case will be reported elsewhere.
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
Topological boundary conditions in abelian Chern-Simons theory
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Kapustin, Anton [California Institute of Technology, Pasadena, CA 91125 (United States); Saulina, Natalia, E-mail: saulina@theory.caltech.ed [Perimeter Institute, Waterloo (Canada)
2011-04-21
We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern-Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.
New Phase Transitions in Chern-Simons Matter Theory
Zahabi, Ali
2015-01-01
Applying the machinery of random matrix theory and Toeplitz determinants we study the level $k$, $U(N)$ Chern-Simons theory coupled with fundamental matter on $S^2\\times S^1$ at finite temperature $T$. This theory admits a discrete matrix integral representation, i.e. a unitary discrete matrix model of two-dimensional Yang-Mills theory. In this study, the partition function and phase structure of the Chern-Simons matter theory in an special case with Gross-Witten-Wadia potential are investigated. We obtain an exact expression for the partition function of the Chern-Simons matter theory as a function of $k,N,T$, for finite values and in the asymptotic regime. In the Gross-Witten-Wadia case, we show that ratio of the Chern-Simons matter partition function and the continuous two-dimensional Yang-Mills partition function, in the asymptotic regime, is the Tracy-Widom distribution. Consequently, using the explicit results for free energy of the theory, new second order and third-order phase transitions are observed...
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1998-01-01
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 slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order ...
Topological entanglement negativity in Chern-Simons theories
Wen, Xueda; Ryu, Shinsei
2016-01-01
We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work (X. Wen, S. Matsuura and S. Ryu, arXiv:1603.08534).
4-d semistrict higher Chern-Simons theory I
Soncini, Emanuele
2014-01-01
We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form. We analyze the gauge invariance of the theory and show that action is invariant under a higher gauge transformation up to a higher winding number. We find that the theory admits two seemingly inequivalent canonical quantizations. The first is manifestly topological, it does not require a choice of any additional structure on the spacial 3-fold. The second, more akin to that of ordinary Chern-Simons theory, involves fixing a CR structure on the latter. Correspondingly, we obtain two sets of semistrict higher WZW Ward identities and we find the explicit expressions of two higher versions of the WZW action. We speculate that the model could be used to define 2-knot invariants of 4-folds.
Topological entanglement negativity in Chern-Simons theories
Wen, Xueda; Chang, Po-Yao; Ryu, Shinsei
2016-09-01
We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work [35].
Schwinger-Dyson functional in Chern-Simons theory
Guadagnini, Enore
2016-01-01
In perturbative SU(N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that the renormalized Schwinger-Dyson functional is related with the generating functional of the correlation functions of the gauge connections by some kind of duality transformation.
Schwinger-Dyson functional in Chern-Simons theory
Guadagnini, E.
2016-11-01
In perturbative SU (N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that the renormalized Schwinger-Dyson functional is related with the generating functional of the correlation functions of the gauge connections by some kind of duality transformation.
Combinatorial quantization of the Hamiltonian Chern-Simons theory, 2
Alekseev, A Yu; Schomerus, V; Grosse, H; Schomerus, V
1994-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \\cite{AGS}. 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 mathe- matically 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 \\omega (``integration''). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly \\cite{FoRo}, 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 Verl...
Higher-spin Chern-Simons theories in odd dimensions
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Engquist, Johan [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: j.engquist@phys.uu.nl; Hohm, Olaf [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: o.hohm@phys.uu.nl
2007-12-10
We construct consistent bosonic higher-spin gauge theories in odd dimensions D>3 based on Chern-Simons forms. The gauge groups are infinite-dimensional higher-spin extensions of the anti-de Sitter groups SO(D-1,2). We propose an invariant tensor on these algebras, which is required for the definition of the Chern-Simons action. The latter contains the purely gravitational Chern-Simons theories constructed by Chamseddine, and so the entire theory describes a consistent coupling of higher-spin fields to a particular form of Lovelock gravity. It contains topological as well as non-topological phases. Focusing on D=5 we consider as an example for the latter an AdS{sub 4}xS{sup 1} Kaluza-Klein background. By solving the higher-spin torsion constraints in the case of a spin-3 field, we verify explicitly that the equations of motion reduce in the linearization to the compensator form of the Fronsdal equations on AdS{sub 4}.
Topics In Gauge Theory (effective Action, Quantum Electrodynamics, Chern Simons)
Hall, T M
1998-01-01
This dissertation will present studies in three distinct areas of gauge theories. In Chern-Simons theories, the fate of the quantized Chern-Simons coupling constant upon renormalization of the theory is investigated. We find the Chern-Simons coupling constant remains quantized in the presence of residual non-abelian gauge symmetry. A two-flavor model of fermions is studied to determine the extent at which the vacuum condensate is locally proportional to the magnetic field. We find the proportionality is local in the limit of large flux. Using resolvent techniques, we find the exact effective action in a single pulsed electric background gauge field $E\\sb1$(t) = Esech $\\sp2$($t\\over r$). We derive the zero and first order derivative expansion for this electric field and compare with our exact results. Dispersion relations between the real and imaginary parts of the exact effective action are derived. In a uniform semi-classical approximation, we find the exact effective action for a spatially homogeneous backg...
Chern-Simons theory, Stokes' Theorem, and the Duflo map
Sahlmann, Hanno
2011-01-01
We consider a novel derivation of the expectation values of holonomies in Chern-Simons theory, based on Stokes' Theorem and the functional properties of the Chern-Simons action. It involves replacing the connection by certain functional derivatives under the path integral integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity.
Entanglement from Topology in Chern-Simons Theory
Salton, Grant; Walter, Michael
2016-01-01
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 3-manifolds with a fixed number of torus boundaries in both abelian U(1) and non-abelian SO(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...
Link Invariants from Classical Chern-Simons Theory
Leal, L C
2002-01-01
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present this expressions in a manifestly diffeomorphism-invariant form, we introduce a set of differential forms associated with submanifolds in Euclidean three-space that allow us to write the link invariants as a kind of surface-dependent diffeomorphism-invariants that present certain Abelian gauge symmetry.
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.
Extended higher cup-product Chern-Simons theories
Fiorenza, Domenico; Schreiber, Urs
2013-01-01
It is well known that the proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors is given on gauge equivalence classes of fields by the fiber integration of the cup product square of classes in degree-(2k+2) differential cohomology. We first refine this statement from gauge equivalence classes to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String^c-2-connections appearing in quantum-corrected 11-dimensional supergravity and M-branes. We discuss aspects of the off-shell extended geometric pre-quantization (in the sense of extended or multi-tiered QFT) of these theories, where there is a prequantum circle k-bundle (equivalently: (k-1)-bundle gerbe) in each codimension k. Examples we find include moduli stacks for differential T-du...
Extended higher cup-product Chern-Simons theories
Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs
2013-12-01
The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k+2) differential cohomology. We first refine this statement from the moduli space to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String-2-connections appearing in quantum-corrected 11-dimensional supergravity and M-branes. We discuss aspects of the off-shell extended geometric prequantization (in the sense of extended or multi-tiered QFT) of these theories, where there is a prequantum U(1)-k-bundle (equivalently: a U(1)-(k - 1)-bundle gerbe) in each codimension k. Examples we find include moduli stacks for differential T-duality structures as well as the anomaly line bundles of higher electric/magnetic charges, such as the 5-brane charges appearing in heterotic supergravity, appearing as line bundles with connection on the smooth higher moduli stacks of field configurations.
L∞-algebra models and higher Chern-Simons theories
Ritter, Patricia; Sämann, Christian
2016-10-01
We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L∞-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie p-algebra extensions of 𝔰𝔬(p + 2). Finally, we study a number of L∞-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
Z Extremization in Chiral-Like Chern Simons Theories
Amariti, Antonio
2011-01-01
We study the localized free energy on S^3 of three-dimensional N=2 Chern-Simons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard saddle point approximation for large N. We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.
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.
Deformation of surfaces, integrable systems, and Chern-Simons theory
Martina, L.; Myrzakul, Kur.; Myrzakulov, R.; Soliani, G.
2001-03-01
A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via the reduction of the gauge connection in Hermitian symmetric spaces. In this article we show that the methods developed in studying classical non-Abelian pure Chern-Simons actions can be naturally implemented by means of a geometrical interpretation of such systems. The Chern-Simons equation of motion turns out to be related to time evolving two-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss-Mainardi-Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed.
Dynamical Chern-Simons Theory in the Brillouin Zone
Lian, Biao; Vafa, Farzan; Zhang, Shou-Cheng
2016-01-01
Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a dynamical fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.
Quantum modularity and complex Chern-Simons theory
Dimofte, Tudor
2015-01-01
The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of the knot complement and a geometric solution to the gluing equations) and a complex root of unity $\\zeta$. We prove that the coefficients of our series lie in the trace field of the knot, adjoined a complex root of unity. We conjecture that our series are those that appear in the Quantum Modularity Conjecture and confirm that they match the numerical asymptotics of the Kashaev invariant (at various roots of unity) computed by Zagier and the first author. Our construction is motivated by the analysis of singular limits in Chern-Simons theory with gauge group $SL(2,C)$ at fixed level $k$, where $\\zeta^k=1$.
Fermionic impurities in Chern-Simons-matter theories
Benincasa, Paolo; Ramallo, Alfonso V.
2012-02-01
We study the addition of quantum fermionic impurities to the mathcal{N} = 6 super-symmetric Chern-Simons-matter theories in 2 + 1 spacetime dimensions. The impurities are introduced by means of Wilson loops in the antisymmetric representation of the gauge group. In a holographic setup, the system is represented by considering D6-branes probing the AdS 4 × mathbb{C}mathbb{P} 3 background of type IIA supergravity. We study the thermodynamic properties of the system and show how a Kondo lattice model with holographic dimers can be constructed. By computing the Kaluza-Klein fluctuation modes of the probe brane we determine the complete spectrum of dimensions of the impurity operators. A very rich structure is found, depending both on the Kaluza-Klein quantum numbers and on the filling fraction of the impurities.
Fermionic impurities in Chern-Simons-matter theories
Benincasa, Paolo
2011-01-01
We study the addition of quantum fermionic impurities to the N=6 supersymmetric Chern-Simons-matter theories in 2+1 spacetime dimensions. The impurities are introduced by means of Wilson loops in the antisymmetric representation of the gauge group. In a holographic setup, the system is represented by considering D6-branes probing the AdS_4 x CP^3 background of type IIA supergravity. We study the thermodynamic properties of the system and show how a Kondo lattice model with holographic dimers can be constructed. By computing the Kaluza-Klein fluctuation modes of the probe brane we determine the complete spectrum of dimensions of the impurity operators. A very rich structure is found, depending both on the Kaluza-Klein quantum numbers and on the filling fraction of the impurities.
Superconformal Chern-Simons-matter theories in N =4 superspace
Kuzenko, Sergei M.; Samsonov, Igor B.
2015-11-01
In three dimensions, every known N =4 supermultiplet has an off-shell completion. However, there is no off-shell N =4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N =4 superfield realizations for the equations of motion which correspond to various N =4 and N =6 superconformal CS theories, including the Gaiotto-Witten theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. These superfield realizations demonstrate that the superconformal CS theories with N ≥4 (except for the Gaiotto-Witten theory) require a reducible long N =4 vector multiplet, from which the standard left and right N =4 vector multiplets are obtained by constraining the field strength to be either self-dual or antiself-dual. Such a long multiplet naturally originates upon reduction of any off-shell N >4 vector multiplet to N =4 superspace. For the long N =4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N =4 supergravity-matter systems in arXiv:1101.4013. We also couple N =4 superconformal CS theories to N =4 conformal supergravity.
Eta-invariants and anomalies in U(1)-Chern-Simons theory
Jeffrey, Lisa
2010-01-01
This paper studies U(1)-Chern-Simons theory and its relation to a construction of Chris Beasley and Edward Witten. The natural geometric setup here is that of a three-manifold with a Seifert structure. Based on a suggestion of Edward Witten we are led to study the stationary phase approximation of the path integral for U(1)-Chern-Simons theory after one of the three components of the gauge field is decoupled. This gives an alternative formulation of the partition function for U(1)-Chern-Simons theory that is conjecturally equivalent to the usual U(1)-Chern-Simons theory. The goal of this paper is to establish this conjectural equivalence rigorously through appropriate regularization techniques. This approach leads to some rather surprising results and opens the door to studying hypoelliptic operators and their associated eta invariants in a new light.
Wave function of the Universe and Chern-Simons Perturbation Theory
Soo, C P
2002-01-01
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variable as the partition function of a Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wave function 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.
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1999-06-01
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.
Embedded graph invariants in Chern-Simons theory
Major, S 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 slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some 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. Though, 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.
Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
Yokoyama, Shuichi
2016-01-01
A general class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. We confirm that the subleading correction in the free energy correctly reproduces the one obtained by expanding the past exact result in the case of pure Chern-Simons theory.
Explicit connection between conformal field theory and 2+1 Chern-Simons theory
Cabra, D C
1995-01-01
We give explicit field theoretical representations for the observables in the transverse lattice version of 2+1 dimensional Chern-Simons theory in terms of gauge invariant composites of 2D WZW fields. Wilson loop correlators are evaluated in the path integral framework using decoupling techniques, thus confirming previous results.
Chern-Simons theory on a lattice and a new description of 3-manifolds invariants
Buffenoir, E
1995-01-01
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice gauge theory based on a quantum group. After a generalization of the formalism of q-deformed gauge theory to the case of root of unity, we compute explicitely the correlation functions associated to Wilson loops (and more generally to graphs) on a surface with punctures, which are the interesting quantity in the study of moduli space. We then give a new description of Chern-Simons three manifolds invariants based on a description in terms of the mapping class group of a surface. At last we introduce a three dimensional lattice gauge theory based on a quantum group which is a lattice regularization of Chern-Simons theory.
Batalin-Tyutin quantization of the Chern-Simons-Proca theory
Park, E B; Park, Y J; Kim, Y; Kim, W T; Park, Ei Byung; Kim, Yong Wan; Park, Young Jai; Kim, Yongduk; Kim, Won Tae
1995-01-01
We quantize the Chern-Simons-Proca theory in three dimensions by using the Batalin-Tyutin Hamiltonian method, which systematically embeds second class constraint system into first class by introducing new fields in the extended phase space. As results, we obtain simultaneously the St\\"uckelberg scalar term, which is needed to cancel the gauge anomaly due to the mass term, and the new type of Wess-Zumino action, which is irrelevant to the gauge symmetry. We also investigate the infrared property of the Chern-Simons-Proca theory by using the Batalin-Tyutin formalism comparing with the symplectic formalism. As a result, we observe that the resulting theory is precisely the gauge invariant Chern-Simons-Proca quantum mechanical version of this theory.
Chern-Simons theory for frustrated quantum magnets
Kumar, Krishna; Fradkin, Eduardo
2013-03-01
We study the problem of frustrated quantum magnets by mapping models with Heisenberg spins, which are hard-core bosons, onto a problem of fermions coupled to a Chern-Simons gauge field. Similar methods have been used successfully in the case of unfrustrated systems like the square lattice. However, in the case of frustrated systems there always exists some arbitrariness in defining the problem. At the mean-field level these issues can be over looked but the effects of fluctuations, which are generally strong in these systems, are expected to alter the mean-field physics. We discuss the difficulties involved in setting up this problem on a triangular or kagome lattice and some approaches to tackle these issues. We study the effects of fluctuations in these systems and the possibility of spin-liquid type phases.
Quantum Hairs and Isolated Horizon Entropy from Chern-Simons Theory
Majhi, Abhishek
2013-01-01
We articulate the fact that the loop quantum gravity description of the quantum states of black hole horizons, modeled as Quantum Isolated Horizons (QIHs), is completely characterized in terms of two independent integer-valued quantum 'hairs', viz,. the coupling constant of the quantum SU(2) Chern Simons theory describing QIH dynamics, and the number of punctures produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the Chern Simons fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this Chern-Simons theory, using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semi-classical input from general relativity vis-a-vis the functional dependence of the IH mass on its area, or indeed, without having to restrict to any special clas...
Gauge and supersymmetry invariance of N = 2 boundary Chern-Simons theory
Faizal, Mir; Luo, Yuan; Smith, Douglas J.; Tan, Meng-Chwan; Zhao, Qin
2017-01-01
In this paper, we study the restoration of gauge symmetry and up to half the supersymmetry (N = (2 , 0) or N = (1 , 1) in two dimensions) for N = 2 non-Abelian Chern-Simons theories in the presence of a boundary. We describe the boundary action which is a supersymmetric WZW model coupled to the bulk Chern-Simons theory. Unlike the N = 1 case, higher supersymmetry (N = (2 , 0)) will endow the group manifold of the WZW model with a complex structure. Therefore, the N = (2 , 0) WZW model in our paper is constructed via a coset space Gc / G, where G is the same as the gauge group in the Chern-Simons action.
Remarks on the solutions of the Maxwell- Chern-Simons theories
Németh, Z A
1998-01-01
The large distance behavior of the Maxwell- Chern-Simons (MCS) equations is analyzed, and it is found that the pure Chern-Simons limit, (when the Maxwell term is dropped from the equations), does not describe the large distance limit of the MCS model. This necessitates the solution of the original problem. The MCS gauge theory coupled to a nonrelativistic matter field, (governed by the gauged non-linear Schrödinger equation), is studied. It turns out, that there are no regular self-dual solutions as in the pure Chern-Simons case, but the model admits interesting, though singular self-dual solutions. The properties of these solutions, and their large distance limits are analyzed.
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.)
Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories
Bonora, Loriano; Goncalves, Antonio E
2016-01-01
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 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.
Chern-Simons Supersymmetric Branes
Mora, P
2001-01-01
In this paper we continue the study of the model proposed in the previous paper hep-th/0002077. The model consist of a system of extended objects of diverse dimensionalities, with or without boundaries, with actions of the Chern-Simons form for a supergroup. We also discuss possible connections with Superstring/M-theory.
Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity
Hartong, Jelle; Lei, Yang; Obers, Niels A.
2016-09-01
We show that certain three-dimensional Hořava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various nonrelativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schrödinger algebras each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Hořava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Hořava-Lifshitz gravity with a local U (1 ) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schrödinger algebra containing three extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of nonprojectable conformal Hořava-Lifshitz gravity that we refer to as Chern-Simons Schrödinger gravity. This theory has a z =2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.
Quaternion based generalization of Chern-Simons theories in arbitrary dimensions
D'Adda, Alessandro; Shimode, Naoki; Tsukioka, Takuya
2016-01-01
A generalization of Chern-Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree. The quaternion algebra structure of this formulation is shown to be equivalent to a three Z(2)-gradings structure, thus clarifying the quaternion role in a previous formulation.
Knots in $SU\\left(M|N\\right) $ Chern-Simons Field Theory
Liu, Xin
2010-01-01
Knots in the Chern-Simons field theory with Lie super gauge group $SU\\left(M|N\\right) $ are studied, and the $% S_{L}\\left(\\alpha,\\beta,z\\right) $ polynomial invariant with skein relations are obtained under the fundamental representation of $\\mathfrak{su}\\left(M|N\\right) $.
Canonical quantization of the WZW model with defects and Chern-Simons theory
DEFF Research Database (Denmark)
Sarkissian, Gor
2010-01-01
We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with $N$ defects on cylinder and phase space of Chern-Simons theory on annulus times $R$ with $N$ Wilson lines, and between phase space of WZW mo...
Dimensionally compactified Chern-Simon theory in 5D as a gravitation theory in 4D
Morales, Ivan; Oporto, Zui; Piguet, Olivier
2016-01-01
We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) -- the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.
SL(2,C) Chern-Simons Theory and Quantum Gravity with a Cosmological Constant
Haggard, Hal; Han, Muxin; Kaminski, Wojciech; Riello, Aldo
2015-04-01
We show a relation between 4-dimensional quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in 3-dimensions with knotted graph defects. In particular, we study the expectation value of a non-planar Wilson graph operator in SL(2,C) Chern-Simons theory on S3. We analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. We find that a class of flat connections in the graph complement manifold are in correspondence with the geometries of constant curvature 4-simplices. We show that the asymptotic behavior of the amplitude contains an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. This work was supported by the U.S. National Science Foundation, the European Marie Curie actions, and the Perimeter Institute.
Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Based on the decomposition theory of the U(1) gauge potential, the inner structure of the statistical gauge potential in the Chern-Simons-Ginzburg-Landau (CSGL) theory is studied. We give a new creation mechanism of the statistical gauge potential. Furthermore, making use of the φ-mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.
Holographic Chern-Simons Defects
Fujita, Mitsutoshi; Meyer, Rene; 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 two-dimensional QCD.
Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-11
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Symmetry algebras in Chern-Simons theories with boundary: canonical approach
Energy Technology Data Exchange (ETDEWEB)
Park, Mu-In. E-mail: mipark@physics.sogang.ac.kr
1999-04-05
I consider the classical Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary within Dirac's canonical method and Noether's procedure. It is shown that the usual (bulk) Gauss law constraint becomes a second-class constraint because of the boundary effect. From this fact, the Dirac bracket can be constructed explicitly without introducing additional gauge conditions and the classical Kac-Moody and Virasoro algebras are obtained within the usual Dirac method. The equivalence to the symplectic reduction method is presented and the connection to the Banados' work is clarified. Also the generalization to the Yang-Mills-Chern-Simons theory is considered where the diffeomorphism symmetry is broken by the (three-dimensional) Yang-Mills term. In this case, the same Kac-Moody algebras are obtained although the two theories are sharply different in the canonical structures. Both models realize the holography principle explicitly and the pure CS theory reveals the correspondence of the Chern-Simons theory with boundary/conformal field theory, which is more fundamental and generalizes the conjectured anti-de Sitter/conformal field theory correspondence.
Split Chern-Simons theory in the BV-BFV formalism
Cattaneo, Alberto; Wernli, Konstantin
2015-01-01
The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to perform perturbative quantisation of Lagrangian field theories on manifolds with boundary, and present a special case of Chern-Simons theory as a new example.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
Light States in Chern-Simons Theory Coupled to Fundamental Matter
Banerjee, Shamik; Maltz, Jonathan; Shenker, Stephen H
2012-01-01
Motivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to matter fields in the fundamental representation on various spatial manifolds. On the spatial torus T^2, we find light states at small `t Hooft coupling \\lambda=N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order \\sqrt {\\lambda}/N and in the critical scalar theory and the free fermion theory they are of order \\lambda/N. The entropy of these states grows like N Log(k). We briefly consider spatial surfaces of higher genus. Based on results from pure Chern-Simons theory, it appears that there are light states with entropy that grows even faster, like N^2 Log(k). This is consistent with the log of the partition function on the three sphere S^3, which also behaves like N^2 Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.
Cabra, D C; Rossini, L; Schaposnik, F A; Fradkin, Eduardo
1995-01-01
We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be {\\it at most} an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.
Torsion as a Gauge Field in a Lorentz-Chern-Simons Theory
del Pino, Simón
2016-01-01
We explore a model of gravity that arises from the consideration of the Chern-Simons form in 2+1 dimensions for a spin connection with a contorsion described by a scalar and a vector field. The effective Lagrangian presents a local Weyl symmetry allowing us to gauge the scalar field to a constant value. From a gauge field theory perspective, it is shown that the vector part of the torsion (related to its trace) is a gauge field for the Weyl group, which allows the interpretation of the torsion as an electromagnetic field. In the gauge of constant scalar field we obtain Chiral Gravity coupled to a Chern-Simons-Proca theory for the vector field, that at the level of equations of motion is equivalent to Topologically Massive Electrodynamics minimally coupled to Chiral Gravity. Electrodynamics and gravity appear here unified as geometrical features of a Riemann-Cartan manifold.
Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm
Dimofte, Tudor Dan
In this thesis, we consider two main subjects: the refined BPS invariants of Calabi-Yau threefolds, and three-dimensional Chern-Simons theory with complex gauge group. We study the wall-crossing behavior of refined BPS invariants using a variety of techniques, including a four-dimensional supergravity analysis, statistical-mechanical melting crystal models, and relations to new mathematical invariants. We conjecture an equivalence between refined invariants and the motivic Donaldson-Thomas invariants of Kontsevich and Soibelman. We then consider perturbative Chern-Simons theory with complex gauge group, combining traditional and novel approaches to the theory (including a new state integral model) to obtain exact results for perturbative partition functions. We thus obtain a new class of topological invariants, which are not of finite type, defined in the background of genuinely nonabelian flat connections. The two main topics, BPS invariants and Chern-Simons theory, are connected at both a formal and (we believe) deeper conceptual level by the striking central role that the quantum dilogarithm function plays in each.
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Torsten
2009-05-13
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.)
Exact Chern-Simons / Topological String duality
Krefl, Daniel
2015-01-01
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N as well. In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extend to refined Chern-Simons with orthogonal groups.
F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
Morita, Takeshi
2011-01-01
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partition functions computed via localization. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.
Blázquez-Salcedo, Jose Luis; Navarro-Lérida, Francisco; Radu, Eugen
2016-01-01
We consider rotating black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and a generic value of the Chern-Simons coupling constant $\\lambda$. Using both analytical and numerical techniques, we focus on cohomogeneity-1 configurations, with two equal-magnitude angular momenta, which approach at infinity a globally AdS background. We find that the generic solutions share a number of basic properties with the known Cvetic, L\\"u and Pope black holes which have $\\lambda=1$. New features occur as well, for example, when the Chern-Simons coupling constant exceeds a critical value, the solutions are no longer uniquely determined by their global charges. Moreover, the black holes possess radial excitations which can be labelled by the node number of the magnetic gauge potential function. Solutions with small values of $\\lambda$ possess other distinct features. For instance, the extremal black holes there form two disconnected branches, while not all near-h...
Chern-Simons theory for Heisenberg spins on the Kagome Lattice
Kumar, Krishna; Sun, Kai; Fradkin, Eduardo
2015-03-01
We study the problem of Heisenberg spins on the frustrated Kagome lattice using a 2D Jordan-Wigner transformation that maps the spins (hard-core bosons) onto a system of (interacting) fermions coupled to a Chern-Simons gauge field. This mapping requires us to define a discretized version of the Chern-Simons term on the lattice. Using a recently developed result on how to define Chern-Simons theories on a class of planar lattices, we can consistently study spin models beyond the mean-field level and include the effects of fluctuations, which are generally strong in frustrated systems. Here, we apply these results to study magnetization plateau type states on the Kagome lattice in the regime of XY anisotropy. We find that the 1/3 and 2/3 magnetization plateaus are chiral spin liquid states equivalent to a primary Laughlin fractional quantum Hall state of bosons with (spin) Hall conductivity 1/2 1/4 π and semionic excitations. The 5/9 plateau is a chiral spin liquid equivalent to the first Jain descendant. We also consider the spin-1/2 Heisenberg model on the Kagome lattice with a chirality-breaking term on the triangular plaquettes. This situation also leads to a primary Laughlin bosonic fractional quantum Hall type state with filling fraction 1 / 2 .
Evolution of Nielsen-Olesen's String from Chern-Simons Field Theory
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; SHI Xu-Guang
2007-01-01
We study the topology of Nielsen-Olesen's local field theory of single dual string. Based on the Chern-Simons field theory in three dimensons, we find many strings that can form world sheets in four dimensions. These strings have important relation to the zero point of the complex scalar field. These world sheets of strings can be expressed by the topological invariant number, Hopf index, and Brower degree. Nambu-Goto's action is obtained from the Nielsen's action definitely by using o-mapping theory.
Instability of Chern-Simons Theory with Fermions at Large N
Zhang, Chen
2016-01-01
We study the (in)stability around the dynamical gap solution of the $U(N)$ Chern-Simons gauge theory with fundamental fermions (massless or massive) coupled in $D=3$ at large $N$. Explicit analyses on both the Auxiliary-Field (AF) and the Cornwall-Jackiw-Tomboulis (CJT) effective potentials are given. In both approaches we manage to analytically identify the saddle-point instability around the gap solution. We also give a comparison with the QCD-like theories. This study can help understanding the scale symmetry breaking picture of this theory.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Di Bartolo, Cayetano; Leal, Lorenzo
2012-01-01
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.
Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
Marino, Marcos
2011-01-01
In these lectures I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N^{3/2} behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals, and large N techniques in matrix models
Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories
Ouyang, Hao; Wu, Jun-Bao; Zhang, Jia-ju
2016-02-01
We show that generic three-dimensional N = 2 quiver super Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops happens for special values of the parameters.
A geometric discretisation scheme applied to the Abelian Chern-Simons theory
Sen, S; Sexton, J C; Adams, D H; Sen, Samik; Sen, Siddhartha; Sexton, James C.; Adams, David H
2000-01-01
We give a detailed general description of a recent geometrical discretisation scheme and illustrate, by explicit numerical calculation, the scheme's ability to capture topological features. The scheme is applied to the Abelian Chern-Simons theory and leads, after a necessary field doubling, to an expression for the discrete partition function in terms of untwisted Reidemeister torsion and of various triangulation dependent factors. The discrete partition function is evaluated computationally for various triangulations of $S^3$ and of lens spaces. The results confirm that the discretisation scheme is triangulation independent and coincides with the continuum partition function
Observables, skein relations, and tetrahedra in Chern-Simons gauge theory
Martin, Stephen P.
1990-07-01
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.
The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Gammelgaard, Niels Leth
We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order operator on the quantum spaces. Projective flatness follows...... if the Kähler structures do not admit holomorphic vector fields. Following Witten, we define a complex variant of the Hitchin connection on the bundle of prequantum spaces. The curvature is essentially unchanged, so projective flatness holds in the same cases. Finally, the results are applied to quantum Chern......-Simons theory, both for compact and complex gauge groups....
Chern-Simons-Higgs theory with visible and hidden sectors and its N = 2 SUSY extension
Arias, Paola; Ireson, Edwin; Schaposnik, Fidel A.; Tallarita, Gianni
2015-10-01
We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors. We first consider the case in which the two sectors are connected through a BF-like gauge mixing term with no explicit interaction between the two scalars. Since first order Bogomolny equations do not exist in this case, we derive the second order field equations. We then proceed to an N = 2 supersymmetric extension including a Higgs portal mixing among the visible and hidden charged scalars. As expected, Bogomolny equations do exist in this case and we study their string-like solutions numerically.
Transgression forms as source for topological gravity and Chern-Simons-Higgs theories
Valdivia, Omar
2014-01-01
Two main gauge invariant off-shell models are studied in this Thesis. I) Poincare-invariant topological gravity in even dimensions is formulated as a transgression field theory whose gauge connections are associated to linear and nonlinear realizations of the Poincare group ISO(d-1,1). The resulting theory is a gauged Wess-Zumino-Witten model whereby the transition functions relating gauge fields belong to the coset ISO(d-1,1)/SO(d-1,1). The supersymmetric extension leads to topological supergravity in two dimensions starting from a transgression field theory for the super-Poincare group in three dimensions. The construction is extended to a three-dimensional Chern-Simons theory of gravity invariant under the Maxwell algebra, where the corresponding Maxwell gauged Wess-Zumino-Witten model is obtained. II) dimensional reduction of Chern-Simons theories with arbitrary gauge group in a formalism based on equivariant principal bundles is considered. For the classical gauge groups the relations between equivariant...
Mutual Chern-Simons theory and its applications in condensed matter physics
Institute of Scientific and Technical Information of China (English)
KOU Su-peng; WENG Zheng-yu; WEN Xiao-gang
2007-01-01
In this paper, the mutual Chern-Simons (MCS) theory is introduced as a new kind of topological gauge theory in 2+1 dimensions. We use the MCS theory in gapped phase as an effective low energy theory to describe the Z2 topological order of the Kitaev-Wen model. Our results show that the MCS theory can catch the key properties for the Z2 topological order. On the other hand, we use the MCS theory as an effective model to deal with the doped Mott insulator. Based on the phase string theory, the t-J model reduces to a MCS theory for spinons and holons. The related physics in high Tc cuprates is discussed.
Duality, Quantum Vortices and Anyons in Maxwell-Chern-Simons-Higgs Theories
Marino, E C
1993-01-01
The order-disorder duality structure is exploited in order to obtain a quantum description of anyons and vortices in: a) the Maxwell theory; b) the Abelian Higgs Model; c) the Maxwell-Chern-Simons theory; d) the Maxwell-Chern-Simons-Higgs theory. A careful construction of a charge bearing order operator($\\sigma$) and a magnetic flux bearing disorder operator (vortex operator) ($\\mu$) is performed, paying attention to the necessary requirements for locality. An anyon operator is obtained as the product $\\varphi=\\sigma\\mu$. A detailed and comprehensive study of the euclidean correlation functions of $\\sigma$, $\\mu$ and $\\varphi$ is carried on in the four theories above. The exact correlation functions are obtained in cases $\\underline{a}$ and $\\underline{c}$. The large distance behavior of them is obtained in cases $\\underline{b}$ and $\\underline{d}$. The study of these correlation functions allows one to draw conclusions about the condensation of charge and magnetic flux, establishing thereby an analogy with t...
String Theory Origin of Dyonic N=8 Supergravity and Its Chern-Simons Duals.
Guarino, Adolfo; Jafferis, Daniel L; Varela, Oscar
2015-08-28
We clarify the higher-dimensional origin of a class of dyonic gaugings of D=4 N=8 supergravity recently discovered, when the gauge group is chosen to be ISO(7). This dyonically gauged maximal supergravity arises from consistent truncation of massive IIA supergravity on S^6, and its magnetic coupling constant descends directly from the Romans mass. The critical points of the supergravity uplift to new four-dimensional anti-de Sitter space (AdS4) massive type IIA vacua. We identify the corresponding three-dimensional conformal field theory (CFT3) duals as super-Chern-Simons-matter theories with simple gauge group SU(N) and level k given by the Romans mass. In particular, we find a critical point that uplifts to the first explicit N=2 AdS4 massive IIA background. We compute its free energy and that of the candidate dual Chern-Simons theory by localization to a solvable matrix model, and find perfect agreement. This provides the first AdS4/CFT3 precision match in massive type IIA string theory.
The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
Tong, David
2015-01-01
In d=2+1 dimensions, there exist gauge theories which are supersymmetric but non-relativistic. We solve the simplest U(1) gauge theory in this class and show that the low-energy physics is that of the fractional quantum Hall effect, with ground states given by the Laughlin wavefunctions. We do this by quantising the vortices and relating them to the quantum Hall matrix model. We further construct coherent state representations of the excitations of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.
Chern-Simons theory with finite gauge group
Freed, Daniel S.; Quinn, Frank
1993-10-01
We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the “Verlinde formula”. The careful development may serve as a model for dealing with similar issues in more complicated cases.
Heavy operators in superconformal Chern-Simons theory
de Mello Koch, Robert; Kreyfelt, Rocky; Smith, Stephanie
2014-12-01
We study the anomalous dimensions for scalar operators in Aharony-Bergman-Jafferis-Maldacena theory in the S U (2 ) sector. The operators we consider have a classical dimension that grows as N in the large N limit. Consequently, the large N limit is not captured by summing planar diagrams—nonplanar contributions have to be included. We find that the mixing matrix at two-loop order is diagonalized using a double coset ansatz, reducing it to the Hamiltonian of a set of decoupled oscillators. The spectrum of anomalous dimensions, when interpreted in the dual gravity theory, shows that the energy of the fluctuations of the corresponding giant graviton is dependent on the size of the giant. The first subleading corrections to the large N limit are also considered. These subleading corrections to the dilatation operator do not commute with the leading terms, indicating that integrability may not survive beyond the large N limit.
Transgressions and Holographic Conformal Anomalies for Chern-Simons Gravities
Mora, Pablo
2010-01-01
I present two calculations of the holographic Weyl anomalies induced by Chern-Simons gravity theories alternative to the ones presented in the literature. The calculations presented here rest on the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, which automatically yields the boundary terms suitable to regularize the theory. The procedure followed here sheds light in the structure of Chern-Simons gravities and their regularization.
3d N = 1 Chern-Simons-matter theory and localization
Tsimpis, Dimitrios; Zhu, Yaodong
2016-10-01
We consider the most general, classically-conformal, three-dimensional N = 1 Chern-Simons-matter theory with global symmetry Sp (2) and gauge group U (N) × U (N). We show that the Lagrangian in the on-shell formulation of the theory admits one more free parameter as compared to the theory formulated in off-shell N = 1 superspace. The theory on T3 can be formally localized. We partially carry out the localization procedure for the theory on T3 with periodic boundary conditions. In particular we show that restricting to the saddle points with vanishing gauge connection gives a trivial contribution to the partition function, i.e. the bosonic and fermionic contributions exactly cancel each other.
Construction of novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories
Ouyang, Hao; Zhang, Jia-ju
2015-01-01
In this paper, we construct novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines in $\\mathcal N=2,3$ quiver super Chern-Simons-matter (CSM) theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\\mathcal N=4$ orbifold ABJM theory. There are several free complex parameters in the DT type BPS Wilson loops, and for Wilson loops in ABJM theory and $\\mathcal N=4$ orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and Gaiotto-Yin (GY) type Wilson loops are $Q$-exact with $Q$ being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the Wilson loops in matrix models if they are still BPS quantum mechanically.
Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity
Dijkgraaf, Robbert
2007-01-01
Motivated by the six dimensional formulation of Kodaira-Spencer theory for Calabi-Yau threefolds, we formulate a two dimensional version and argue that this is the relevant field theory for the target space of local topological B-model with a geometry based on a Riemann surface. We show that the Ward identities of this quantum theory is equivalent to recursion relations recently proposed by Eynard and Orantin to solve the topological B model. Our derivation provides a conceptual explanation of this link and reveals a hidden affine SL(2,R) symmetry. Moreover we argue that our results provide the strongest evidence yet of the existence of topological M theory in one higher dimension, which in this case can be closely related to SL(2,R)Chern-Simons formulation of three dimensional gravity.
Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
Dandekar, Yogesh; Minwalla, Shiraz
2014-01-01
An all orders formula for the $S$-matrix for 2 $\\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.
Induced spin from the ISO(2,1) gauge theory with the gravitational Chern-Simons term
Cho, J H; Cho, Jin Ho
1994-01-01
In the context of ISO(2,1) gauge theory, we consider (2+1)-dimensional gravity with the gravitational Chern-Simons term (CST). This formulation allows the `exact' solution for the system coupled to a massive point particle (which is not the case in the conventional Chern-Simons gravity). The solution exhibits locally trivial structure even with the CST, although still shows globally nontrivialness such as the conical space and the helical time structure. Since the solution is exact, we can say the CST induces spin even for noncritical case of \\s+\\al m\
Extension of the Chern-Simons Theory: Conservation Laws, Lagrange Structures, and Stability
Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.
2017-03-01
We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern-Simons operator. For the nth order theory of this type, we provide a covariant procedure for constructing n-parameter family of conservation laws associated with spatiotemporal symmetries. This family includes the canonical energy that is unbounded from below, whereas others conservation laws from the family can be bounded from below for certain combinations of the Lagrangian parameters, even though higher derivatives are present in the Lagrangian. We prove that any conserved quantity bounded from below is related with invariance of the theory with respect to the time translations and ensures the stability of the model.
Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity
Giusto, Stefano; Rosa, Dario
2012-01-01
We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be written as a BRST-commutator on a functional space containing the anti-fields of both the dynamical fields and the gravitational backgrounds. We derive from this result a Ward identity that determines the anti-holomorphic dependence of physical correlators.
Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity
Giusto, Stefano; Imbimbo, Camillo; Rosa, Dario
2012-10-01
We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be written as a BRST-commutator on a functional space containing the anti-fields of both the dynamical fields and the gravitational backgrounds. We derive from this result a Ward identity that determines the anti-holomorphic dependence of physical correlators.
Chern-Simons theory and Wilson loops in the Brillouin zone
Lian, Biao; Vafa, Cumrun; Vafa, Farzan; Zhang, Shou-Cheng
2017-03-01
Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3D) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the six-dimensional phase space, where the physical space defects play the role of topological D-branes.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, L; Rocek, M; Von Unge, R; Hadasz, Leszek; Lindstrom, Ulf; Rocek, Martin; Unge, Rikard von
2003-01-01
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 it is not possible to find the dynamics of the solitons using traditional moduli space techniques. To do better we have found exact time dependent one soliton solutions to the full equations of motion. They represent solitons moving in straight lines with constant velocity. Surprisingly we find that the set of allowed velocities is quantized! The allowed velocities are proportional to the square root of an integer. In the relativistic case we find the metric on the two soliton moduli space and using techinques developed in the nonrelativistic case we also find exact time dependent one-soliton solutions. Again the allowed velocities are quantized, though in a slightly more complicated fashion.
The sky is the limit: free boundary conditions in AdS$_3$ Chern-Simons theory
Apolo, Luis
2016-01-01
We test the effects of new diffeomorphism invariant boundary terms in SL(2,R)$\\times$SL(2,R) Chern-Simons theory. The gravitational interpretation corresponds to free AdS$_3$ boundary conditions, without restrictions on the boundary geometry. The boundary theory is the theory of a string in a target AdS$_3$. Its Virasoro conditions can eliminate ghosts. Generalisations to SL(N,R)$\\times$SL(N,R) higher spin theories and many other questions are still unexplored.
On superconformal Chern-Simons-matter theories in N=4 superspace
Kuzenko, Sergei M
2015-01-01
In three dimensions, every known N=4 supermultiplet has an off-shell completion. However, there is no off-shell N=4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N=4 superfield realisations for the equations of motion which correspond to various N=4 and N=6 superconformal CS theories, including the Gaiotto-Witten theory and the ABJM theory. These superfield realisations demonstrate that the superconformal CS theories with N>3 (except for the Gaiotto-Witten theory) require a reducible long N=4 vector multiplet, from which the standard left and right N=4 vector multiplets are obtained by constraining the field strength to be either self-dual or anti self-dual. Such a long multiplet naturally originates upon reduction of any off-shell N>4 vector multiplet to N=4 superspace. For the long N=4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subj...
D2-brane Chern-Simons theories: F-maximization = a-maximization
Fluder, Martin
2015-01-01
We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a superconformal fixed point in the IR, and construct the dual AdS_4 solution in massive IIA supergravity. We compute the free energy F of the gauge theory on S^3 using localization. In the large N limit we find F = c(nN)^{1/3}a^{2/3}, where c is a universal constant and a is the a-function of the "parent" four-dimensional N = 1 theory on N D3-branes probing the same Calabi-Yau singularity. It follows that maximizing F over the space of admissible R-symmetries is equivalent to maximizing a for this class of theories. Moreover, we show that the gauge theory result precisely matches the holographic free energy of the supergravity solution, and provide a similar matching of the VEV of a BPS Wilson loop operator.
Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants
Balasubramanian, Vijay; Leigh, Robert G; Parrikar, Onkar
2016-01-01
We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor product of the torus Hilbert space. We focus on the case where $M_n$ is the link-complement of some $n$-component link inside the three-sphere $S^3$. The entanglement entropies of the resulting states define new, framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level $k$ ($G= U(1)_k$) 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...
Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems
Borot, Gaetan
2015-01-01
We consider the Gopakumar-Ooguri-Vafa correspondence, relating U(N) Chern-Simons theory at large N to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $S^\\Gamma=S^3/\\Gamma$ of the three-sphere by the free action of a finite isometry group. Guided by string theory dualities, we propose a large N dual description in terms of both A- and B-twisted topological strings on (in general non-toric) local Calabi-Yau threefolds. The target space of the B-model theory is obtained from the spectral curve of Toda-type integrable systems constructed on the double Bruhat cells of the simply-laced group identified by the ADE label of $\\Gamma$. Its mirror A-model theory is realized as the local Gromov-Witten theory of suitable ALE fibrations on $CP^1$ generalizing the results known for lens spaces. We propose an explicit construction of the family of target manifolds relevant for the correspondence, which we verify through a large N analysis of the matrix model that expresses the contri...
Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories
Ouyang, Hao; Wu, Jun-Bao; Zhang, Jia-ju
2016-09-01
In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in N = 2 , 3 quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and N = 4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N = 4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.
Kauffman Knot Invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts Model
Astorino, Marco
2010-01-01
The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polynomial arises as special cases: Sp(2), SO(-2) and SL(2,R). These results are confirmed and extended up to the second order, by means of perturbation theory, which moreover let us establish a duality relation between SO(+/-N) and Sp(-/+N) invariants. A correspondence between the firsts orders in perturbation theory of SO(-2), Sp(2) or SU(2) Chern-Simons quantum holonomies and the partition function of the Q=4 Potts Model is built.
Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
Caspar, Stephan; Olesen, Therkel Z; Vlasii, Nadiia D; Wiese, Uwe-Jens
2016-01-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group $G$ in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm pha...
Effective action of 6D F-Theory with U(1) factors: Rational sections make Chern-Simons terms jump
Grimm, Thomas W; Keitel, Jan
2013-01-01
We derive the six-dimensional (1,0) effective action arising from F-theory on an elliptically fibered Calabi-Yau threefold with multiple sections. The considered theories admit both non-Abelian and Abelian gauge symmetries. Our derivation employs the M-theory to F-theory duality in five-dimensions after circle reduction. Five-dimensional gauge and gravitational Chern-Simons terms are shown to arise at one-loop by integrating out massive Coulomb branch and Kaluza-Klein modes. In the presence of a non-holomorphic zero section, we find an improved systematic for performing the F-theory limit by using the concept of the extended relative Mori cone. In this situation Kaluza-Klein modes can become lighter than Coulomb branch modes and a jump in the Chern-Simons levels occurs. By determining Chern-Simons terms for various threefold examples we are able to compute the complete six-dimensional charged matter spectrum and show consistency with six-dimensional anomalies.
Palese, Marcella; Winterroth, Ekkehart
2017-02-01
We relate the existence of Noether global conserved currents associated with locally variational field equations to the existence of global solutions for a local variational problem generating global equations. Both can be characterized as the vanishing of certain cohomology classes. In the case of a 3-dimensional Chern-Simons gauge theory, the variationally featured cohomological obstruction to the existence of global solutions is sharp and equivalent to the usual obstruction in terms of the Chern characteristic class for the flatness of a principal connection. We suggest a parallelism between the geometric interpretation of characteristic classes as obstruction to the existence of flat principal connections and the interpretation of certain de Rham cohomology classes to be the obstruction to the existence of global extremals for a local variational principle.
Palese, Marcella
2016-01-01
We relate the existence of Noether global conserved currents associated with locally variational field equations to existence of global solutions for a local variational problem generating global equations. Both can be characterized as the vanishing of certain cohomology classes. In the case of a 3-dimensional Chern-Simons gauge theory, the variationally featured cohomological obstruction to the existence of global solutions is sharp and equivalent to the usual obstruction in terms of the Chern characteristic class for the flatness of a principal connection. We suggest a parallelism between the geometric interpretation of characteristic classes as obstruction to the existence of flat principal connections and the interpretation of certain de Rham cohomology classes to be the obstruction to the existence of global extremals for a local variational principle.
Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
Santamaria, Ricardo Couso; Putrov, Pavel
2010-01-01
We study various aspects of the matrix models calculating free energies and Wilson loop observables in supersymmetric Chern-Simons-matter theories on the three-sphere. We first develop techniques to extract strong coupling results directly from the spectral curve describing the large N master field. We show that the strong coupling limit of the gauge theory corresponds to the so-called tropical limit of the spectral curve. In this limit, the curve degenerates to a planar graph, and matrix model calculations reduce to elementary line integrals along the graph. As an important physical application of these tropical techniques, we study N=3 theories with fundamental matter, both in the quenched and in the unquenched regimes. We calculate the exact spectral curve in the Veneziano limit, and we evaluate the planar free energy and Wilson loop observables at strong coupling by using tropical geometry. The results are in agreement with the predictions of the AdS duals involving tri-Sasakian manifolds
Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
Couso Santamaría, Ricardo; Mariño, Marcos; Putrov, Pavel
2011-10-01
We study various aspects of the matrix models calculating free energies and Wilson loop observables in supersymmetric Chern-Simons-matter theories on the three-sphere. We first develop techniques to extract strong coupling results directly from the spectral curve describing the large N master field. We show that the strong coupling limit of the gauge theory corresponds to the so-called tropical limit of the spectral curve. In this limit, the curve degenerates to a planar graph, and matrix model calculations reduce to elementary line integrals along the graph. As an important physical application of these tropical techniques, we study mathcal{N} = 3 theories with fundamental matter, both in the quenched and in the unquenched regimes. We calculate the exact spectral curve in the Veneziano limit, and we evaluate the planar free energy and Wilson loop observables at strong coupling by using tropical geometry. The results are in agreement with the predictions of the AdS duals involving tri-Sasakian manifolds.
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
Németh, Z A
1997-01-01
The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of Lévy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a consistent possibility of coupling them also by axial or chiral type currents. Static self dual vortex solutions together with a vortex-lattice are found with the new couplings.
Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model
Energy Technology Data Exchange (ETDEWEB)
Paschoal, Ricardo C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Servico Nacional de Aprendizagem Industrial (SENAI), Rio de Janeiro, RJ (Brazil). Centro de Tecnologia da Industria Quimica e Textil (CETIQT); Helayel Neto, Jose A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); E-mails: paschoal@cbpf.br; helayel@cbpf.br
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)
‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern-Simons theory
Majhi, Abhishek; Majumdar, Parthasarathi
2014-10-01
We articulate the fact that the loop quantum gravity (LQG) description of the quantum macrostates of black hole horizons, modeled as quantum isolated horizons (QIHs), is completely characterized in terms of two independent integer-valued ‘quantum hairs’, viz, the coupling constant (k) of the quantum SU(2) Chern-Simons (CS) theory describing QIH dynamics, and the number of punctures (N) produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the CS fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this CS theory using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semiclassical input from general relativity vis-a-vis the functional dependence of the isolated horizon mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein-Hawking area law relates these two parameters (as an equilibrium ‘equation of state’), and consequently allows the Barbero-Immirzi parameter to take any real and positive value depending on the value of k/N. The logarithmic correction to the area law obtained a decade ago by R Kaul and one of us (PM), ensues straightforwardly, with precisely the coefficient -3/2, making it a signature of the LQG approach to black hole entropy.
Anomalies, Chern-Simons Terms and Black Hole Entropy
Azeyanagi, Tatsuo; Ng, Gim Seng
2015-01-01
Recent derivations of Cardy-like formulae in higher dimensional field theories have opened up a way of computing, via AdS/CFT, universal contributions to black hole entropy from gravitational Chern-Simons terms. Based on the manifestly covariant formulation of the differential Noether charge for Chern-Simons terms proposed in arXiv:1407.6364, we compute the entropy and asymptotic charges for the rotating charged AdS black holes in higher dimensions at leading order of the fluid/gravity derivative expansion in the Einstein-Maxwell-Chern-Simons system. This gives a result that exactly matches the field theory predictions from Cardy-like formulae.
Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group
Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.
2016-11-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.
Quantum Computation and Non-Abelian Statistics in Chern-Simons-Higgs Theory
Brozeguini, J C
2013-01-01
We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum vortex topological excitations occurring in this system and show that self-adjoint (Majorana-like) combinations of these vortices and anti-vortices have in general non-Abelian statistics. The associated unitary monodromy braiding matrices become the required logic gates in the special case when the vortex spin is $s=1/4$. We explicitly construct the vortex field operators, show that they carry both magnetic flux and charge and obtain their euclidean correlation functions by using the method of quantization of topological excitations, which is based on the order-disorder duality. These correlators are in general multivalued, the number of sheets being determined by the vortex spin. This, by its turn, is proportional to the vacuum expectation value of the Higgs field and therefore...
Maxwell-Chern-Simons Casimir Effect
Milton, K A
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. For the case of parallel conducting lines the result is the same as for a scalar field. For the case of circular boundary conditions the results are completely different, with even the sign of the effect being opposite for Maxwell-Chern-Simons fields and scalar fields. We further examine the effect of finite temperature. The Casimir stress is found to be attractive at both low and high temperature. Possibilities of observing this effect in the laboratory are discussed.
The Chern-Simons Number as a Dynamical Variable
Tye, S -H Henry
2016-01-01
In the standard electroweak theory that describes nature, the Chern-Simons number associated with the vacua as well as the unstable sphaleron solutions play a crucial role in the baryon number violating processes. We recall why the Chern-Simons number should be generalized from a set of discrete values to a dynamical (quantum) variable. Via the construction of an appropriate Hopf invariant and the winding number, we discuss how the geometric information in the gauge fields is also captured in the Higgs field. We then discuss the choice of the Hopf variable in relation to the Chern-Simons variable.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bardeen, William A. [Fermilab
2015-09-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 0t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bardeen, William [Fermilab
2014-10-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 1t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Copsey, Keith
2011-01-01
We point out that the metrics recently proposed by K. Balasubramanian and J. McGreevy \\cite{BalaMcGreevyLifshitz} as gravitational duals to Lifshitz Chern-Simons gauge theories contain both a hidden null singularity and a region of closed timelike curves accessible to asymptotic observers. Like the singularity in the original Liftshitz spacetime given by Kachru, Liu, and Mulligan, this singularity does not include large $\\alpha'$ or $g_s$ corrections and hence appears to be singular in string theory as well as classically.
Ouyang, Hao; Zhang, Jia-ju
2015-01-01
We show that generic three-dimensional $\\mathcal N=2$ quiver Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that the generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for the generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops only happens for special values of the parameters.
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 ingr
Chern-Simons Dynamics and the Quantum Hall Effect
Balachandran, A P
1991-01-01
Theoretical developments during the past several years have shown that large scale properties of the Quantum Hall system can be successfully described by effective field theories which use the Chern-Simons interaction. In this article, we first recall certain salient features of the Quantum Hall Effect and their microscopic explanation. We then review one particular approach to their description based on the Chern-Simons Lagrangian and its variants.
N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
Ahn, Changrim
2008-01-01
We propose the exact S-matrix for the planar limit of the N=6 super Chern-Simons theory recently proposed by Aharony, Bergman, Jafferis, and Maldacena for the AdS_4/CFT_3 correspondence. Assuming SU(2|2) symmetry, factorizability and certain crossing-unitarity relations, we find the S-matrix including the dressing phase. We use this S-matrix to formulate the asymptotic Bethe ansatz. Our result for the Bethe-Yang equations and corresponding Bethe ansatz equations confirms the all-loop Bethe ansatz equations recently conjectured by Gromov and Vieira.
Chern-Simons-Higgs Theory with Visible and Hidden Sectors and its ${\\cal N}=2$ SUSY Extension
Arias, Paola; Schaposnik, Fidel A; Tallarita, Gianni
2015-01-01
We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors. We first consider the case in which the two sectors are connected through a BF-like gauge mixing term with no explicit interaction between the the two scalars. Since first order Bogomolny equations do not exist in this case, we derive the second order field equations. We then proceed to an ${\\cal N}=2$ supersymmetric extension including a Higgs portal mixing among the visible and hidden charged scalars. As expected, Bogomolnyi equations do exist in this case and we study their string-like solutions numerically.
Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector
Lozano, Gustavo; Schaposnik, Fidel A
2015-01-01
In this paper we study a $2+1$ dimensional system in which fermions are coupled to the self-dual topological vortex in $U(1) \\times U(1)$ 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.
Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J
2006-01-01
We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with ...
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; LIU Xin; FU Li-Bin
2003-01-01
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using thisdecomposition, the spinor structures of Chern-Simons form and the Chern density are obtained. Furthermore, the knotquantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the secondChern number is characterized by the Hopf indices and the Brouwer degrees of φ-mapping.
Institute of Scientific and Technical Information of China (English)
DUANYi-Shi; LIUXin; FULi-Bin
2003-01-01
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.
Setare, M. R.; Adami, H.
2016-01-01
In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern-Simons-like theories of gravity (CSLTG) and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
Setare, M R
2016-01-01
In the first order formalism of gravity theories, may be exist some theories which are not Lorentz-difeomorphism covariant so for such theories a method for which one can calculate conserved charges of Lorentz-difeomorphism covariant theories are useless. In this letter we introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Then using this concept, in order to obtain the conserved charges in Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa's method \\cite{3} so that it includes Lorentz gauge transformation in addition to diffeomorphism. We apply this method on the Chern-Simons-like theories of gravity and we find out a general formula for the entropy of black holes in those theories. Eventually, we consider some examples and calculate entropy of the BTZ black hole in the context of this examples.
The moduli spaces of $3d$ ${\\cal N} \\ge 2$ Chern-Simons gauge theories and their Hilbert series
Cremonesi, Stefano; Zaffaroni, Alberto
2016-01-01
We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\\cal N} \\ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperK\\"ahler twofold singularities with ${\\cal N} = 2$ and ${\\cal N} = 3$ supersymmetry.
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)
Multiple Chern-Simons fields on a torus
Wesolowski, D J; Ho, C L
1994-01-01
Intertwined multiple Chern-Simons gauge fields induce matrix statistics among particles. We analyse this theory on a torus, focusing on the vacuum structure and the Hilbert space. The theory can be mimicked, although not completely, by an effective theory with one Chern-Simons gauge field. The correspondence between the Wilson line integrals, vacuum degeneracy and wave functions for these two theories are discussed. Further, it is obtained in both of these cases that the two total momenta and Hamiltonian commute only in the physical Hilbert space.
Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei
2016-06-01
We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g , which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.
Fainberg, V Ya; Shikakhwa, M S
1996-01-01
The cvariant path integral quantization of the theory of the scalar and spinor particles interacting through the abelian and non-Abelian Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the absence of the transverse components of these gauge fields. This is remedied by the introduction of the Maxwell or the Maxwell-type (in the non-Abelian case)term which makes the theory superrenormalizable and guarantees its gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be formally the same as those of QED (or QCD) in 2+1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern-Simons and QED (QCD) after renormalization is demonstrated. By carrying out carefully the path integral quantization of the non-Abelian Chern-Simons theories using the De Witt-Fadeev-Popov and the Batalin-Fradkin-...
The quantum 1/2 BPS Wilson loop in ${\\cal N}=4$ Chern-Simons-matter theories
Bianchi, Marco S; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-01-01
In three dimensional ${\\cal N}=4$ Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.
Haggard, Hal M.; Han, Muxin; Kamiński, Wojciech; Riello, Aldo
2015-11-01
We study the expectation value of a nonplanar Wilson graph operator in SL (2, C) Chern-Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. This can be understood as arising from the relation between Chern-Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL (2, C) Chern-Simons theory in 3 dimensions with knotted graph defects.
Renormalization of the N = 1 Abelian super-Chern-Simons theory coupled to parity-preserving matter
Energy Technology Data Exchange (ETDEWEB)
Colatto, L.P.; Andrade, M.A. de; Franco, D.H.T.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Del Cima, O.M. [Technische Universitat Wien (Austria). Institut fuer Theoretische Physik; Piguet, O. [Espirito Santo Univ., Vitoria, ES (Brazil). Dept. de Fisica
1997-12-01
We analyse the renormalizability of an Abelian N=1 super-Chern-Simons model coupled to parity-preserving matter on the light of the regularization independent algebraic method. The model shows to be stable under radiative corrections and to gauge anomaly free. (author) 7 refs.
Thermodynamics of Relativistic Fermions with Chern-Simons Coupling
Bralic, N; Schaposnik, F A
1994-01-01
We study the thermodynamics of the relativistic Quantum Field Theory of massive fermions in three space-time dimensions coupled to an Abelian Maxwell-Chern-Simons gauge field. We evaluate the specific heat at finite temperature and density and find that the variation with the statistical angle is consistent with the non-relativistic ideas on generalized statistics.
Setare, M R
2016-01-01
In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern-Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity( GMMG) and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. ...
Setare, M. R.; Adami, H.
2017-01-01
In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern-Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity (GMMG) and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. Also the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the black hole.
Gaete, Patricio
2016-01-01
By using the gauge-invariant but path-dependent, variables formalism, we consider a recently proposed topologically massive $U{\\left( 1 \\right)_{\\cal W}} \\times U{(1)_{\\cal Y}}$ Chern-Simons-Higgs theory in $2+1$ dimensions. In particular, we inspect the impact of a Chern-Simons mixing term between two Abelian gauge fields on physical observables. We pursue our investigation by analysing the model in two different situations. In the first case, where we integrate out the massive excitation and consider an effective model for the massless field, we show that the interaction energy contains a linear term leading to the confinement of static charge probes along with a screening contribution. The second situation, where the massless field can be exactly integrated over with its constraint duly taken into account, the interesting feature is that the resulting effective model describes a purely screening phase, without any trace of a confining regime.
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.
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; REN Ji-Rong; LI Ran
2007-01-01
In this paper, spinor and vector decompositions of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2)massive gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU(2) Chern-Simons filed theory is discussed in terms of the φ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of φ-mapping.
Chern-Simons Invariants of Torus Knots and Links
Stevan, Sébastien
2010-01-01
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
Setare, M. R.; Adami, H.
2016-08-01
The Chern-Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz-Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Enhancement of hidden symmetries and Chern-Simons couplings
Henneaux, Marc; Lekeu, Victor
2015-01-01
We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories. It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific value. This is heralded by an enhanced isotropy group of the metric on the scalar manifold. Examples of this phenomenon are discussed as well as the relation to supersymmetry. Our results are also connected with rigidity theorems of Borel-like algebras.
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramírez, Ricardo; Rodríguez, Eduardo
2012-10-01
A genuine gauge theory for the Poincaré, 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 Γab 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 Γab can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient αs. We then give a general algorithm that computes the α-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors Bab 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.
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.
Chern-Simons Supergravity in D=3 and Maxwell superalgebras
Concha, P K; Rodríguez, E K; Salgado, P
2015-01-01
We present the construction of the $D=3$ Chern-Simons supergravity action from the Maxwell superalgebra $s\\mathcal{M}$, which can be obtained from the anti-De Sitter superalgebra by combining the abelian semigroup expansion procedure and the In\\"{o}n\\"{u}-Wigner contraction. \\ The Chern-Simons supergravity action from a generalized Maxwell superalgebra is also introduced.
Generalized self-dual Chern-Simons vortices
Bazeia, D.(Departamento de Física, Universidade Federal da Paraíba, João Pessoa, PB, 58051-970, Brazil); da Hora, E.; Santos, C. dos(Centro de Física e Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, 4169-007, Porto, Portugal); Menezes, R.(Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB, Brazil)
2010-01-01
We search for vortices in a generalized Abelian Chern-Simons model with a nonstandard kinetic term. We illustrate our results, plotting and comparing several features of the vortex solution of the generalized model with those of the vortex solution found in the standard Chern-Simons model.
Accelerated FRW solutions in Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Cataldo, Mauricio [Universidad del Bio-Bio, Departamento de Fisica, Concepcion (Chile); Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Campo, Sergio del [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Quinzacara, Cristian C. [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Universidad San Sebastian, Facultad de Ingenieria y Tecnologia, Concepcion (Chile)
2014-10-15
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{sup 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.)
Chern-Simons production during preheating in hybrid inflation models
García-Bellido, J; González-Arroyo, A; Garcia-Bellido, Juan; Perez, Margarita Garcia; Gonzalez-Arroyo, Antonio
2004-01-01
We study the onset of symmetry breaking after hybrid inflation in a model having the field content of the SU(2) gauge-scalar sector of the standard model, coupled to a singlet inflaton. This process is studied in (3+1)-dimensions in a fully non-perturbative way with the help of lattice techniques within the classical approximation. We focus on the role played by gauge fields and, in particular, on the generation of Chern-Simons number. Our results are shown to be insensitive to the various cut-offs introduced in our numerical approach. The spectra preserves a large hierarchy between long and short-wavelength modes during the whole period of symmetry breaking and Chern-Simons generation, confirming that the dynamics is driven by the low momentum sector of the theory. We establish that the Chern-Simons production mechanism is associated with local sphaleron-like structures. The corresponding sphaleron rates are of order 10^{-5} m^{-4}, which, within certain scenarios of electroweak baryogenesis and a (not unnat...
The Topological Inner Structure of Chern-Simons Tensor Current and the World-Sheet of Strings
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; YANG Jie
2005-01-01
@@ Using the decomposition theory of U(1) gauge potential and φ-mapping topological current theory, we investigate the topological inner structure of Chern-Simons tensor current. It is proven that the U(1) Chern-Simons tensor current in four-dimensional manifold is just the topological current of creating the string world-sheets.
The effects of Chern-Simons gravity on bodies orbiting the Earth
Smith, Tristan L; Caldwell, Robert R; Kamionkowski, Marc
2007-01-01
One of the possible low-energy consequences of string theory is the addition of a Chern-Simons term to the standard Einstein-Hilbert action of general relativity. It can be argued that the quintessence field should couple to this Chern-Simons term, and if so, it drives in the linearized theory a parity-violating interaction between the gravito-electric and gravitomagnetic fields. In this paper, the linearized spacetime for Chern-Simons gravity around a massive spinning body is found to include new modifications to the gravitomagnetic field that have not appeared in previous work. The orbits of test bodies and the precession of gyroscopes in this spacetime are calculated, leading to new constraints on the Chern-Simons parameter space due to current satellite experiments.
Exact Slope and Interpolating Functions in N=6 Supersymmetric Chern-Simons Theory
Gromov, Nikolay; Sizov, Grigory
2014-09-01
Using the quantum spectral curve approach we compute, exactly, an observable (called slope function) in the planar Aharony-Bergman-Jafferis-Maldacena theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semiclassical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization based calculation for a similar observable in Marino and Putrov [J. High Energy Phys. 06 (2010) 011], we conjecture an exact expression for h(λ).
Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sanchez Madrigal, S; Raya, A [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Ciudad Universitaria, Morelia, Michoacan 58040 (Mexico); Hofmann, C P, E-mail: saul@ifm.umicri.mx, E-mail: christoph@ucol.mx, E-mail: raya@ifm.umich.mx [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima 28045 (Mexico)
2011-04-01
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 in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D
Picariello, M; Sorella, S P; Picariello, Marco; Quadri, Andrea; Sorella, Silvio P.
2002-01-01
A cohomological BRST characterization of the Seiberg-Witten (SW) map is given. We prove that the coefficients of the SW map can be identified with elements of the cohomology of the BRST operator modulo a total derivative. As an example, it will be illustrated how the first coefficients of the SW map can be written in terms of the Chern-Simons three form. This suggests a deep topological and geometrical origin of the SW map. The existence of the map for both Abelian and non-Abelian case is discussed. By using a recursive argument and the associativity of the $\\star$-product, we shall be able to prove that the Wess-Zumino consistency condition for non-commutative BRST transformations is fulfilled. The recipe of obtaining an explicit solution by use of the homotopy operator is briefly reviewed in the Abelian case.
Schnitzer, Howard J
2016-01-01
R\\'enyi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When $q=\\exp[2\\pi i/(N+K)]$, and $K$ is odd, the topological R\\'enyi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, $\\rm{\\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the R\\'enyi and entanglement entropies, and Wilson line observables.
Chern-Simons terms from thermal circles and anomalies
Jensen, Kristan; Yarom, Amos
2013-01-01
We compute the full contribution of flavor and (or) Lorentz anomalies to the thermodynamic partition function. Apart from the Wess-Zumino consistency condition the Euclidean generating function must satisfy an extra requirement which we refer to as `consistency with the Euclidean vacuum.' The latter requirement fixes all Chern-Simons terms that arise in a particular Kaluza-Klein reduction of the theory. The solution to both conditions may be encoded in a `thermal anomaly polynomial' which we compute. Our construction fixes all the thermodynamic response parameters of a hydrodynamic theory associated with anomalies.
Haggard, Hal M; Kamiński, Wojciech; Riello, Aldo
2014-01-01
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains at the leading order an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged ...
Induced magnetic moment in noncommutative Chern-Simons scalar QED
Panigrahi, P K; Panigrahi, Prasanta K.
2005-01-01
We compute the one loop, $O(\\th)$ correction to the vertex in the noncommutative Chern-Simons theory with scalar fields in the fundamental representation. Emphasis is placed on the parity odd part of the vertex, since the same leads to the magnetic moment structure. We find that, apart from the commutative term, a $\\th$-dependent magnetic moment type structure is induced. In addition to the usual commutative graph, cubic photon vertices also give a finite $\\th$ dependent contribution. Furthermore, the two two-photon vertex diagrams, that give zero in the commutative case yield finite $\\th$ dependent terms to the vertex function.
SIM(1)-VSR Maxwell-Chern-Simons electrodynamics
Bufalo, R.
2016-06-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM (1)-VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and healthy departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges is derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics
Bufalo, R
2016-01-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
On Chern-Simons Quivers and Toric Geometry
Belhaj, Adil; del Moral, Maria Pilar Garcia; Segui, Antonio
2011-01-01
We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex 4-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V^2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V^2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V^2.
Giambelli Identity in Super Chern-Simons Matrix Model
Matsuno, Satsuki
2016-01-01
A classical identity due to Giambelli in representation theory states that the character in any representation is expressed as a determinant whose components are characters in the hook representation constructed from all the combinations of the arm and leg lengths of the original representation. Previously it was shown that the identity persists in taking, for each character, the matrix integration in the super Chern-Simons matrix model in the grand canonical ensemble. We prove here that this Giambelli compatibility still holds in the deformation of the fractional-brane background.
Self-Dual Chern-Simons Vortices in Higgs Field
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; ZHONG Wo-Jun; SI Tie-Yan
2005-01-01
@@ By decomposing the Bogomol'nyi self-dual equation in the Abelian Chern-Simons Higgs model, we find a selfdual topological term that was ignored all the time in the Bogomol'nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a new self-dual equation that includes the topological term. It is shown that the self-dual vortex just arises from the symmetric phase of the Higgs field φ = 0. Using our φ-mapping theory, the inner topological structure of the vortex and double vortex is given.
Topological aspect of Chern-Simons p-branes
Institute of Scientific and Technical Information of China (English)
Duan Yi-Shi; Zhao Li; Liu Yu-Xiao; Ren Ji-Rong
2007-01-01
By generalizing the topological current of Abelian Chern Simons (CS) vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ(x), and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.
Lecture notes on Chern-Simons (super-)gravities
Zanelli, J
2005-01-01
This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The starting point is a gravitational action which generalizes the Einstein theory for dimensions D>4 --Lovelock gravity. It is then shown that in odd dimensions there is a particular choice of the arbitrary parameters of the action that makes the theory gauge invariant under the (anti-)de Sitter or the Poincare groups. The resulting lagrangian is a Chern-Simons form for a connection of the corresponding gauge groups and the vielbein and the spin connection are parts of this connection field. These theories also admit a natural supersymmetric extension for all odd D where the local supersymmetry algebra closes off-shell and without a need for auxiliary fields. No analogous constructi...
Anomalous spin of the Chern-Simons-Georgi-Glashow model
Qiu-Hong, Huo
2012-01-01
With the Coulomb gauge, the Chern-Simons-Georgi-Glashow (CSGG) model is quantized in the Dirac formalism for the constrained system. Combining the Gauss law and Coulomb gauge consistency condition, the difference between the Schwinger angular momentum and canonical angular momentum of the system is found to be an anomalous spin. The reason for this result lies in that the Schwinger energy momentum tensor and the canonical one have different symmetry properties in presence of the Chern-Simons term.
Real-time Chern-Simons term for hypermagnetic fields
M. Laine
2005-01-01
If non-vanishing chemical potentials are assigned to chiral fermions, then a Chern-Simons term is induced for the corresponding gauge fields. In thermal equilibrium anomalous processes adjust the chemical potentials such that the coefficient of the Chern-Simons term vanishes, but it has been argued that there are non-equilibrium epochs in cosmology where this is not the case and that, consequently, certain fermionic number densities and large-scale (hypermagnetic) field strengths get coupled ...
Extremal Black Holes in Dynamical Chern-Simons Gravity
McNees, Robert; Yunes, Nicolás
2015-01-01
Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity (GR). Such solutions are often difficult to find in beyond-GR theories due to the inclusion of additional fields that couple to the metric non-linearly and non-minimally. In this paper, we consider rotating black hole solutions in one such theory, dynamical Chern-Simons gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dynamical Chern-Simons gravity as an effective field theory and thus work in the decoupling limit, where corrections are treated as small perturbations from general relativity. We perturb about the maximally-rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct sol...
Gauge Symmetries and Holographic Anomalies of Chern-Simons and Transgression AdS Gravity
Mora, Pablo
2014-01-01
We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravities. Those anomalies are either gauge anomalies associated to the AdS gauge group of the theory or diffeomorphism anomalies, with each kind related to the other. As a result of using suitable action principles por Chern-Simons AdS gravities, coming from Transgression forms, we obtain finite results without the need for further regularization. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories. The Wess-Zumino consistency condition ensures that anomalies of the generic form computed here should appear for these and other theories.
Toric Fano varieties and Chern-Simons quivers
Closset, Cyril
2012-01-01
In favourable cases the low energy dynamics of a stack of M2-branes at a toric Calabi-Yau fourfold singularity can be described by an N=2 supersymmetric Chern-Simons quiver theory, but there still does not exists an "inverse algorithm" going from the toric data of the CY_4 to the CS quiver. We make progress in that direction by deriving CS quiver theories for M2-branes probing cones over a large class of geometries Ypq(B_4), which are S^3/\\bZ_p bundles over toric Fano varieties B_4. We rely on the type IIA understanding of CS quivers, giving a firm string theory footing to our CS theories. In particular we give a derivation of some previously conjectured CS quivers in the case B_4= CP^1*CP^1, as field theories dual to M-theory backgrounds with nontrivial torsion G_4 fluxes.
Seiberg duality for Chern-Simons quivers and D-brane mutations
Closset, Cyril
2012-03-01
Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the {Y^{{p,q}}}left( {mathbb{C}{mathbb{P}^{{2}}}} right) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.
Seiberg duality for Chern-Simons quivers and D-brane mutations
Closset, Cyril
2012-01-01
Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the Y^{p,q}(CP^2) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.
Dense Chern-Simons Matter with Fermions at Large N
Geracie, Michael; Son, Dam T
2015-01-01
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 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 ...
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...
Self-dual vortices in Chern-Simons hydrodynamics
Li, D K
2001-01-01
One studies effect of nonlinear quantum potential on planar vortices occurring in (2+1)-dimensional problem for the Schroedinger equation with interaction with the Chern-Simons (CS) gauge field. Classical dynamics of a charged nonrelativistic particle moving in U(1)-gauge field is described in the form of the Schroedinger nonlinear (SN) wave equation with quantum potential. it is shown that deformation introduction into coupling constant of quantum potential depending on the Plank constant results either in the Schroedinger standard model or in diffusion-antidiffusion equations. The gauge theory in the form of the Abelian CS-theory interacting with SN field boils down to the theory of vortex hydrodynamics. Problem for a static flux moving with speed equal to quantum speed boils down to the Liouville equation. Paper contains description of the relevant vortex configurations
Chern-Simons modified gravity and closed time-like curves
Porfirio, P J; Nascimento, J R; Petrov, A Yu; Ricardo, J; Santos, A F
2016-01-01
We verify the consistency of the G\\"odel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.
Real-time Chern-Simons term for hypermagnetic fields
Laine, Mikko
2005-01-01
If non-vanishing chemical potentials are assigned to chiral fermions, then a Chern-Simons term is induced for the corresponding gauge fields. In thermal equilibrium anomalous processes adjust the chemical potentials such that the coefficient of the Chern-Simons term vanishes, but it has been argued that there are non-equilibrium epochs in cosmology where this is not the case and that, consequently, certain fermionic number densities and large-scale (hypermagnetic) field strengths get coupled to each other. We generalise the Chern-Simons term to a real-time situation relevant for dynamical considerations, by deriving the anomalous Hard Thermal Loop effective action for the hypermagnetic fields, write down the corresponding equations of motion, and discuss some exponentially growing solutions thereof.
Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity
Molina, C; Cardoso, Vitor; Gualtieri, Leonardo
2010-01-01
Dynamical Chern-Simons gravity is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard General Relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.
Perturbations of Schwarzschild black holes in Dynamical Chern-Simons modified gravity
Cardoso, V
2009-01-01
Dynamical Chern-Simons (DCS) modified gravity is an attractive, yet relatively unexplored, candidate to an alternative theory of gravity. The DCS correction couples a dynamical scalar field to the gravitational field. In this framework, we analyze the perturbation formalism and stability properties of spherically symmetric black holes. Assuming that no background scalar field is present, gravitational perturbations with polar and axial parities decouple. We find no effect of the Chern-Simons coupling on polar sector, while axial perturbations couple to the Chern-Simons scalar field. The axial sector can develop strong instabilities if the coupling parameter beta, associated to the dynamical coupling of the scalar field, is enough small; this yields a constraint on beta which is much stronger than the constraints previously known in the literature.
Qiang, Li-E
2015-01-01
High precision Superconductivity Gravity Gradiometers (SGG) are powerful tools for relativistic experiments. In this paper, we work out the tidal signals in non-dynamical Chern-Simons modified gravity, which could be measured by orbiting SGGs around Earth. We find that, with proper orientations of multi-axes SGGs, the tidal signals from the Chern-Simons modification can be isolated in the combined data of different axes. Furthermore, for three-axes SGGs, such combined data is the trace of the total tidal matrix, which is invariant under the rotations of SGG axes and thus free from axis pointing errors. Following nearly circular orbits, the tests of the parity-violating Chern-Simons modification and the measurements of the gravitomagnetic sector in parity-conserving metric theories can be carried out independently in the same time. A first step analysis on noise sources is also included.
Anomalous spin of the Chern-Simons-Georgi-Glashow model
Institute of Scientific and Technical Information of China (English)
HUO Qiu-Hong; JIANG Yun-Guo; WANG Ru-Zhi; YAN Hui
2013-01-01
With the Coulomb gauge,the Chern-Simons-Georgi-Glashow (CSGG) model is quantized in the Dirac formalism for the constrained system.Combining the Gauss law and Coulomb gauge consistency condition,the difference between the Schwinger angular momentum and canonical angular momentum of the system is found to be an anomalous spin.The reason for this result lies in the fact that the Schwinger energy momentum tensor and the canonical one have different symmetry properties in the presence of the Chern-Simons term.
Maxwell-Chern-Simons Hydrodynamics for the Chiral Magnetic Effect
Ozonder, Sener
2010-01-01
The rate of vacuum changing topological solutions of the gluon field, sphalerons, is estimated to be large at the typical temperatures of heavy-ion collisions, particularly at the Relativistic Heavy Ion Collider. Such windings in the gluon field are expected to produce parity-odd bubbles, which cause separation of positively and negatively charged quarks along the axis of the external magnetic field. This Chiral Magnetic Effect can be mimicked by Chern-Simons modified electromagnetism. Here we present a model of relativistic hydrodynamics including the effects of axial anomalies via the Chern-Simons term.
AdS Chern-Simons Gravity induces Conformal Gravity
Aros, Rodrigo
2013-01-01
The leitmotif of this paper is the question of whether four- and higher even-dimensional Conformal Gravities do have a Chern-Simons pedigree. We show that Weyl gravity can be obtained as dimensional reduction of a five-dimensional Chern-Simons action for a suitable (gauged-fixed, tractor-like) five-dimensional AdS connection. The gauge-fixing and dimensional reduction program admits a readily generalization to higher dimensions for the case of certain conformal gravities obtained by contractions of the Weyl tensor.
Chern-Simons functional under gauge transformations on flat bundles
Byun, Yanghyun; Kim, Joohee
2017-01-01
We describe the effect of a gauge transformation on the Chern-Simons functional in a thorough and unifying manner. We use the assumptions that the structure group is compact and connected and, in particular, that the principal bundle is flat. The Chern-Simons functional we consider is the one defined by choosing a flat reference connection. The most critical step in arriving at the main result is to show both the existence and the uniqueness of a cohomology class on the adjoint bundle such that it is the class of the so-called Maurer-Cartan 3-form when restricted to each fiber.
Resolution of Chern--Simons--Higgs Vortex Equations
Han, Xiaosen; Yang, Yisong
2015-01-01
It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.
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.
Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
Aharony, Ofer; Hsin, Po-Shen; Seiberg, Nathan
2016-01-01
In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between $SO(N)_k$ Chern-Simons theories coupled to $N_f$ real scalars in the fundamental representation, and $SO(k)_{-N+N_f/2}$ coupled to $N_f$ real (Majorana) fermions in the fundamental. For $N_f=0$ these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For $k=1$ we get an interesting low-energy duality between $N_f$ free Majorana fermions and an $SO(N)_1$ Chern-Simons theory coupled to $N_f$ scalar fields (with $N_f \\leq N-2$).
The genus one Complex Quantum Chern-Simons representation of the Mapping Class Group
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Marzioni, Simone
In this paper we compute explicitly, following Witten’s prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to the complex gauge group SL(2, C). We use the k’th order Weil-Gel’fand-Zak transform to exhibit an explicit...
A first-class approach of higher derivative Maxwell-Chern-Simons-Proca model
Energy Technology Data Exchange (ETDEWEB)
Sararu, Silviu-Constantin [University of Craiova, Department of Physics, Craiova (Romania)
2015-11-15
The equivalence between a higher derivative extension of Maxwell-Chern-Simons-Proca model and some gauge invariant theories from the point of view of the Hamiltonian path integral quantization in the framework of the gauge-unfixing approach is investigated. The Hamiltonian path integrals of the first-class systems take manifestly Lorentz-covariant forms. (orig.)
Institute of Scientific and Technical Information of China (English)
张龙; 翁征宇
2015-01-01
The fermion sign plays a dominant role in Fermi liquid theory. However, in Mott insulators, the strong Coulomb interaction suppresses the charge fluctuations and eliminates the fermion signs due to electron permutation. In this article, we first review the phase string theory of the Hubbard model for a bipartite lattice, which unifies the Fermi liquid at weak coupling and the antiferromagnetic Mott insulator at strong coupling. We first derive the exact sign structure of the Hubbard model for an arbitrary Coulomb interaction U . In small U limit, the conventional fermion sign is restored, while at large U limit, it leads to the phase string sign structure of the t-J model. For half filling, we construct an electron fractionalization representation, in which chargons and spinons are coupled to each other via emergent mutual Chern-Simons gauge fields. The corresponding ground state ansatz and low energy effective theory capture the ground state phase diagram of the Hubbard model qualitatively. For weak coupling regime, the Fermi liquid quasiparticle is formed by the bound state of a chargon and a spinon, and the long range phase coherence is determined by the background spin correlation. The Mott transition can be realized either by forming the chargon gap or by condensing the background spinons.
Supersymmetric Chern-Simons terms in ten dimensions
Bergshoeff, E.; Roo, M. de
1989-01-01
We construct a supersymmetric extension of the Lorentz and Yang-Mills Chern-Simons terms in ten dimensions. In terms of dimensionful parameters Î± (Lorentz) and Î² (Yang-Mills), we obtain the complete O(Î±) supersymmetrization. Furthermore, we present the leading O(Î±2) and O(Î±Î²) corrections requi
Action Principles for Transgression and Chern-Simons AdS Gravities
Mora, Pablo
2014-01-01
Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times. In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge...
The Chern-Simons invariant as the natural time variable for classical and quantum cosmology
Smolin, L; Smolin, Lee; Soo, Chopin
1995-01-01
We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is the natural internal time coordinate for classical and quantum cosmology. The reasons for this are a number of interesting properties of this functional, which we describe here. 1)It is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom, in the metric defined by the Ashtekar formulation of general relativity. 2)The imaginary part of the Chern-Simons form reduces in the limit of small cosmological constant, \\Lambda, and solutions close to DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field excitations of the Chern-Simons state satisfy, by virtue of the quantum constraints, a functional Schroedinger equation in which the matter fields evolve on a DeSitter background in the Chern-Simons time. We then n propose this is the natural vacuum state of the theory for \\Lambda \
3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction
Kiran, K Surya; Raju, Avinash
2014-01-01
These are notes of introductory lectures on (a) elements of 2+1 dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein-Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.
Gauged Baby Skyrme Model with Chern-Simons term
Samoilenka, A
2016-01-01
The properties of the multisoliton solutions of the (2+1)-dimensional Maxwell-Chern-Simons-Skyrme model are investigated numerically. Coupling to the Chern-Simons term allows for existence of the electrically charge solitons which may also carry magnetic fluxes. Two particular choices of the potential term is considered: (i) the weakly bounded potential and (ii) the double vacuum potential. In the absence of the gauge interaction in the former case the individual constituents of the multisoliton configuration are well separated, while in the latter case the rotational invariance of the configuration remains unbroken. It is shown that coupling of the planar multi-Skyrmions to the electric and magnetic field strongly affects the pattern of interaction between the constituents. We analyze the dependency of the structure of the solutions, the energies, angular momenta, electric and magnetic fields of the configurations on the gauge coupling constant $g$, and the electric potential. It is found that, generically, ...
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, Muhammad Jamil
2014-01-01
This paper is devoted to investigate the gravitational perfect fluid collapse in the framework of Chern-Simon modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. The Israel junction conditions are used to match the interior and exterior spacetimes. For the sake of simplicity, we take the external field $\\Theta$ as a function of time parameter $t$ and obtain the solution of the field equations of Chern-Simon modified gravity. Junction conditions have been used to calculate the gravitational mass. We discuss the apparent horizons and their physical consequences. It is mentioning here that our results will reduce to those of general relativity, available in literature, if the external field is taken to be constant.
Higgs- and Skyrme-Chern-Simons densities in all dimensions
Tchrakian, D H
2015-01-01
Two types of new Chern-Simons (CS) densities, both defined in all odd and even dimensions, are proposed. These new CS densities feature a scalar field interacting with a scalar. In one case this is a Higgs scalar while in the other it is a Skyrme scalar. The motivation is to study the effects of adding these new CS terms to a Lagrangian which supports static soliton solutions prior to their introduction.
Causality aspects of the dynamical Chern-Simons modified gravity
Porfírio, P. J.; Fonseca-Neto, J. B.; Nascimento, J. R.; Petrov, A. Yu.
2016-11-01
We discuss the Gödel-type solutions within the dynamical Chern-Simons modified gravity in four dimensions. Within our study, we show that in the vacuum case causal solutions are possible that cannot take place within the nondynamical framework. Another result of ours consists in the possibility for completely causal solutions for all of the types of matter we study in the paper, that is, relativistic fluid, cosmological constant, scalar, and electromagnetic fields.
Edge Currents and Vertex Operators for Chern-Simons Gravity
Bimonte, G; Stern, A
1993-01-01
We apply elementary canonical methods for the quantization of 2+1 dimensional gravity, where the dynamics is given by E. Witten's $ISO(2,1)$ Chern-Simons action. As in a previous work, our approach does not involve choice of gauge or clever manipulations of functional integrals. Instead, we just require the Gauss law constraint for gravity to be first class and also to be everywhere differentiable. When the spatial slice is a disc, the gravitational fields can either be unconstrained or constrained at the boundary of the disc. The unconstrained fields correspond to edge currents which carry a representation of the $ISO(2,1)$ Kac-Moody algebra. Unitary representations for such an algebra have been found using the method of induced representations. In the case of constrained fields, we can classify all possible boundary conditions. For several different boundary conditions, the field content of the theory reduces precisely to that of 1+1 dimensional gravity theories. We extend the above formalism to include sou...
Standard general relativity from Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, F. [Departamento de Matematica y Fisica Aplicadas, Universidad, Catolica de la Santisima Concepcion, Alonso de Rivera 2850, Concepcion (Chile); Minning, P. [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Perez, A. [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Max Planck Institut fuer Gravitationsphysik, Albert Einstein, Institut. Am Muehlenberg1, D-14476 Golm bei Potsdam (Germany); Rodriguez, E. [Departamento de Matematica y Fisica Aplicadas, Universidad, Catolica de la Santisima Concepcion, Alonso de Rivera 2850, Concepcion (Chile); Salgado, P. [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)], E-mail: pasalgad@udec.cl
2009-07-13
Chern-Simons models for gravity are interesting because they provide a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been its perceived remoteness from standard General Relativity, based on the presence of higher powers of the curvature in the Lagrangian (except, remarkably, for three-dimensional spacetime). Here we report on a simple model that suggests a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point in the space of couplings, where additional degrees of freedom and corresponding 'anomalous' Gauss-Bonnet constraints drop out from the Chern-Simons action. To achieve this goal, both the Lie algebra g and the symmetric g-invariant tensor that define the Chern-Simons Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite Abelian semigroup S. The results are generalized to arbitrary odd dimensions, and the possible extension to the case of eleven-dimensional supergravity is briefly discussed.
Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity
Cacciatori, S L; Giacomini, A; Klemm, D; Mansi, D S; Cacciatori, Sergio L.; Caldarelli, Marco M.; Giacomini, Alex; Klemm, Dietmar; Mansi, Diego S.
2005-01-01
We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern-Simons theories with suitable gauge groups. Using the groups ISO(2,1), SL(2,C) or SL(2,R) x SL(2,R), and the fact that they admit two independent coupling constants, we obtain the Mielke-Baekler model for zero, positive or negative effective cosmological constant respectively. Choosing SO(3,2) as gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an SL(4,R) Chern-Simons theory.
Extremal black holes in dynamical Chern-Simons gravity
McNees, Robert; Stein, Leo C.; Yunes, Nicolás
2016-12-01
Rapidly rotating black hole (BH) solutions in theories beyond general relativity (GR) play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of GR. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric nonlinearly and non-minimally. In this paper, we consider rotating BH solutions in one such theory, dynamical Chern-Simons (dCS) gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dCS gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from GR. We perturb about the maximally rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dCS horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.
Anacleto, M A; Nascimento, J R S; Ribeiro, R F; Wotzasek, C
2001-01-01
We study the equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models coupled to dynamical, U(1) charged matter, both fermionic and bosonic. This is done through an iterative procedure of gauge embedding that produces the dual mapping of the self-dual vector field theory into a Maxwell-Chern-Simons version. In both cases, to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. Moreover, the minimal coupling of the original self-dual model is replaced by a non-minimal magnetic like coupling in the MCS side. Unlike the fermionic instance however, in the bosonic example the dual mapping proposed here leads to a Maxwell-Chern-Simons theory immersed in a field dependent medium.
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators
Dasgupta, Keshav; Ramadevi, P; Tatar, Radu
2016-01-01
Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N = 4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show th...
Charged Rotating AdS Black Holes with Chern-Simons coupling
Mir, Mozhgan
2016-01-01
We obtain a perturbative solution for rotating charged black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to forth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Chern-Simons coefficient. In particular, for values of CS coupling constant beyond its supergravity amount, due to a rotational instability, counterrotating black holes arise. Also the rotating solutions appear to have vanishing angular momenta and do not manifest uniquely by their global charges.
Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications
Apruzzi, Fabio; Parameswaran, Susha; Zagermann, Marco
2014-01-01
We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete intersection Calabi-Yau compactification and choice of Wilson lines. We do so by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding how the Wilson lines project onto these submanifolds, and computing their Chern-Simons invariants. We illustrate our procedure with the quintic hypersurface as well as the split-bicubic, which can provide a potentially realistic three generation model.
Adiabatic pumping of Chern-Simons axion coupling.
Taherinejad, Maryam; Vanderbilt, David
2015-03-06
We study the adiabatic pumping of the Chern-Simons axion (CSA) coupling along a parametric loop characterized by a nonzero second Chern number C^{(2)} from the viewpoint of the hybrid Wannier representation, in which the Wannier charge centers are visualized as sheets defined over a projected 2D Brillouin zone. We derive a new formula for the CSA coupling, expressing it as an integral involving Berry curvatures and potentials defined on the Wannier charge center sheets. We show that a loop characterized by a nonzero C^{(2)} requires a series of sheet-touching events at which 2π quanta of Berry curvature are passed from sheet to sheet, in such a way that e^{2}/h units of CSA coupling are pumped by a lattice vector by the end of the cycle. We illustrate these behaviors via explicit calculations on a model tight-binding Hamiltonian and discuss their implications.
Gravitational waves from extreme mass-ratio inspirals in Dynamical Chern-Simons gravity
Pani, Paolo; Gualtieri, Leonardo
2011-01-01
Dynamical Chern-Simons gravity is an interesting extension of General Relativity, which finds its way in many different contexts, including string theory, cosmological settings and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasi-circular inspiralling of a small, stellar-mass object into a large non-rotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green's function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LIS...
Gravitational waves from extreme mass-ratio inspirals in dynamical Chern-Simons gravity
Pani, Paolo; Cardoso, Vitor; Gualtieri, Leonardo
2011-05-01
Dynamical Chern-Simons gravity is an interesting extension of general relativity, which finds its way in many different contexts, including string theory, cosmological settings, and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasicircular inspiralling of a small, stellar-mass object into a large nonrotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green’s function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LISA, this effect can be used to constrain the coupling parameter effectively.
Translational Chern-Simons Action and New Planar Particle Dynamics
Lukierski, J; Zakrzewski, W J
2000-01-01
We consider a nonstandard $D=2+1$ gravity described by a translational Chern--Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. The phase space Hamiltonian $H$ describing two-body interactions satisfies a nonlinear equation $H={\\cal H}(\\vec{x},\\vec{p};H)$ what implies, after quantization, a nonstandard form of the Schr\\"{o}dinger equation with energy-dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles $r\\leq r_0$) and the scattering states with continuous energy correspond to classical motion for $r>r_0$.
Noncommutative ${\\cal N}=2$ Chern-Simons-matter model
Bevilaqua, L Ibiapina
2014-01-01
In this work we study the three-dimensional ${\\cal N}=2$ supersymmetric Chern-Simons-matter model in a noncommutative space-time. We construct the action of the noncommutative $U(N)$ non-Abelian model in terms of explicit ${\\cal N}=2$ supervariables by dimensionally reducing a four-dimensional ${\\cal N}=1$ supermultiplet. We also obtain the on-shell ${\\cal N}=2$ supersymmetric model writing it in terms of ${\\cal N}=1$ superfields. In the noncommutative Abelian case, we show that linear UV divergences are cancelled in Feynman diagrams and logarithmic divergences are absent up to one-loop order, stating that our model is free of UV/IR mixing.
Chern-Simons states in spin-network quantum gravity
Gambini, R; Pullin, J; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge
1997-01-01
In the context of canonical quantum gravity in terms of Ashtekar's new variables, it is known that there exists a state that is annihilated by all the quantum constraints and that is given by the exponential of the Chern--Simons form constructed with the Asthekar connection. We make a first exploration of the transform of this state into the spin-network representation of quantum gravity. The discussion is limited to trivalent nets with planar intersections. We adapt an invariant of tangles to construct the transform and study the action of the Hamiltonian constraint on it. We show that the first two coefficients of the expansion of the invariant in terms of the inverse cosmological constant are annihilated by the Hamiltonian constraint. We also discuss issues of framing that arise in the construction.
A New Look at Chern-Simons on Circle Bundles I: The Caloron Correspondence
Mickler, Ryan
2015-01-01
We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with structure group given by the full affine level $k$ central extension of the loop group $LG$. The space of fields of this 2d theory is naturally symplectic, and this provides a new formulation of a result of Beasley-Witten about the equivariant localization of the Chern-Simons path integral. The main tool that we employ is the Caloron correspondence, originally due to Murray-Garland, that relates the space of gauge fields on $M$ with a certain enlarged space of connections on an equivariant version of the loop space of the $G$-bundle. We show that the symplectic structure that Beasley-Witten found is related to a looped version of the Atiyah-Bott construction in 2-dimensional Yang-Mills theory. ...
Visible and hidden sectors in a model with Maxwell and Chern-Simons gauge dynamics
Ireson, Edwin; Schaposnik, Fidel A.; Tallarita, Gianni
2016-11-01
We study a U(1) × U(1) gauge theory discussing its vortex solutions and supersymmetric extension. In our set-up, the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern-Simons term. The two sectors interact via a BF gauge field mixing and a Higgs portal term that connects the two complex scalars. We also consider the supersymmetric version of this system which allows to find for the bosonic sector BPS equations in which an additional real scalar field enters into play. We study numerically the field equations finding vortex solutions with both magnetic flux and electric charge.
Remarks on the Taub-NUT solution in Chern-Simons modified gravity
Brihaye, Yves; Radu, Eugen
2017-01-01
We discuss the generalization of the NUT spacetime in General Relativity (GR) within the framework of the (dynamical) Einstein-Chern-Simons (ECS) theory with a massless scalar field. These configurations approach asymptotically the NUT spacetime and are characterized by the 'electric' and 'magnetic' mass parameters and a scalar 'charge'. The solutions are found both analytically and numerically. The analytical approach is perturbative around the Einstein gravity background. Our results indicate that the ECS configurations share all basic properties of the NUT spacetime in GR. However, when considering the solutions inside the event horizon, we find that in contrast to the GR case, the spacetime curvature grows (apparently) without bound.
Vanishing magnetic mass in QED$_{3}$ with a Chern-Simons term
Das, Ashok; Perez, Silvana
2002-01-01
We show that, at one loop, the magnetic mass vanishes at finite temperature in QED in any dimension. In QED$_{3}$, even the zero temperature part can be regularized to zero. We calculate the two loop contributions to the magnetic mass in QED$_{3}$ with a Chern-Simons term and show that it vanishes. We give a simple proof which shows that the magnetic mass vanishes to all orders at finite temperature in this theory. This proof also holds for QED in any dimension.
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
Energy Technology Data Exchange (ETDEWEB)
Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2015-11-15
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.)
Visible and hidden sectors in a model with Maxwell and Chern-Simons gauge dynamics
Ireson, Edwin; Tallarita, Gianni
2016-01-01
We study a $U(1) \\times U(1)$ gauge theory discussing its vortex solutions and supersymmetric extension. In our set-upon the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern-Simons term. The two sectors via a BF gauge field mixing and a Higgs portal term that connects the two complex scalars. We also consider the supersymmetric version of this system which allows to find for the bosonic sector BPS equations in which an additional real scalar field enters into play. We study numerically the field equations finding vortex solutions with both magnetic flux and electric charge.
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].
Derivative expansion and the induced Chern-Simons term in N=1, d=3 superspace
Gama, F S; Petrov, A Yu
2015-01-01
In this paper we apply a supersymmetric generalization of the method of derivative expansion to compute the induced non-Abelian Chern-Simons term in $\\mathcal{N}=1$, $d=3$ superspace, for an arbitrary gauge group.
Loop Representation of charged particles interacting with Maxwell and Chern-Simons fields
Fuenmayor, E; Revoredo, R; Fuenmayor, Ernesto; Leal, Lorenzo; Revoredo., Ryan
2002-01-01
The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists an unitary transformation that allows to remove the degrees of freedom associated with the paths. As a general result, we find that charge quantization is necessary for the geometric representation to be consistent.
Yelnykov, O V
2005-01-01
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern- Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space o...
Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
Benini, Francesco; Cremonesi, Stefano
2011-01-01
We study the quantum moduli space of N=2 Chern-Simons quivers with generic ranks and CS levels, proving along the way exact formulas for the charges of bare monopole operators. We then derive N=2 Chern-Simons quiver theories dual to AdS_4 x Y^{p,q}(CP2) M-theory backgrounds, for the whole family of Sasaki-Einstein seven-manifolds and for any value of the torsion G_4 flux. The derivation of the gauge theories relies on the reduction to type IIA string theory, in which M2-branes become D2-branes while the conical geometry maps to RR flux and D6-branes wrapped on compact four-cycles. M5-branes on torsion cycles map to flux and wrapped D4-branes. The moduli space of the quiver is shown to contain the corresponding CY_4 cone and all its crepant resolutions.
Some cosmological solutions in Einstein-Chern-Simons gravity
Avilés, Luis; Quinzacara, Cristian; Salgado, Patricio
2016-01-01
In this paper we find new solutions for the so called Einstein-Chern-Simons Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84 (2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in the first case we find some solutions of the five-dimensional ChS-FRW field equations when the $h^a$ field is a perfect fluid that obeys a barotropic equation of state; (ii) in the second case we study the solutions, for the cases $\\gamma =1/2,\\ 3/4$, when the $h^a$ field is a five dimensional politropic fluid that obeys the equation $P^{(h)}=\\omega ^{(h)}\\rho ^{(h)\\gamma }$; (iii) in the third case we find the scale factor and the state parameter $\\omega (t)$ when the $h^a$ field is a variable modified Chaplygin gas. We consider also a space-time metric which contains as a subspace to the usual four-dimensional FRW and then we study the same three cases considered in the five-dimensional, namely when (i) the $h^a$ field is a perfect fluid, (ii) the $h^a$ field is a five dimensiona...
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, M. Jamil; Ali, Sarfraz
2016-04-01
This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.
Chern-Simons diffusion rate across different phase transitions
Rougemont, Romulo
2016-01-01
We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate $\\Gamma_{\\textrm{CS}}$ divided by the product of the entropy density $s$ and temperature $T$ behaves across different kinds of phase transitions in the class of bottom-up non-conformal Einstein-dilaton holographic models originally proposed by Gubser and Nellore. By tuning the dilaton potential, one is able to holographically mimic a first order, a second order, or a crossover transition. In a first order phase transition, $\\Gamma_{\\textrm{CS}}/sT$ jumps at the critical temperature (as previously found in the holographic literature), while in a second order phase transition it develops an infinite slope. On the other hand, in a crossover, $\\Gamma_{\\textrm{CS}}/sT$ behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. Furthermore, we also find that $\\Gamma_{\\textrm{CS}}/sT$ increases by orders of magnitude below the critical temperature in a second order phase transition and in a crossov...
The Chern-Simons term in a dual Josephson junction
Grigorio, L S; Rougemont, R; Wotzasek, C; Zarro, C A D
2013-01-01
A dual Josephson junction corresponding to a (2+1)-dimensional non-superconducting layer sandwiched between two (3+1)-dimensional dual superconducting regions constitutes a model of localization of a U(1) gauge field within the layer. Monopole tunneling currents flow from one dual superconducting region to another due to a phase difference between the wave functions of the monopole condensate below and above the non-superconducting layer. These magnetic currents appear within the (2+1)-dimensional layer as a gas of magnetic instanton events and a weak electric charge confinement is expected to take place at very long distances within the layer. In the present work, we consider what happens when one introduces fermions in this physical scenario. Due to the dual Meissner effect featured in the dual superconducting bulk, it is argued that unconfined fermions would be localized within the (2+1)-dimensional layer, where their quantum fluctuations radiatively induce a Chern-Simons term, which is known to destroy th...
Vortex Solutions in the Chern-Simons Stueckelberg Model
McKeon, D G C
1998-01-01
Vortex solutions to the classical field equations in a massive, renormalizable U(1) gauge model are considered in (2+1) dimensions. A vector field whose kinetic term consists of a Chern-Simons term plus a Stuekelberg mass term is coupled to a scalar field. If the classical scalar field is set equal to zero, then there are classical configurations of the vector field in which the magnetic flux is non-vanishing and finite. In contrast to the Nielsen-Olesen vortex, the magnetic field vanishes exponentially at large distances and diverges logarithmicly at short distances. This divergence, although not so severe as to cause the flux to diverge, results in the Hamiltonian becoming infinite. If the classical scalar field is no longer equal to zero, then the magnetic flux is not only finite, but quantized and the asymptotic behaviour of the field is altered so that the Hamiltonian no longer suffers from a divergence due to the field configuration at the origin. Furthermore, the asymptotic behaviour at infinity is dep...
Entropy for gravitational Chern-Simons terms by squashed cone method
Guo, Wu-zhong
2015-01-01
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 we find no anomaly of entropy appears. But the 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 $d\\bm{\\Omega_{4n-1}}=tr(\\bm{R}^{2n})$. We notice that the entropy of $tr(\\bm{R}^{2n})$ is a total derivative locally, i.e. $S=d s_{CS}$. We propose to identify $s_{CS}$ with the entropy of gravitational Chern-Simons terms $\\Omega_{4n-1}$. In the first method ...
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)
Dyon of a non-Abelian Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
Navarro-Lerida, Francisco
2013-01-01
Dyons of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions are presented. These solitons carry both magnetic and electric global charges. The SO(3)xSO(2) solutions are constructed numerically. These are Chern-Simons dyons, differing radically from Julia-Zee dyons. The Chern-Simons densities employed are defined in 3+1 dimensions, and they are the first two of the 'new' Chern-Simons densities introduced recently. They are defined in terms of both Yang-Mills fields and a 5-component isomultiplet Higgs. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
Chern-Simons effect on the dual hydrodynamics in the Maxwell-Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Hu Yapeng, E-mail: huyp@pku.edu.cn [Center for High-Energy Physics, Peking University, Beijing 100871 (China); Center for Quantum Spacetime, Sogang University, Seoul 121-742 (Korea, Republic of); Park, Chanyong, E-mail: cyong21@sogang.ac.kr [Center for Quantum Spacetime, Sogang University, Seoul 121-742 (Korea, Republic of)
2012-08-14
Following the previous work (arXiv:1103.3773 [hep-th]), we give a more general and systematic discussion on the Chern-Simons effect in the 5-dimensional Maxwell-Gauss-Bonnet gravity. After constructing the first order perturbative black brane solution, we extract the stress tensor and charge current of dual fluid. From these results, we find out the dependence of some transport coefficients on the Gauss-Bonnet coupling {alpha} and Chern-Simons coupling {kappa}{sub cs}. We also show that the new anomalous term can provide an additional contribution to the anomalous chiral magnetic conductivity.
Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity
Yokokura, Ryo
2016-01-01
We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional ${\\cal N}=1$ supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the $p$-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the $p$-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.
Self-Dual Chern-Simons Solitons and Generalized Heisenberg Ferromagnet Models
Oh, P; Oh, Phillial
1996-01-01
We consider the (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with the Chern-Simons gauge fields. Self-dual Chern-Simons solitons, the static zero energy solution saturating Bogomol'nyi bounds, are shown to exist when the generalized spin variable is valued in the Hermitian symmetric spaces G/H. By gauging the maximal torus subgroup of H, we obtain self-dual solitons which satisfy vortex-type nonlinear equations thereby extending the two dimensional instantons in a nontrivial way. An explicit example for the CP(N) case is given.
Remarks on the Taub-NUT solution in Chern-Simons modified gravity
Brihaye, Yves
2016-01-01
We discuss the generalization of the NUT spacetime in General Relativity (GR) within the framework of the (dynamical) Einstein--Chern-Simons (ECS) theory with a massless scalar field. These configurations approach asymptotically the NUT spacetime and are characterized by the `electric' and `magnetic' mass parameters and a scalar `charge'. %NUT parameter, the mass and a scalar 'charge'. The solutions are found both analytically and numerically. The analytical approach is perturbative around the Einstein gravity background. Our results indicate that the ECS configurations share all basic properties of the NUT spacetime in GR. However, when considering the solutions inside the event horizon, we find that in contrast to the GR case, the spacetime curvature grows (apparently) without bound.
Kikuchi, Daiki; Yamada, Kei; Asada, Hideki
2014-01-01
Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada, Phys. Rev. Lett. 109, 231101 (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity. We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter $m_{CS}$. Therefore, the international space station site as well as a ground-based experiment is also discussed.
Quinto, A. G.; Ferrari, A. F.; Lehum, A. C.
2016-06-01
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2 + 1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.
On the causality aspects of the dynamical Chern-Simons modified gravity
Porfirio, P J; Nascimento, J R; Petrov, A Yu
2016-01-01
We verify the consistency of the G\\"odel-type solutions within the dynamical Chern-Simons modified gravity in four dimensions, for different forms of matter including dust, fluid, scalar and electromagnetic fields and their combinations, and discuss the possibility of arising the closed timelike curves.
Dirac Branes and Anomalies/Chern-Simons terms in any D
Hill, Christopher T
2009-01-01
The Dirac quantization procedure of a magnetic monopole can be used to derive the coefficient of the D=3 Chern-Simons term through a self-consistency argument, and generalized to any odd D. This yields consistent and covariant axial anomaly coefficients on a D-1 boundary, and Chern-Simons term coefficients. In D=3 magnetic monopoles cannot exist if the Chern-Simons AdA term is present, but the Dirac solenoid becomes a physical closed string carrying electric current. The charge carriers on the string must be consistent with the charge used to quantize the Dirac solenoidal flux, yielding the Chern-Simons term coefficient. In higher odd D the intersection of (D-1)/2 Dirac branes yields a charged world-line permitting the consistency argument. The covariant anomaly coefficients follow readily from generalizing the counterterm. This purely bosonic derivation of anomalies is simple, involving semiclassical evaluation of operators like dAdA...dA in a coherent state representing the brane intersection, and determine...
The ambiguity-free four-dimensional Lorentz-breaking Chern-Simons action
Energy Technology Data Exchange (ETDEWEB)
Brito, F.A. [Departamento de Fisica, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraiba (Brazil); Nascimento, J.R.; Passos, E. [Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, 58051-970 Joao Pessoa, Paraiba (Brazil); Petrov, A.Yu. [Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, 58051-970 Joao Pessoa, Paraiba (Brazil)], E-mail: petrov@fisica.ufpb.br
2008-06-12
The four-dimensional Lorentz-breaking finite and determined Chern-Simons like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the gauge field with the spinor field. Unlike the known schemes of calculations, within this scheme this term is found to be regularization independent.
Chern-Simons forms and four-dimensional N=1 superspace geometry
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Grimm, R.
1987-09-21
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.
Chern-Simons matrix model coherent states and relation to Laughlin wavefunctions
Karabali, Dimitra; Karabali, Dimitra; Sakita, Bunji
2001-01-01
We present two coherent state representations for the Chern-Simons matrix model proposed by Polychronakos and compare the resulting probability distributions to the Laughlin ones. We find that there is agreement on the long distance behavior, but the short distance behavior is different.
Canizares, Priscilla; Gair, Jonathan R.; Sopuerta, Carlos F.
2012-08-01
The detection of gravitational waves from extreme-mass-ratio inspirals (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA) or evolved LISA/New Gravitational Observatory (eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by general relativity and even to test whether general relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. However, up to now, only a restricted class of theories has been investigated. In this paper, we explore to what extent EMRI observations with a space-based gravitational-wave observatory like LISA or eLISA/NGO might be able to distinguish between general relativity and a particular modification of it, known as dynamical Chern-Simons modified gravity. Our analysis is based on a parameter estimation study which uses approximate gravitational waveforms obtained via a radiative-adiabatic method. In this framework, the trajectory of the stellar object is modeled as a sequence of geodesics in the spacetime of the modified-gravity massive black hole. The evolution between geodesics is determined by flux formulae based on general relativistic post-Newtonian and black hole perturbation theory computations. Once the trajectory of the stellar compact object has been obtained, the waveforms are computed using the standard multipole formulae for gravitational radiation applied to this trajectory. Our analysis is restricted to a five
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)
Girardi, G; Girardi, Georges; Grimm, Richard
1999-01-01
The superspace geometry of Chern-Simons forms is shown to be closely related to that of the 3-form multiplet. This observation allows to simplify considerably the geometric structure of supersymmetric Chern-Simons forms and their coupling to linear multiplets. The analysis is carried through in U_K(1) superspace, relevant at the same time for supergravity-matter couplings and for chirally extended supergravity.
Randall-Sundrum brane Universe as a ground state for Chern-Simons gravity
Cordonier-Tello, Fabrizio; Izaurieta, Fernando; Mella, Patricio; Rodríguez, Eduardo
2016-12-01
In stark contrast with the three-dimensional case, higher-dimensional Chern-Simons (CS) theories can have non-topological, propagating degrees of freedom. Finding those vacua that allow for the propagation of linear perturbations, however, proves to be surprisingly challenging. The simplest solutions are somehow ‘hyper-stable’, preventing the construction of realistic, four-dimensional physical models. Here, we show that a Randall-Sundrum (RS) brane Universe can be regarded as a vacuum solution of CS gravity in five-dimensional spacetime, with non vanishing torsion along the dimension perpendicular to the brane. Linearized perturbations around this solution not only exist, but behave as standard gravitational waves on a four-dimensional Minkowski background. In the non-perturbative regime, the solution leads to a four-dimensional ‘cosmological function’ {{Λ }}(x) which depends on the Euler density of the brane. Interestingly, the fact that the solution admits nontrivial linear perturbations seems to be related to an often neglected property of the RS spacetime: that it is a group manifold, or, more precisely, two identical group manifolds glued together along the brane. The gravitational theory is then built around this fact, adding the Lorentz generators and one scalar generator needed to close the algebra. In this way, a conjecture emerges: a spacetime that is also a group manifold can be regarded as the ground state of a CS theory for an appropriate Lie algebra.
Qiang, Li-E
2016-01-01
With continuous advances in related technologies, relativistic gravitational experiments with orbiting gradiometers becomes feasible, which could naturally be incorporated into future satellite gravity missions. Tests of Chern-Simons modified gravity are meaningful since such a modification gives us insights into (possible) parity-violations in gravitation. In this work, we derive, at the post-Newtonian level, the new observables of secular gradients from the non-dynamical Chern-Simons modified gravity, which will greatly improve the constraint on the mass scale $M_{CS}$ that may be drawn from satellite gradiometry measurements. For superconducting gradiometers, a strong bound $M_{CS}\\geq 10^{-7}\\ eV$ could in principle be obtained. For future optical gradiometers based on similar technologies from the LISA PathFinder mission, a even stronger bound $M_{CS}\\geq 10^{-5}\\ eV$ might be expected.
Diphoton signal via Chern-Simons interaction in a warped geometry scenario
Chakrabarty, Nabarun; Mukhopadhyaya, Biswarup; SenGupta, Soumitra
2017-01-01
The Kalb-Ramond field, identifiable with bulk torsion in a five-dimensional Randall Sundrum (RS) scenario, has Chern-Simons interactions with gauge bosons, from the requirement of gauge anomaly cancellation. Its lowest Kaluza Klein (KK) mode on the visible 3-brane can be identified with a spin-0 C P -odd field, namely, the axion. By virtue of the warped geometry and Chern-Simons couplings, this axion has unsuppressed interactions with gauge bosons in contrast to ultra-suppressed interactions with fermions. The ensuing dynamics can lead to a peak in the diphoton spectrum, which could be observed at the LHC, subject to the prominence of the signal. Moreover, the results can be numerically justified when the warp factor is precisely in the range required for stabilization of the electroweak scale.
Maxwell-Chern-Simons Casimir entropy%Maxwell-Chern-Simons规范场的Casimir熵
Institute of Scientific and Technical Information of China (English)
李长松; 刘畅; 姜文英; 杨慧; 潘淑梅; 郑泰玉
2013-01-01
利用泛函积分量子化方法研究了2个平行的、理想的金属线之间在有限温度下Maxwell-Chern-Simons规范场的Casimir熵.分别讨论了低温和高温2种极限情况下的Casimir熵.给出了Maxwell-Chern-Simons规范场的质量为零时的高温和低温的Casimir熵的表达式.结果显示,在绝对零度下,Maxwell-Chern-Simons规范场的Casimir熵等于零,满足热力学第三定律.
Higgs-and Skyrme-Chern-Simons densities in all dimensions
Tchrakian, D. H.
2015-09-01
Two types of new Chern-Simons (CS) densities, both defined in all odd and even dimensions, are proposed. These new CS densities feature a scalar field interacting with the gauge field. In one case this is a Higgs scalar while in the other it is a Skyrme scalar. The motivation is to study the effects of adding these new CS terms to a Lagrangian which supports static soliton solutions prior to their introduction.
N=2-Maxwell-Chern-Simons Model with Anomalous Magnetic Moment Coupling via Dimensional Reduction
Christiansen, H R; Helayël-Neto, José A; Mansur, L R; Nogueira, A L M A
1999-01-01
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.
Chern-Simons functions on toric Calabi-Yau threefolds and virtual motives
Hua, Zheng
2011-01-01
In this note, we give a construction of Chern-Simons functions for toric Calabi-Yau stacks of dimension three using strong exceptional collections. The moduli spaces of sheaves on such stacks can be identified with critical loci of these functions. As an application, we prove a dimension reduction formula for virtual motives. We also compute several recursion formulas for motivic Donaldson-Thomas invariants.
On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
Giombi, S; Kirilin, V; Prakash, S; Skvortsov, E
2016-01-01
Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N. In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the 't Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the 't Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This...
On the higher-spin spectrum in large N Chern-Simons vector models
Giombi, S.; Gurucharan, V.; Kirilin, V.; Prakash, S.; Skvortsov, E.
2017-01-01
Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N . In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1 /N expansion and exactly in the 't Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the 't Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This logarithmic behavior disappears in the strong coupling limit, where the anomalous dimensions turn into those of the critical O( N ) or Gross-Neveu models, in agreement with the conjectured 3d bosonization duality.
Quinto, A G
2016-01-01
We studied the Dynamical Symmetry Breaking (DSB) mechanism in a supersymmetric Chern-Simons theory in $\\left(2+1\\right)$ dimensions coupled to $N$ matter superfields in the superfield formalism. For this purpose, we developed a mechanism to calculate the effective superpotencial $K_{\\mathrm{eff}}\\left(\\sigma_{\\mathrm{cl}},\\alpha\\right)$, where $\\sigma_{\\mathrm{cl}}$ is a background superfield, and $\\alpha$ a gauge-fixing parameter that is introduced in the quantization process. The possible dependence of the effective potential on the gauge parameter have been studied in the context of quantum field theory. We developed the formalism of the Nielsen identities in the superfield language, which is the appropriate formalism to study DSB when the effective potential is gauge dependent. We also discuss how to calculate the effective superpotential via the Renormalization Group Equation (RGE) from the knowledge of the renormalization group functions of the theory, i.e., $\\beta$ functions and anomalous dimensions $\\...
Qiang, Li-E
2014-01-01
Having great accuracy in the range and range rate measurements, the operating GRACE mission and the planed GRACE Follow On mission can in principle be employed to place strong constraints on certain relativistic gravity theories. In this paper, we work out in details the range observable in the non-dynamical Chern-Simons modified gravity for these Satellite-Satellite Tracking measurements. We find out that an characteristic time accumulating signal appears in the range observable in the non-dynamical Chern-Simons gravity, which has no analogy found in the standard metric theories of gravity. The magnitude of this Chern-Simons range signal will reach to a few times of $(\\frac{\\dot{\\theta}}{100r})meters$ for each free flight of these SST missions, here $\\dot{\\theta}$ measures the length scale of the theory and $r$ denotes the orbital radius of the SST mission. Therefore, with the 12 years data from the GRACE mission and the proper data analysis methods, one expects that the mass scale of the non-dynamical CS gr...
Chern-Simons interactions in AdS$_3$ and the current conformal block
Keranen, Ville
2014-01-01
We compute the four point function of scalar fields in AdS$_3$ charged under $U(1)$ Chern-Simons fields using the bulk version of the operator state mapping. Then we show how this four point function is reproduced from a CFT$_2$ with a global $U(1)$ symmetry, through the contribution of the corresponding current operator in the operator product expansion, i.e. through the conformal block of the current operator. We work in a "probe approximation" where the gravitational interactions are ignored, which corresponds to leaving out the energy momentum tensor from the operator product expansion.
A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity
Ali, Sarfraz; Amir, M. Jamil
2016-12-01
This paper is devoted to study some holographic dark energy models in the context of Chern-Simon modified gravity by considering FRW universe. We analyze the equation of state parameter using Granda and Oliveros infrared cut-off proposal which describes the accelerated expansion of the universe under the restrictions on the parameter α. It is shown that for the accelerated expansion phase -1tachyon and dilaton field models and holographic dark energy models on similar fashion. To discuss the accelerated expansion of the universe, we explore the potential and the dynamics of quintessence, K-essence, tachyon and dilaton field models.
Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
Becker, Katrin; Linch, William D; Robbins, Daniel
2016-01-01
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield analogs for the tensor fields, along with covariant superfield strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1 cases, and note that the condition of gauge invariance can be presented cohomologically. Finally, we provide an explicit realization of these structures by dimensional reduction, for example by reducing the three-form of eleven-dimensional supergravity into a superspace with manifest 4D, N=1 supersymmetry.
Chern-Simons couplings at order O (α'2)
Babaei Velni, Komeil; Jalali, Ali
2017-01-01
Using the explicit string scattering calculation and the linear T-dual ward identity, we evaluate the string theory disc amplitude of one Ramond-Ramond field C(p +1 ) and two Neveu-Schwarz B-fields in the presence of a single Dp -brane in type I I B string theory. From this amplitude we extract the O (α'2) (or equivalently four-derivative) part of the Dp-brane couplings involving these fields.
The Chern-Simons Source as a Conformal Family and Its Vertex Operators
Balachandran, A P; Sen-Gupta, K; Stern, A
1992-01-01
In a previous work, a straightforward canonical approach to the source-free quantum Chern-Simons dynamics was developed. It makes use of neither gauge conditions nor functional integrals and needs only ideas known from QCD and quantum gravity. It gives Witten's conformal edge states in a simple way when the spatial slice is a disc. Here we extend the formalism by including sources as well. The quantum states of a source with a fixed spatial location are shown to be those of a conformal family, a result also discovered first by Witten. The internal states of a source are not thus associated with just a single ray of a Hilbert space. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. We also argue in favor of a similar nonabelian result. The spin-statistics theorem is established for Chern-Simons dynamics even though the sources are not described by relativistic quantum fields. The proof employs geometrical methods whi...
Dimensional Reduction of a Lorentz- and CPT-violating Chern-Simons Model
Belich, H; Orlando, M T D
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 reduction 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, $v^{\\mu}$. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of $v^{\\mu}$. The solution of the wave equations shows a behavior similar but which deviates from the usual MCS electrodynamics by some correction-terms (dependent on the background field). These solutions also indicate the existence of spatial-anisotropy in the case $v^{\\mu}$ is purely space-like, which is consistent with the determination of a privileged direction is space, v. The reduced model exhibits stability, but the causality can be jeopardized by some modes. PACS numbers: 11.10.Kk; 11.30.Cp; 11.30.Er; 1...
Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons $QED_{3}$?
Belich, H; Helayël-Neto, José A
2000-01-01
The low-energy electron-electron scattering potential is derived and discussed for the Maxwell-Chern-Simons model coupled to QED_3 with spontaneous symmetry breaking. One shows that the Higgs mechanism might favour electron-electron bound states.
Ham, Ji-Young; Lee, Joongul
2016-11-01
We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3) using the Schläfli formula for the generalized Chern-Simons function on the family of C(2n, 3) cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee's methods. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic C(2n, 3) orbifolds.
Finite action principle for Chern-Simons AdS gravity
Mora, P; Troncoso, R; Zanelli, J
2004-01-01
A finite action action 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 the 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.
Primordial massive gravitational waves from Einstein-Chern-Simons-Weyl gravity
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Myung, Yun Soo; Moon, Taeyoon, E-mail: ysmyung@inje.ac.kr, E-mail: tymoon@inje.ac.kr [Institute of Basic Sciences and Department of Computer Simulation, Inje University, Gimhae 621-749 (Korea, Republic of)
2014-08-01
We investigate the evolution of cosmological perturbations during de Sitter inflation in the Einstein-Chern-Simons-Weyl gravity. Primordial massive gravitational waves are composed of one scalar, two vector and four tensor circularly polarized modes. We show that the vector power spectrum decays quickly like a transversely massive vector in the superhorizon limit z → 0. In this limit, the power spectrum coming from massive tensor modes decays quickly, leading to the conventional tensor power spectrum. Also, we find that in the limit of m{sup 2} → 0 (keeping the Weyl-squared term only), the vector and tensor power spectra disappear. It implies that their power spectra are not gravitationally produced because they (vector and tensor) are decoupled from the expanding de Sitter background, as a result of conformal invariance.
Diphoton excess via Chern-Simons interaction in a warped geometry scenario
Chakrabarty, Nabarun; SenGupta, Soumitra
2016-01-01
We offer an explanation of the recently observed 750 GeV diphoton peak at the Large Hadron Collider (LHC) in terms of an axion related to the 5-dimensional Kalb-Ramond (KR) field in a Randall-Sundrum warped geometry scenario. The KR field, identifiable with bulk torsion, has Chern-Simons interactions with gauge boson pairs. These in turn yield unsuppressed coupling of the torsion to gluon as well as photon pairs in (3+1) dimensions, while the warped geometry enforces ultra-suppressed interaction with fermion pairs . We show that the observed results can be numerically justified when the warp factor is precisely in the range required for stabilisation of the electroweak scale.
Phase space structure of non-abelian Chern-Simons particles
Kim, M H; Myung-Ho Kim; Phillial Oh
1994-01-01
We investigate the classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles by first constructing the product space of associated SU(n+1) bundle with {\\bf CP}^n as the fiber. We calculate the Poisson bracket using the symplectic structure on the associated bundle and find that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, we take a direct product of the associated bundle by the space of all connections and choose a specific connection by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Ref.\\cite{lo1}.
Santangelo, E M
2008-01-01
This talk presents a study of massless relativistic Dirac fields in three Euclidean dimensions, at finite temperature and density, in the presence of a uniform electromagnetic background. Apart from explaining the behavior of Hall's conductivity for graphene, our results show a direct relationship between the selection of a phase for the Dirac determinant and the generation (or lack thereof) of Berry's phases and Chern-Simons terms.
de Azcárraga, J A; Picon, M; Varela, O; Azcarraga, Jose A. de; Izquierdo, Jose M.; Picon, Moises; Varela, Oscar
2003-01-01
We study how to generate new Lie algebras $\\mathcal{G}(N_0,..., N_p,...,N_n)$ from a given one $\\mathcal{G}$. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter $\\lambda$ which rescales the coordinates of the Lie (super)group $G$, $g^{i_p} \\to \\lambda^p g^{i_p}$, in a way subordinated to the splitting of $\\mathcal{G}$ as a sum $V_0 \\oplus ... \\oplus V_p \\oplus ... \\oplus V_n$ of vector subspaces. We also show that, under certain conditions, one of the obtained algebras may correspond to a generalized \\.In\\"on\\"u-Wigner contraction in the sense of Weimar-Woods, but not in general. The method is used to derive the M-theory superalgebra, including its Lorentz part, from $osp(1|32)$. It is also extended to include gauge free differential (super)algebras and Chern-Simons theories, and then applied to D=3 CS supergravity.
Rostam Zadeh, S.; Gousheh, S. S.
2017-03-01
In this paper, we study the significance of the UY(1 ) Chern-Simons term in general, and its baryonic contribution in particular, for the evolution of the matter asymmetries and the hypermagnetic field in the temperature range 100 GeV ≤T ≤10 TeV . We show that an initial helical hypermagnetic field, denoted by BY(0 ), can grow matter asymmetries from zero initial value. However, the growth which is initially quadratic with respect to BY(0 ) saturates for values larger than a critical value. The inclusion of the baryonic contribution reduces this critical value, leading to smaller final matter asymmetries. Meanwhile, BY(TEW) becomes slightly larger than BY(0 ). In the absence of the UY(1 ) Chern-Simons term, the final values of matter asymmetries grow without saturation. Conversely, we show that an initial matter asymmetry can grow an initial seed of a hypermagnetic field, provided the Chern-Simons term is taken into account. The growth process saturates when the matter asymmetry drops abruptly. When the baryonic contribution is included, the saturation occurs at an earlier time, and BY(TEW) becomes larger. We also show that the baryonic asymmetry and the magnetic field strength can be within the acceptable range of present day data, provided the inverse cascade process is also taken into account; however, the magnetic field scale obtained from this simple model is much lower than the ones usually assumed for gamma-ray propagation.
Ham, J.-Y.; Lee, J.
2016-09-01
We calculate the Chern-Simons invariants of twist-knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present concrete formulae and calculations. We use the Pythagorean Theorem, which was used by Ham, Mednykh and Petrov, to relate the complex length of the longitude and the complex distance between the two axes fixed by two generators. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic twist-knot orbifolds. We also derive some interesting results. The explicit formulae of the A-polynomials of twist knots are obtained from the complex distance polynomials. Hence the edge polynomials corresponding to the edges of the Newton polygons of the A-polynomials of twist knots can be obtained. In particular, the number of boundary components of every incompressible surface corresponding to slope -4n+2 turns out to be 2. Bibliography: 39 titles.
Lu, Yuan-Ming; Vishwanath, Ashvin
2016-04-01
We study (2+1)-dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry-enriched topological (SET) phases. Here, we present a K -matrix Chern-Simons approach to identify distinct phases with Abelian topological order, in the presence of unitary or antiunitary global symmetries. A key step is the identification of a smooth edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method by classifying Z2 topological order (Z2 spin liquids) in the presence of an internal Z2 global symmetry for which we find six distinct phases. These include two phases with an unconventional action of symmetry that permutes anyons leading to symmetry-protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry-enriched Laughlin states and double-semion theories are also discussed. Somewhat surprisingly, we observe that (i) gauging the global symmetry of distinct SET phases leads to topological orders with the same total quantum dimension, and (ii) a pair of distinct SET phases can yield the same topological order on gauging the symmetry.
Cosmological Analysis of Dynamical Chern-Simons Modified Gravity via Dark Energy Scenario
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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.
Chern-Simons improved Hamiltonians for strings in three space dimensions
Gordeli, Ivan; Melnikov, Dmitry; Niemi, Antti J.; Sedrakyan, Ara
2016-07-01
In the case of a structureless string the extrinsic curvature and torsion determine uniquely its shape in three-dimensional ambient space, by way of solution of the Frenet equation. In many physical scenarios there are in addition symmetries that constrain the functional form of the ensuing energy function. For example, the energy of a structureless string should be independent of the way the string is framed in the Frenet equation. Thus the energy should only involve the curvature and torsion as dynamical variables, in a manner that resembles the Hamiltonian of the Abelian Higgs model. Here we investigate the effect of symmetry principles in the construction of Hamiltonians for structureless strings. We deduce from the concept of frame independence that in addition to extrinsic curvature and torsion, the string can also engage a three-dimensional Abelian bulk gauge field as a dynamical variable. We find that the presence of a bulk gauge field gives rise to a long-range interaction between different strings. Moreover, when this gauge field is subject to Chern-Simons self-interaction, it becomes plausible that interacting strings are subject to fractional statistics in three space dimensions.
Bazeia, D; Nascimento, J R S; Ribeiro, R F; Wotzasek, C
2001-01-01
We study the equivalence between a nonlinear self-dual model (NSD) with the Born-Infeld-Chern-Simons (BICS) models using an iterative gauge embedding procedure that produces the duality mapping, including the case where the NSD model is minimally coupled to dynamical, U(1) charged fermionic matter. The duality mapping introduces a current-current interaction term while at the same time the minimal coupling of the original nonlinear self-dual model is replaced by a non-minimal magnetic like coupling in the BICS side.
Rostam Zadeh, S.; Gousheh, S. S.
2016-09-01
We study the simultaneous evolution of electron, neutrino, and quark asymmetries and large-scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range 100 GeV ≤T ≤10 TeV , taking into account the chirality flip processes via inverse Higgs decays and fermion number violation due to Abelian anomalies. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The UY(1 ) Chern-Simons term affects the resulting anomalous magnetohydrodynamic equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition (TEW˜100 GeV ) for a variety of critical ranges for their initial values at T =10 TeV . We first investigate the results of this sign change by directly comparing our results with those obtained in one of the previous works and find that matter asymmetry generation increases considerably in the presence of a strong hypermagnetic field. Furthermore, we find that a strong hypermagnetic field can generate matter asymmetry starting from absolutely zero asymmetry, while matter asymmetry can generate a hypermagnetic field provided the initial value of the latter is nonzero.
Haggard, Hal M.; Muxin Han; Wojciech Kamiński; Aldo Riello
2015-01-01
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat co...
Quinto, A G
2016-01-01
In this paper we study the Nielsen identity for the supersymmetric Chern-Simons-matter model in the superfield formalism, in three spacetime dimensions. The Nielsen identity is essential to understand the gauge invariance of the symmetry breaking mechanism, and it is calculated by using the BRST invariance of the model. We discuss the technical difficulties in applying this identity to the complete effective superpotential, but we show how we can study in detail the gauge independence of one part of the effective superpotential, $K_{eff}$. We calculate the renormalization group functions of the model for arbitrary gauge-fixing parameter, finding them to be independent of the gauge choice. This result can be used to argue that $K_{eff}$ also does not depend on the gauge parameter. We discuss the possibility of the extension of these results to the complete effective superpotential.
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Cantanhede, Carlisson M. [Instituto de Fisica Teorica (IFT/UNESP), Sao Paulo, SP (Brazil); Casana, Rodolfo; Ferreira Junior, Manoel M. [Universidade Federal do Maranhao (UFMA), MA (Brazil). Dept. de Fisica; Hora, Eduardo da [Universidade Federal da Paraiba (UFPB), PB (Brazil). Dept. de Fisica
2012-07-01
Full text: Since the seminal works by Abrikosov [1] and Nielsen-Olesen [2] showing the existence of uncharged vortex, such nonperturbative solutions have been a theoretical issue of enduring interest. Already, the electrically charged vortices are obtained only in abelian models endowed with the Chern-Simons term [3,4]. This remains valid even in the context of highly nonlinear models, such as the Born-Infield electrodynamics. In this work, we demonstrated the existence of electrically charged BPS vortices in a Maxwell-Higgs model without the Chern- Simons term but endowed with a CPT-even and parity-odd Lorentz-violating (LV) structure. The LV term belonging to the CPT-even electrodynamics of the Standard Model Extension [5] plays a similar role that of the Chern-Simons term, mixing the electric and magnetic sectors. Besides the LV coefficients provide a very rich set of vortex configurations exhibiting electric's field inversion also are responsible by controlling the characteristic length of the vortex and by the flipping of the magnetic flux. [1] A. Abrikosov, Sov. Phys. JETP 32, 1442 (1957). [2] H. Nielsen, P. Olesen, Nucl. Phys. B 61, 45 (1973). [3] R. Jackiw and E. J. Weinberg, Phys. Rev. Lett. 64, 2234 (1990). [4] C.K. Lee, K.M. Lee, H. Min, Phys. Lett. B 252, 79 (1990) [5] D. Colladay and V. A. Kostelecky, Phys. Rev. D 55, 6760 (1997); Phys. Rev. D 58, 116002 (1998). (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)
Chern–Simons theory in SIM(1) superspace
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Vohánka, Jiří [Department of Theoretical Physics and Astrophysics, Masaryk University, Kotlářská 267/2, 611 37, Brno (Czech Republic); Faizal, Mir, E-mail: mirfaizalmir@gmail.com [Department of Physics and Astronomy, University of Waterloo, N2L 3G1, Waterloo, ON (Canada)
2015-12-14
In this paper, we will analyze a three-dimensional supersymmetric Chern–Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern–Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern–Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern–Simons action using these SIM(1) superfields. Furthermore, we will analyze the gauge symmetry of this Chern–Simons theory. This is the first time that a Chern–Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary.
New phase transitions in Chern–Simons matter theory
Directory of Open Access Journals (Sweden)
Ali Zahabi
2016-02-01
Full Text Available Applying the machinery of random matrix theory and Toeplitz determinants we study the level k, U(N Chern–Simons theory coupled with fundamental matter on S2×S1 at finite temperature T. This theory admits a discrete matrix integral representation, i.e. a unitary discrete matrix model of two-dimensional Yang–Mills theory. In this study, the effective partition function and phase structure of the Chern–Simons matter theory, in a special case with an effective potential namely the Gross–Witten–Wadia potential, are investigated. We obtain an exact expression for the partition function of the Chern–Simons matter theory as a function of k, N, T, for finite values and in the asymptotic regime. In the Gross–Witten–Wadia case, we show that ratio of the Chern–Simons matter partition function and the continuous two-dimensional Yang–Mills partition function, in the asymptotic regime, is the Tracy–Widom distribution. Consequently, using the explicit results for free energy of the theory, new second-order and third-order phase transitions are observed. Depending on the phase, in the asymptotic regime, Chern–Simons matter theory is represented either by a continuous or discrete two-dimensional Yang–Mills theory, separated by a third-order domain wall.
Navarro-Lerida, Francisco
2014-01-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons--Yang-Mills-Higgs (HCS-YMH) models in $3+1$ dimensions, one with gauge group $SO(5)$ and the other with $SU(3)$. The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so they do not vanish. The solutions of the $SO(5)$ model carry only electric charge and zero magnetic charge, while the solutions of the $SU(3)$ model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HC...
Navarro-Lérida, Francisco; Tchrakian, D. H.
2015-05-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons-Yang-Mills-Higgs (HCS-YMH) models in 3+1 dimensions, one with gauge group SO(5) and the other with SU(3). The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so that they do not vanish. The solutions of the SO(5) model carry only electric charge and zero magnetic charge, while the solutions of the SU(3) model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter, however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the SU(3) HCS-YMH, we have considered the question of angular momentum and it turns out that it vanishes.
Zadeh, S Rostam
2015-01-01
We study simultaneous evolution of fermion asymmetries and large scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range $100$GeV$\\leq T\\leq 10$TeV, taking into account the chirality flip processes via Higgs inverse decays and fermion number violation due to Abelian anomalies for electrons, neutrinos and quarks in the presence of hypermagnetic fields. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The Chern-Simons term affects the resulting anomalous magnetohydrodynamic (AMHD) equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition ($T_{EW} \\sim 100$GeV) for a...
Searching for a Connection Between Matroid Theory and String Theory
Nieto, J A
2004-01-01
We make a number of observations about matter-ghost string phase, which may eventually lead to a formal connection between matroid theory and string theory. In particular, in order to take advantage of the already established connection between matroid theory and Chern-Simons theory, we propose a generalization of string theory in terms of some kind of Kahler metric. We show that this generalization is closely related to the Kahler-Chern-Simons action due to Nair and Schiff. We also add new information about the relationship between matroid theory, D=11 supergravity and Chern-Simons formalism.
Battistel, O A
2001-01-01
We investigate the possibility of Lorentz and CPT violations in the photon sector, of the Chern-Simons form, be induced by radiative corrections arising from the Lorentz and CPT non-invariant fermionic sector of an extended version of QED. By analyzing the modified vacuum polarization tensor, three contributions are considered: two of them can be identified with well known amplitudes; the (identical) QED vacuum polarization tensor and the (closely related) $AVV$ triangular amplitude. These amplitudes are evaluated in their most general form (to include in our discussion automatically the question of ambiguities) on the point of view of a strategy to manipulate and calculate divergent amplitudes that can avoid the explicit calculation of divergent integrals. Rather than this only general properties are used in intermediary steps. With this treatment, the results obtained by others authors can be easily recovered and we show that, if we choose to impose U(1) gauge invariance maintenance in the pure QED calculat...
Energy Technology Data Exchange (ETDEWEB)
Huang Yongchang [Institute of Theoretical Physics, Beijing University of Technology, Beijing 100022 (China); CCAST (World Laboratory), Beijing 100080 (China)], E-mail: ychuang@bjut.edu.cn; Huo Qiuhong [Institute of Theoretical Physics, Beijing University of Technology, Beijing 100022 (China)
2008-04-24
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{sub 0}{sup s}(x) charge.
Energy Technology Data Exchange (ETDEWEB)
Battistel, O.A. [Dept. of Physics - CCNE, Universidade Federal de Santa Maria, RS (Brazil); Dallabona, G. [Dept. of Physics - ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, MG (Brazil)
2004-07-01
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.)
Invariants from classical field theory
Diaz, Rafael
2007-01-01
We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory.
Schwinger–Dyson functional in Chern–Simons theory
Directory of Open Access Journals (Sweden)
E. Guadagnini
2016-11-01
Full Text Available In perturbative SU(N Chern–Simons gauge theory, it is shown that the Schwinger–Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that the renormalized Schwinger–Dyson functional is related with the generating functional of the correlation functions of the gauge connections by some kind of duality transformation.
Energy Technology Data Exchange (ETDEWEB)
Menezes, G.; Svaiter, N.F. E-mail: gsm@cbpf.br; nfuxsvai@cbpf.br
2006-04-15
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)
New Products, Chern Classes, and Power Operations in Orbifold K-theory
Edidin, Dan; Kimura, Takashi
2012-01-01
We develop a theory of inertial pairs on smooth, separated Deligne-Mumford quotient stacks. An inertial pair determines inertial products and an inertial Chern character. Every vector bundle V on such a stack defines two new inertial pairs and we recover, as special cases, both the orbifold product and the virtual product of [GLSUX07]. We show that for strongly Gorenstein inertial pairs there is also a theory of Chern classes and compatible power operations. An important application is to show that there is a theory of Chern classes and compatible power operations for the virtual product. We also show that when the stack is a quotient [X/G], with G diagonalizable, inertial K-theory has a lambda-ring structure. This implies that for toric Deligne-Mumford stacks there is a corresponding lambda-ring structure associated to virtual K-theory. As an example we compute the semi-group of lambda-positive elements in the virtual lambda-ring of the weighted projective stack P(1,2). Using the virtual orbifold line elemen...
Higher Spin Lifshitz Theory and Integrable Systems
Gutperle, Michael
2014-01-01
In this note we construct asymptotically Lifshitz spacetimes in the Chern-Simons formulation of three dimensional higher spin gravity and relate the resulting theories to integrable systems which are elements of the KdV hierarchy.
Canizares, Priscilla; Sopuerta, Carlos F
2012-01-01
[abridged] The detection of gravitational waves from extreme-mass-ratio (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA or eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by General Relativity and even to test whether General Relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. In this paper, we explore to what extent EMRI observations with LISA or eLISA/NGO might be able to distinguish between G...
Level N Teichmüller TQFT and Complex Chern–Simons Theory
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Marzioni, Simone
In this manuscript we review the construction of the Teichmüller TQFT in [AK1], upgrading it to a theory dependent on an extra odd integer N using results developed in [AK3]. We also describe how this theory is related with quantum Chern–Simons Theory at level N with gauge group PSL(2, C)....
Composite fermions for fractionally filled Chern bands
Shankar, R.
2012-02-01
We consider fractionally filled bands with a non-zero Chern index that exhibit the Fractional Quantum Hall Effect in zero external fieldootnotetextR. Roy and S. Sondhi, Physics 4, 46 (2011) and papers reviewed therein. a possibility supported by numerical work.ootnotetextIbid. Analytic treatments are complicated by a non-constant Berry flux and the absence of Composite Fermions (CF), which would not only single out preferred fractions, but also allow us compute numerous response functions at nonzero frequencies, wavelengths and temperature using either Chern-Simons field theory or our Hamiltonian formalism.ootnotetextG. Murthy and R. Shankar, Rev. Mod. Phys., 75, 1101, (2003) We describe a way to introduce CF's by embedding the Chern band in an auxiliary problem involving Landau levels. The embedded band can be designed to approximate a prescribed Chern density in k space which determines the commutation relations of the charge densities and hence preserve all dynamical and algebraic aspects of the original problem. We find some states for which the filling fraction and dimensionless Hall conductance are not equal. The approach extends to two-dimensional time-reversal invariant topological insulators and to composite bosons.
Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
Möller, Gunnar; Cooper, Nigel R.
2015-09-01
The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number C . We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with |C |>1 . We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor ν , defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors ν =r /(r |C |+1 ) for bosons, or ν =r /(2 r |C |+1 ) for fermions. This series includes a bosonic integer quantum Hall state in |C |=2 bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions.
Kosambi-Cartan-Chern (KCC) theory for higher-order dynamical systems
Harko, Tiberiu; Pantaragphong, Praiboon; Sabau, Sorin V.
2016-12-01
The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, with the solution curves of the dynamical system described by methods inspired by the theory of geodesics in a Finsler spaces. The evolution of a dynamical system is geometrized by introducing a nonlinear connection, which allows the construction of the KCC covariant derivative, and of the deviation curvature tensor. In the KCC theory, the properties of any dynamical system are described in terms of five geometrical invariants, with the second one giving the Jacobi stability of the system. Usually, the KCC theory is formulated by reducing the dynamical evolution equations to a set of second-order differential equations. In this paper, we introduce and develop the KCC approach for dynamical systems described by systems of arbitrary n-dimensional first-order differential equations. We investigate in detail the properties of the n-dimensional autonomous dynamical systems, as well as the relationship between the linear stability and the Jacobi stability. As a main result we find that only even-dimensional dynamical systems can exhibit both Jacobi stability and instability behaviors, while odd-dimensional dynamical systems are always Jacobi unstable, no matter their Lyapunov stability. As applications of the developed formalism we consider the geometrization and the study of the Jacobi stability of the complex dynamical networks, and of the Λ-Cold Dark Matter (ΛCDM) cosmological models, respectively.
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
Novel BPS Wilson loops in three-dimensional quiver Chern–Simons-matter theories
Directory of Open Access Journals (Sweden)
Hao Ouyang
2016-02-01
Full Text Available We show that generic three-dimensional N=2 quiver super Chern–Simons-matter theories admit Bogomol'nyi–Prasad–Sommerfield (BPS Drukker–Trancanelli (DT type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy–Bergman–Jafferis–Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto–Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops happens for special values of the parameters.
Instanton Effects in Orientifold ABJM Theory
Moriyama, Sanefumi
2015-01-01
We investigate another supersymmetric Chern-Simons theory called orientifold ABJM theory, which replaces the unitary supergroup structure of the ABJM theory by an orthosymplectic one. The non-perturbative structure of it is completely clarified by considering the duplication of the quiver.
Undergraduate Lecture Notes in Topological Quantum Field Theory
2008-01-01
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon
Energy Technology Data Exchange (ETDEWEB)
Canfora, Fabrizio, E-mail: canfora@cecs.cl [Centro de Estudios Cientificos (CECs), Valdivia (Chile); Universidad Andres Bello, Av. Republica 440, Santiago (Chile); Gomez, Arturo, E-mail: arturo.gomez@proyectos.uai.cl [Departamento de Ciencias, Facultad de Artes Liberales y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Viña del Mar. (Chile); Sorella, Silvio Paolo, E-mail: sorella@uerj.br [UERJ, Universidade do Estado do Rio de Janeiro (UERJ), Instituto de Física Teórica, Rua São Francisco Xavier 524, 20550-013, Maracaná, Rio de Janeiro (Brazil); Vercauteren, David, E-mail: vercauteren.uerj@gmail.com [UERJ, Universidade do Estado do Rio de Janeiro (UERJ), Instituto de Física Teórica, Rua São Francisco Xavier 524, 20550-013, Maracaná, Rio de Janeiro (Brazil)
2014-06-15
The two-point gauge correlation function in Yang–Mills–Chern–Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory. -- Highlights: •We implement the Gribov quantization to the Topologically massive Yang–Mills theory. •We find a modified propagator at strong coupling by the Gribov horizon. •The gauge propagator depends on the topological mass and the coupling constant. •By studying the gauge propagator we describe the confined–deconfined regimes.
Composite particle and field theory in atomic quantum Hall effect
Institute of Scientific and Technical Information of China (English)
Zhao Bo; Chen Zeng-Bing
2005-01-01
In this paper, we explore the composite particle description of the atomic quantum Hall (QH) effect. We further give the Chern-Simon-Gross-Pitaevskii (CSGP) effective theory for the atomic Hall liquid, which is the counterpart of Chern-Simon theory in electron Hall effect. What we obtained is equivalent to the Laughlin wavefunction approach.Our results show that in terms of composite particles, the atomic Hall effect is really the same as the electronic QH effect. The CSGP effective theory would shed new light on the atomic QH effect.
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.
The Chern Character of Certain Infinite Rank Bundles arising in Gauge Theory
Mickelsson, Jouko
2012-01-01
A cocycle $\\Omega: P \\times G \\to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$ defines then characteristic classes on $X.$ This observation becomes useful in the case of infinite dimensional groups. It typically happens that a representation of $G$ is not given by linear operators which differ from the indentity by a trace-class operator. For this reason the Chern character of a vector bundle associated to the principal fibration $P \\to P/G$ is ill-defined. But it may happen that the Lie algebra representations of the group $H$ are given in terms of trace-class operators and therefore the Chern character is well-defined; this observation is useful especially if the map $g\\mapsto \\Omega(p;g)$ is a homotopy equivalence on the image for any $p\\in P.$ We apply this method to the case $P= \\Cal A,$ the space of gauge connections in a finite-dimensional vector ...
Fifty Years of Yang-Mills Theory and my Contribution to it
Jackiw, Roman W
2004-01-01
On the fiftieth anniversary of Yang-Mills theory, I review the contribution to its understanding by my collaborators and me. Contents: 1.Gauge Theories and Quantum Anomalies; 2.Mathematical Connections; 3. Gauge Field Dynamics other than Yang-Mills; 4. Gauge Formalism for General Relativity Variables; A. Christoffel connection as a gauge potential, B. Gravitational Chern-Simons term from gauge theory Chern-Simons term, C. Coordinate transformations in general relativity and gauge theory, (i) Response to changes in coordinates (ii) Invariant fields and constants of motion. References.
Higher Spin Lifshitz Theories and the KdV-Hierarchy
Beccaria, Matteo; Li, Yi; Macorini, Guido
2015-01-01
In this paper three dimensional higher spin theories in the Chern-Simons formulation with gauge algebra $sl(N,R)$ are investigated which have Lifshitz symmetry with scaling exponent $z$. We show that an explicit map exists for all $z$ and $N$ relating the Lifshitz Chern-Simons theory to the $(n,m)$ element of the KdV hierarchy. Furthermore we show that the map and hence the conserved charges are independent of $z$. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.
Nekrasov, Nikita
2004-01-01
We present the evidence for the existence of the topological string analogue of M-theory, which we call Z-theory. The corners of Z-theory moduli space correspond to the Donaldson-Thomas theory, Kodaira-Spencer theory, Gromov-Witten theory, and Donaldson-Witten theory. We discuss the relations of Z-theory with Hitchin's gravities in six and seven dimensions, and make our own proposal, involving spinor generalization of Chern-Simons theory of three-forms. Based on the talk at Strings'04 in Paris.
Construction and classification of novel BPS Wilson loops in quiver Chern–Simons-matter theories
Directory of Open Access Journals (Sweden)
Hao Ouyang
2016-09-01
Full Text Available In this paper we construct and classify novel Drukker–Trancanelli (DT type BPS Wilson loops along infinite straight lines and circles in N=2,3 quiver superconformal Chern–Simons-matter theories, Aharony–Bergman–Jafferis–Maldacena (ABJM theory, and N=4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto–Yin (GY type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N=4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.
The Kodama state for topological quantum field theory beyond instantons
Cartas-Fuentevilla, R
2005-01-01
Constructing a symplectic structure that preserves the ordinary symmetries and the topological invariance for topological Yang-Mills theory, it is shown that the Kodama (Chern-Simons) state traditionally associated with a topological phase of unbroken diffeomorphism invariance for instantons, exists actually for the complete topological sector of the theory. The case of gravity is briefly discussed.
Probing Wilson loops in N=4 Chern–Simons-matter theories at weak coupling
Directory of Open Access Journals (Sweden)
Luca Griguolo
2016-02-01
Full Text Available For three-dimensional N=4 super-Chern–Simons-matter theories associated to necklace quivers U(N0×U(N1×⋯U(N2r−1, we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced in arXiv:1506.07614. We perform a two-loop evaluation and find the same result for the two kinds of operators, so moving to higher loops a possible quantum uplift of the classical degeneracy. We also compute the 1/4 BPS bosonic Wilson loop and discuss the quantum version of the cohomological equivalence between fermionic and bosonic Wilson loops. We compare the perturbative result with the Matrix Model prediction and find perfect matching, after identification and remotion of a suitable framing factor. Finally, we discuss the potential appearance of three-loop contributions that might break the classical degeneracy and briefly analyze possible implications on the BPS nature of these operators.
Computing Black Hole entropy in Loop Quantum Gravity from a Conformal Field Theory perspective
Agullo, Ivan; Diaz-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.
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
Energy Technology Data Exchange (ETDEWEB)
Agulló, Iván [Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637 (United States); Borja, Enrique F. [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Díaz-Polo, Jacobo, E-mail: Ivan.Agullo@uv.es, E-mail: Enrique.Fernandez@uv.es, E-mail: Jacobo.Diaz@uv.es [Institute for Gravitation and the Cosmos, Physics Department, Penn State, University Park, PA 16802 (United States)
2009-07-01
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.
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.
Phase diagram of 4D field theories with chiral anomaly from holography
Ammon, Martin; Macedo, Rodrigo P
2016-01-01
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
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.
Remarks on Lorentz and CPT violation in field theory
Mariz, T; Passos, E
2006-01-01
In this brief review we explicitly calculate the radiative corrections to the Chern-Simons-like term in the cases of zero and finite temperature, and in the gravity theory. Our results are obtained under the general guidance of dimensional regularization.
Localization of 3d $\\mathcal{N}=2$ Supersymmetric Theories on $S^1 \\times D^2$
Yoshida, Yutaka
2014-01-01
We study three dimensional N=2 supersymmetric Chern-Simons-Matter theories on the direct product of circle and two dimensional hemisphere (S^1 x D^2) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of three dimensional superpotential term and Chern-Simons term and show inflows of bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional N=(0,2) type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.
Directory of Open Access Journals (Sweden)
M.R. Setare
2016-01-01
Full Text Available In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern–Simons-like theories of gravity (CSLTG and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
Energy Technology Data Exchange (ETDEWEB)
Setare, M.R., E-mail: rezakord@ipm.ir; Adami, H., E-mail: hamed.adami@yahoo.com
2016-01-15
In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern–Simons-like theories of gravity (CSLTG) and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
Hassett, Brendan; Tschinkel, Yuri
2017-01-01
Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail. .
5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory
Energy Technology Data Exchange (ETDEWEB)
Bergman, Oren [Department of Physics, Technion, Israel Institute of Technology,Haifa, 32000 (Israel); Rodríguez-Gómez, Diego [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain); Zafrir, Gabi [Department of Physics, Technion, Israel Institute of Technology,Haifa, 32000 (Israel)
2014-03-25
We present a number of investigations of 5d N=1 supersymmetric gauge theories that make use of 5-brane web constructions and the 5d superconformal index. These include an observation of enhanced global symmetry in the 5d fixed point theory corresponding to SU(N) gauge theory with Chern-Simons level ±N, enhanced global symmetries in quiver theories, and dualities between quiver theories and non-quiver theories. Instanton contributions play a crucial role throughout.
The Topological Theory of the Milnor Invariant $\\bar{\\mu}(1,2,3)$
Leal, Lorenzo
2007-01-01
We study a topological Abelian gauge theory that generalizes the Abelian Chern-Simons one, and that leads in a natural way to the Milnor's link invariant $\\bar{\\mu}(1,2,3)$ when the classical action on-shell is calculated.
Joint Simon effect：Current research, influencing factors and theories%联合 Simon 效应：现状、影响因素与理论解释
Institute of Scientific and Technical Information of China (English)
徐胜; 宋晓蕾
2016-01-01
The Joint Simon Effect (JSE) is a spatial stimulus-response compatibility effect that appears when two participants complete complementary components of a standard Simon task. The effect is considered as a valid index of the degree of self-other integration. Two main factors can influence the effect:social and nonsocial factors. Researchers explain JSE through the social facilitation theory, the co-representation account, the spatial response coding theory and the referential coding account. Future work on JSE should further explore the factors that influence it and the underlying brain mechanism, and further investigate its theoretical underpinnings.%联合 Simon 效应是一种空间刺激–反应相容性效应，它出现在当两个参与者完成 Simon 任务的互补成分时。该效应被认为是反映自我–他人整合程度的一个有效指标。影响此现象的因素主要包括社会和非社会因素。社会促进理论、共同表征理论、空间反应编码理论和参照编码理论对该效应作出了解释。未来关于联合Simon 效应的研究需深入探讨其影响因素以及脑机制，并进一步完善理论解释。
Topological gauge theories and group cohomology
Dijkgraaf, Robbert; Witten, Edward
1990-04-01
We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H 4( BG, Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H 3( G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H 4( BG, Z) to H 3( G, Z). We generalize this correspondence to topological “spin” theories, which are defined on three manifolds with spin structure, and are related to what might be called Z 2 graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.
Entanglement Entropy in Warped Conformal Field Theories
Castro, Alejandra; Iqbal, Nabil
2015-01-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL(2,R)xU(1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
Integrable Lattice Models From Gauge Theory
Witten, Edward
2016-01-01
These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)
Second order higher-derivative corrections in Double Field Theory
Lescano, Eric
2016-01-01
HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives ${\\cal O} (\\alpha'{}^2)$ for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.
Directory of Open Access Journals (Sweden)
Hal M. Haggard
2015-11-01
Full Text Available We study the expectation value of a nonplanar Wilson graph operator in SL(2,C Chern–Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern–Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern–Simons action. This can be understood as arising from the relation between Chern–Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL(2,C Chern–Simons theory in 3 dimensions with knotted graph defects.
Symmetry analysis for anisotropic field theories
Energy Technology Data Exchange (ETDEWEB)
Parra, Lorena; Vergara, J. David [Instituto de Ciencias Nucleares, UNAM, Circuito Exterior s/n, Ciudad Universitaria. Delg. Coyoacan. C.P. 04510 Mexico DF (Mexico)
2012-08-24
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.
Supersymmetric theories on squashed five-sphere
Imamura, Yosuke
2012-01-01
We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.
Jain states in a matrix theory of the quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Cappelli, Andrea [I.N.F.N. and Dipartimento di Fisica, Via G. Sansone 1, 50019 Sesto Fiorentino, Florence (Italy); Rodriguez, Ivan D. [I.N.F.N. and Dipartimento di Fisica, Via G. Sansone 1, 50019 Sesto Fiorentino, Florence (Italy)
2006-12-15
The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension of Susskind's noncommutative approach. The theory describes D0-branes, nonrelativistic particles with matrix coordinates and gauge symmetry, that realize a matrix generalization of the quantum Hall effect. Matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the expected Laughlin and Jain hierarchical states. The Jain composite-fermion construction follows by gauge invariance via the Gauss law constraint. In the limit of commuting, 'normal' matrices the theory reduces to eigenvalue coordinates that describe realistic electrons with Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier noncommutative approaches and could provide another effective theory of the fractional Hall effect.
Mean field theory for fermion-based U(2) anyons
McGraw, P
1996-01-01
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless fermion, we find that this energy is independent of the two Chern-Simons coupling constants and is minimized when the non-Abelian charge density is zero. This suggests that there is no spontaneous breaking of the SU(2) subgroup of the symmetry, at least in this mean-field approximation. For spin-1/2 fermions, we find self-consistent mean-field states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached.
Topological field theories on manifolds with Wu structures
Monnier, Samuel
2016-01-01
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf-Witten theories. We take a general point of view where the Chern-Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern-Simons action. In the three-dimensional spin case, the latter provides a definition of the "fermionic correction" introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the...
Directory of Open Access Journals (Sweden)
M.R. Setare
2017-01-01
Full Text Available In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern–Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity (GMMG and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. Also the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the black hole.
Toward U(N|M) knot invariant from ABJM theory
Eynard, Bertrand; Kimura, Taro
2017-02-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half-BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for the U(N|M) averages and also, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
Towards U(N|M) knot invariant from ABJM theory
Eynard, Bertrand
2014-01-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for all the U(N|M) averages, and in particular, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
Ward identities and gauge flow for M-theory in ${\\cal N}{=}3$ superspace
Upadhyay, Sudhaker
2015-01-01
We derive the BRST symmetry, Slavnov-Taylor identities and Nielsen identities for the ABJM theories in ${\\cal N}{=}3$ harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in such superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters).
Ward identities and gauge flow for M-theory in N =3 superspace
Upadhyay, Sudhaker
2015-09-01
We derive the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, Slavnov-Taylor identities, and Nielsen identities for the Aharony-Bergman-Jafferis-Maldacena theories in N =3 harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in this superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters).
Quasihomomorphisms and the residue Chern character
Perrot, Denis
2008-01-01
We develop a general procedure, based on the renormalized eta-cochain, which allows to find local representatives of the bivariant Chern character of finitely summable quasihomomorphisms. In particular, using zeta-function renormalization we obtain a bivariant generalization of the Connes-Moscovici residue formula, and explain the link with chiral and multiplicative anomalies in quantum field theory.
Quasihomomorphisms and the residue Chern character
Perrot, Denis
2010-10-01
We develop a general procedure, based on the renormalized eta-cochain, which allows to find "local" representatives of the bivariant Chern character of finitely summable quasihomomorphisms. In particular, using zeta-function renormalization we obtain a bivariant generalization of the Connes-Moscovici residue formula, and explain the link with chiral and multiplicative anomalies in quantum field theory.
Energy Technology Data Exchange (ETDEWEB)
Setare, M.R., E-mail: rezakord@ipm.ir; Adami, H., E-mail: hamed.adami@yahoo.com
2016-08-15
The Chern–Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz–Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Directory of Open Access Journals (Sweden)
M.R. Setare
2016-08-01
Full Text Available The Chern–Simons-like theories of gravity (CSLTG are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz–Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Towards a common theory for learning from reward, affect, and motivation: The SIMON framework
Directory of Open Access Journals (Sweden)
Christopher R Madan
2013-10-01
Full Text Available While the effects of reward, affect, and motivation on learning have each developed into their own fields of research, they largely have been investigated in isolation. As all three of these constructs are highly related, and use similar experimental procedures, an important advance in research would be to consider the interplay between these constructs. Here we first define each of the three constructs, and then discuss how they may influence each other within a common framework. Finally, we delineate several sources of evidence supporting the framework. By considering the constructs of reward, affect, and motivation within a single framework, we can develop a better understanding of the processes involved in learning and how they interplay, and work towards a comprehensive theory that encompasses reward, affect, and motivation.
Liu, Chien-Hao
2016-01-01
In earlier works, D(1) (arXiv:0709.1515 [math.AG]), D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we have explained why a D-brane in string theory, when treated as a fundamental dynamical object, can be described by a map $\\varphi$ from an Azumaya/matrix manifold $X^{Az}$ (cf. D-brane world-volume) with a fundamental module with a connection $(E,\
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.
Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory BTZ solution with torsion
Garcia, A A; Heinicke, C; Macías, A; Garcia, Alberto A.; Hehl, Friedrich W.; Heinicke, Christian; Macias, Alfredo
2003-01-01
In (1+2)-dimensional Poincar\\'e gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {\\em translational} and {\\em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss {\\em Cartan's} (3-dimensional) {\\em spiral staircase} and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque. {\\em file 3dexact15.tex}
Herbert Simon's Information Theory and Its Practical Enlightenment%西蒙的决策情报信息论及实践启示
Institute of Scientific and Technical Information of China (English)
颜茵
2014-01-01
有关赫伯特·西蒙理论与学术造诣的研究，学界多聚焦于其管理决策思想，而对其并不十分系统和“显赫”的情报信息论，理论界显然未给予集中关注与研究。以西蒙的文献著述为依据，沿着其“管理就是决策”的总命题，对其情报信息论进行尝试性发掘与总结。西蒙的情报信息论论直接导源于他的“管理就是决策”思想。而“有限理性模型”奠定了其决策情报支持系统的主体框架。作为西蒙决策情报理论中最具应用价值的一部分，情报信息能力建设的方法论，对我们今天建设决策情报支持系统、进而推进国家治理体系和治理能力现代化具有较强的实践意义。%The academicspay more attention on Herbert Simon's administrative decision rather than his information theory. The article tries summarizing his information theory on the base of his thoughts that administration is decision-making in his works. Simon's information theory is directly from his thoughts that administration is decision-making. His bounded rationality model lays a solid foundation for the decision and information support system. Methodology of the information ability architecture, which is the most valuable part in Simon's decision information theory, has the practical significance for us to establish decision information support system, and promote the modern-ization of the national administration system.
Knot Invariants from Classical Field Theories
Leal, L C
1999-01-01
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce knot-invariants associated with the sources. The first contributions are explicitly calculated, and the corresponding knot-invariants are recognized. We conclude that the interplay between Knot Theory and Topological Field Theories is manifested not only at the quantum level, but in a classical context as well.
Global Anomalies and Effective Field Theory
Golkar, Siavash
2015-01-01
We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on %thermal partition functions and thermal effective field theory where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient. This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.
Generalized Higher Gauge Theory
Ritter, Patricia; Schmidt, Lennart
2015-01-01
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid $TM\\oplus T^*M$ over some manifold $M$ and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and their infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.
Effective Field Theory of Fractional Quantized Hall Nematics
Energy Technology Data Exchange (ETDEWEB)
Mulligan, Michael; /MIT, LNS; Nayak, Chetan; /Station Q, UCSB; Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC
2012-06-06
We present a Landau-Ginzburg theory for a fractional quantized Hall nematic state and the transition to it from an isotropic fractional quantum Hall state. This justifies Lifshitz-Chern-Simons theory - which is shown to be its dual - on a more microscopic basis and enables us to compute a ground state wave function in the symmetry-broken phase. In such a state of matter, the Hall resistance remains quantized while the longitudinal DC resistivity due to thermally-excited quasiparticles is anisotropic. We interpret recent experiments at Landau level filling factor {nu} = 7/3 in terms of our theory.
Exact results for Wilson loops in orbifold ABJM theory
Ouyang, Hao; Zhang, Jia-ju
2015-01-01
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d=3 N=4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In literature there is the partition function of the N=4 orbifold ABJM theory, and we re-derive it in a slightly different method. We calculate the vacuum expectation values of the circular 1/4 and 1/2 BPS Wilson loops in both the saddle point approach and Fermi gas approach, and the results are in accord to the gravity ones.
Edge excitations in fractional Chern insulators
Luo, Wei-Wei; Chen, Wen-Chao; Wang, Yi-Fei; Gong, Chang-De
2013-10-01
Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.
Discrete Symmetry Breaking in Fractional Chern Insulators
Kumar, Akshay; Roy, Rahul; Sondhi, S. L.
2014-03-01
We study the interplay between quantum hall ordering and spontaneous translational symmetry breaking in a multiple Chern number (C > 1) band at partial filling. We begin with non-interacting fermions in a family of square lattice models with flat C=2 bands and a wide band gap, and add nearest neighbor density-density repulsive interactions. By means of Hartree-Fock theory supplemented by numerical exact diagonalization for a small system at 1/2 filling, we find that the system generically develops charge density wave order with two degenerate ground states. We note that this physics is especially transparent in the limit in which the C=2 band describes two decoupled C=1 bands. We discuss the nature of domain walls in this phase and note the close analogy to the quantum Hall Ising ferromagnet in the multivalley problem. Finally we discuss generalizations to other fillings and higher Chern numbers.
Confined Vortices in Topologically Massive U(1)$\\times$U(1) Theory
Anber, Mohamed M; Sabancilar, Eray; Shaposhnikov, Mikhail
2015-01-01
We report on a new topological vortex solution in U(1)$\\times$U(1) Maxwell-Chern-Simons theory. The existence of the vortex is envisaged by analytical means, and a numerical solution is obtained by integrating the equations of motion. These vortices have a long-range force because one of the U(1)s remains unbroken in the infrared, which is guarded by the Coleman-Hill theorem. The sum of the winding numbers of an ensemble of vortices has to vanish; otherwise the system would have a logarithmically divergent energy. In turn, these vortices exhibit classical confinement. We investigate the rich parameter space of the solutions, and show that one recovers the Abrikosov-Nielsen-Olesen, U(1) Maxwell-Chern-Simons, U(1) pure Chern-Simons and global vortices as various limiting cases. Unlike these limiting cases, the higher winding solutions of our vortices carry non-integer charges under the broken U(1). This is the first vortex solution exhibiting such behavior.
The a-function for N=2 supersymmetric gauge theories in three dimensions
Gracey, J A; Poole, C; Schroder, Y
2016-01-01
Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.
Kukk, Jaak, 1904-2001
1992-01-01
Aleksander Simon õppis veterinaariat, kuid ei lõpetanud, korporatsiooni astus kohe selle asutamisel ja Jaak Kukk oli tema akadeemiline kasuisa, kellele anti teada, et 1944. a Saksamaale rännanud A. Simon üritas 1946 salaja Rootsi põgeneda
Heukelom, F.
2007-01-01
This paper provides an overview of the work of Herbert Simon and his ideas about rational decision making. By his own standards, Simon is an economist who works in the tradition of Adam Smith and Alfred Marshall. The central theme in Simon’s research is how human beings organize themselves in differ
Quantization conditions and functional equations in ABJ(M) theories
Energy Technology Data Exchange (ETDEWEB)
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
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.
Large N behavior of mass deformed ABJM theory
Nosaka, Tomoki; Shimizu, Kazuma; Terashima, Seiji
2016-03-01
In this paper, using the localization technique we analyze the large N limit of the mass deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory on the three sphere with a finite mass parameter and finite Chern-Simons levels. We find two different solutions of the saddle point equations in the large N limit. With these solutions we compute the free energy limit and find that there is a first order phase transition. Our results may predict a phase transition in the dual gravity theory.
Large N behavior of mass deformed ABJM theory
Nosaka, Tomoki; Terashima, Seiji
2015-01-01
In this paper, using the localization technique we analyze the large N limit of the mass deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory on the three sphere with a finite mass parameter and finite Chern-Simons levels. We find two different solutions of the saddle point equations in the large N limit. With these solutions we compute the free energy and find that there is a first order phase transition. Our results may predict a phase transition in the dual gravity theory.
Directory of Open Access Journals (Sweden)
Herbert Ernst Wiegand
2011-10-01
Full Text Available
ZUSAMMENFASSUNG: In diesem Beitrag werden die Begriffe eingeführt, die man benötigt, um das Datenakzessivitätsprofil von Printwörterbüchern genau beschreiben zu können. Es wird zwischen externer und interner Datenakzessivität unterschieden; erstere ist obligatorisch, letztere ist fakultativ. Die externe Datenakzessivität wird durch äußere, die interne Datenakzessivität durch innere Zugriffsstrukturen innerhalb von akzessiven Wörterbucheinträgen hergestellt. Es werden unterschiedliche Typen von äußeren Zugriffsstrukturen als lineare Ordnungsstrukturen, wie z.B. alphabetische äußere Zugriffsstrukturen, numerische mediostrukturelle Zugriffsstrukturen, Regis-terzugriffsstrukturen u.a., beschrieben und ihr Funktionieren erklärt. Weiterhin werden äußere Zugriffsstrukturen von Zugriffspfaden abgegrenzt, die durch die Ausführung externer Zugriffs-handlungen der Benutzer etabliert werden. Der Beitrag gibt insgesamt fünf Einblicke, aber keine zusammenhängende Übersicht über die vielfachen Ausprägungen der Eigenschaften der Wörter-buchform, die die Datenakzessivität sicherstellen.
Stichwörter: AKZESSIVER WÖRTERBUCHEINTRAG, ALPHABET, ALPHABETISCHE ÄU-ßERE ZUGRIFFSSTRUKTUR, ÄUßERER ZUGRIFFSPFAD, EXTERNE DATENAKZESSIVITÄT, EXTERNE ZUGRIFFSHANDLUNG, INNERE ZUGRIFFSSTRUKTUR, INTERNE DATENAKZES-SIVITÄT, MEDIOSTRUKTURELLES LEITELEMENT, MEDIOSTRUKTURELLE ZUGRIFFSSTRUK-TUR, MONOAKZESSIVES WÖRTERBUCH, REGISTER, REGISTERZUGRIFFSSTRUKTUR, POLY-AKZESSIVES WÖRTERBUCH, SCHNELLZUGRIFFSSTRUKTUR, ZUGRIFFSTEXTELEMENT
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ABSTRACT: On the Data Accessibility in Printed Dictionaries. Insights into Recent Developments of a Theory of the Form of Dictionaries. In this contribu-tion, concepts are introduced that are needed for a precise description of the data accessibility pro-file of printed dictionaries. A distinction is made between external and internal data accessibility, with the first being obligatory and the
Toda Theory From Six Dimensions
Cordova, Clay
2016-01-01
We describe a compactification of the six-dimensional (2,0) theory on a four-sphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and two-dimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.
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.)
Instanton Effects in Orbifold ABJM Theory
Honda, Masazumi
2014-01-01
We study the partition function of the orbifold ABJM theory, which is the N=4 necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.
Political and Legal Doctrine of Simon Bolivar
Directory of Open Access Journals (Sweden)
Mixail V. Fedorov
2014-03-01
Full Text Available Present article is devoted to the legal, political and constitutional ideas of the outstanding leader of war of independence in Latin America Simon Bolivar that was called by his countrymen and contemporaries to be a LIBERATOR. In the present article author discusses complex genesis and evolution of the political and legal doctrine of Simon Bolivar. Review is conducted by author in the context of developing theory and practice of Latin American constitutionalism in the XIX century. Author conceptualized and revealed basic historical patterns of formation and development of Latin American countries during the War of Independence (1810-1826 period. Author conducted comprehensive analysis of the draft constitution which was developed by Simon Bolivar for the newly independent states of Latin America and reveals theoretical and practical problem of choosing Simon Bolivar republican form of government, such as a peculiar institution in the form of principle of the separation of powers, containing the fourth power. Author focuses on the questions of Simon Bolivar’s relationship to the constitutional institute of human rights, idea of relationship between state and church. Article also researches many other political, legal and constitutional ideas of Simon Bolivar, present views of historians, lawyers, political scientists, statesmen and public activists.
Topological gauge theories and group cohomology
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. (Rijksuniversiteit Utrecht (Netherlands). Inst. voor Theoretische Fysica); Witten, E. (Institute for Advanced Study, Princeton, NJ (USA). School of Natural Sciences)
1990-04-01
We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H{sup 4}(BG, Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H{sup 3}(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H{sup 4}(BG, Z) to H{sup 3}(G, Z). We generalize this correspondence to topological 'spin' theories, which are defined on three manifolds with spin structure, and are related to what might be called Z{sub 2} graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models. (orig.).
Topologically Massive Gauge Theory: Wu-Yang Type Solutions
Saygili, K
2006-01-01
We discuss euclidean topologically massive Wu-Yang type solutions of the Maxwell-Chern-Simons and the Yang-Mills-Chern-Simons theories. The most distinctive feature of these solutions is the existence of a natural scale of length which is determined by the topological mass. The topological mass is proportional to the square of the gauge coupling constant. We find the non-abelian solution by a SU(2) gauge transformation of the abelian magnetic monopole type solution. In the topologically massive electrodynamics the field strength locally determines the gauge potential modulo a closed term via the self-duality equation. We present the Hopf map including the topological mass. The Wu-Yang construction is based on patching up the local potentials by means of a gauge transformation which can be expressed in terms of the magnetic or the electric charges. We also discuss solutions with different first Chern numbers. There exists a fundamental scale of length over which the gauge function is single-valued and periodic...
Herbert A. Simon: Nobel Prize in Economic Sciences, 1978.
Leahey, Thomas H
2003-09-01
In 1978, Herbert A. Simon won the Nobel Prize in Economic Sciences, the same Nobel won by Daniel Kahneman in 2002. Simon's work in fact paved the way for Kahneman's Nobel. Although trained in political science and economics rather than psychology, Simon applied psychological ideas to economic theorizing. Classical and neoclassical economic theories assume that people are perfectly rational and strive to optimize economic outcomes. Simon argued that human rationality is constrained, not perfect, and that people seek satisfactory rather than ideal outcomes. Despite his Nobel, Simon felt isolated in economics and ultimately moved into psychology. Nevertheless, his ideas percolated through the economic community, so that Kahneman, whose research advanced Simon's broad perspective, could be the psychologist who won the Nobel in economics.
Levin, Simon, 1928-2008
1987-01-01
Simon Levini seletus Eesti NSV Ülemkohtu Kriminaalasjade kohtukolleegiumi istungil 24. juunil 1982. aastal. Vastav seletus pälvis Eesti NSV advokaatide kohtukõnede konkursil esimese preemia kriminaalasjades peetud kõnede hulgas. Lisatud selgitused kohtuasjale
Light-Front quantization of field theory
Srivastava, P P
1996-01-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincarè 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.
Remembering Roger I. Simon: A Pedagogy of Public Possibility
Farley, Lisa; Tarc, Aparna Mishra
2014-01-01
This special issue of "Canadian Social Studies" is dedicated to Roger I. Simon. Simon's scholarship bequeaths to theorists, teachers, and curators across Canada and beyond a theory of education that opens up responsibilities to past and present others. The papers gathered for this special issue address many of the difficulties that he…
N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2003-01-01
We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1 non-critical bosonic string theory, and express them in a quiver or, equivalently, super matrix model. Moreover we relate, by deconstruction, the uncompactified c=1 theory to the six-dimensional conformal (2,0) theory. Furthermore, we show how we can use the idea of deconstruction to connect 4+k dimensional supersymmetric gauge theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models. Examples of such bosonic systems include unitary matrix models and gauged matrix quantum mechanics, which deconstruct 5-dimensional supersymmetric gauge theories, and Chern-Simons gauge theories, which deconstruct gauge theories living on branes wrapped over cycles in Calabi-Yau threefolds.
QCD axion from a higher dimensional gauge field theory.
Choi, Kiwoon
2004-03-12
We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.
Superstring theories as low-energy limit of supergroup gauge theories
Popov, Alexander D
2016-01-01
We consider Yang-Mills theory with $N=2$ super translation group in $d=10$ auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\\Sigma_2\\times H^2$, where $\\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is the open disc in $\\mathbb{R}^2$ with the boundary $S^1=\\partial H^2$. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills action supplemented by the $d=5$ Chern-Simons term becomes the Green-Schwarz superstring action. More concretely, the Yang-Mills action in the infrared limit flows to the kinetic part of the superstring action and the $d=5$ Chern-Simons action, defined on a 5-manifold with the boundary $\\Sigma_2\\times H^2$, flows to the Wess-Zumino part of the superstring action. The same kind of duality between gauge fields and strings is established for type IIB superstring on AdS$_5\\times S^5$ background and a supergroup gauge theory with PSU(2,2$|$4) as the structure group.
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...
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...
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.
Ketov, S V
1996-01-01
The (2,2) world-sheet supersymmetric string theory is discussed from the viewpoint of string/membrane unification. The effective field theory in the closed string target space is known to be the 2+2 dimensional (integrable) theory of self-dual gravity (SDG). A world-volume supersymmetrization of the Pleba'nski action for SDG naturally implies the maximal N=8 world-volume supersymmetry, while the maximal supersymmetrization of the dual covariant K"ahler-Lorentz-Chern-Simons action for SDG implies gauging a self-dual part of the super-Lorentz symmetry in 2+10 dimensions. The proposed OSp(32|1) supersymmetric action for the M-brane may be useful for a fundamental formulation of uncompactified F theory, with the self-duality being playing the central role both in the world-volume and in the target space of the M-brane.
Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
Bufalo, R
2016-01-01
In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on the obtained results, we compute the one-loop contributions to the neutral and charged scalar field self-energy, as well as to the Chern-Simons polarization tensor. In order to properly define the behaviour of the quantum fields, the known UV/IR mixing due to radiative corrections is analysed in the one-loop physical dispersion relation of the scalar and gauge fields.
A Note on Lifshitz and Schroedinger Solutions in Pure Lovelock theories
Jatkar, Dileep P
2015-01-01
We look for Lifshitz and Schroedinger solutions in Lovelock gravity. We span the entire parameter space and determine parametric relations under which Lifshitz and Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Lifshitz and Schroedinger solutions on a co-dimension two locus in the Lovelock parameter space. This co-dimension two locus precisely corresponds to the subspace over which the Lovelock gravity can be written in the Chern-Simons form. While Lifshitz and Schroedinger solutions do not exist outside this locus, on this locus these solutions exist for arbitrary dynamical exponent z.
Generalized Gauge Theories and Weinberg-Salam Model with Dirac-Kähler Fermions
Kawamoto, N; Umetsu, H; Kawamoto, Noboru; Tsukioka, Takuya; Umetsu, Hiroshi
2001-01-01
We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.
DEFF Research Database (Denmark)
for bedste orkesterværk ved det nyligt overståede musikdage i Donaueschingen samt med Nordisk Råds Musikpris i 2014. Med dette fokus ønsker Seismograf/DMT at fejre komponisten Simon Steen-Andersen. I både en dansk og i en international kontekst ønsker vi at præsentere og reflektere over et lille hjørne af...
Arun, K G
2013-01-01
Gravitational Wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test General Relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories like Scalar-Tensor theories, Dynamical Chern-Simons theory and Massive graviton theories. Model independent tests are attempts to write down a parametrised gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA config...
Energy Technology Data Exchange (ETDEWEB)
Ezawa, Motohiko, E-mail: ezawa@ap.t.u-tokyo.ac.jp
2014-03-01
The Chern number is a genuine topological number. On the other hand, a symmetry protected topological (SPT) charge is a topological number only when a symmetry exists. We propose a formula for the SPT charge as a derivative of the Chern number in terms of the Green function in such a way that it is valid and related to the associated Hall current even when the symmetry is broken. We estimate the amount of deviation from the quantized value as a function of the strength of the broken symmetry. We present two examples. First, we consider Dirac electrons with the spin–orbit coupling on honeycomb lattice, where the SPT charges are given by the spin-Chern, valley-Chern and spin-valley-Chern numbers. Though the spin-Chern charge is not quantized in the presence of the Rashba coupling, the deviation is estimated to be 10{sup −7} in the case of silicene, a silicon cousin of graphene. Second, we analyze the effect of the mirror-symmetry breaking of the mirror-Chern number in a thin-film of topological crystalline insulator.
Exact holography and black hole entropy in N=8 and N=4 string theory
Gomes, Joao
2015-01-01
We compute the exact entropy of one-eighth and one-quarter BPS black holes in N=8 and N=4 string theory respectively. This includes all the N=4 CHL models in both K3 and T^4 compactifications. The main result is a measure for the finite dimensional integral that one obtains after localization of supergravity on AdS_2xS^2. This measure is determined entirely by an anomaly in supersymmetric Chern-Simons theory on local AdS_3 and takes into account the contribution from all the supergravity multiplets. In Chern-Simons theory on compact manifolds this is the anomaly that computes a certain one-loop dependence on the volume of the manifold. For one-eighth BPS black holes our results are a first principles derivation of a measure proposed in arXiv:1111.1161, while in the case of one-quarter BPS black holes our result computes exactly all the perturbative or area corrections. Moreover, we argue that instantonic contributions can be incorporated and give evidence by computing the measure which matches precisely the m...
Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
Aniceto, Inês; Schiappa, Ricardo
2015-01-01
Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N techniques, or else via perturbative expansions in the gauge coupling. Either approximation often leads to observables given in terms of asymptotic series, which need to be properly defined in order to obtain nonperturbative results. At the same time, resurgent analysis has recently been successfully applied to several problems, e.g., in quantum, field and string theories, precisely to overcome this issue and construct nonperturbative answers out of asymptotic perturbative expansions. The present work uses exact results from supersymmetric localization to address the resurgent structure of the free energy and partition function of Chern-Simons and ABJM gauge theories in three dimensions, and of N=2 supersymmetric Yang-Mills theories in four dimensions. For each case, the com...
The tensor hierarchy of 8-dimensional field theories
Andino, Óscar Lasso; Ortín, Tomás
2016-10-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
The tensor hierarchy of 8-dimensional field theories
Andino, Oscar Lasso
2016-01-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories
Energy Technology Data Exchange (ETDEWEB)
Hohm, Olaf [Spinoza Institute and Institute for Theoretical Physics, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2007-06-07
We analyse the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this, we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated with SL(D-2,R) together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the 'broken phase' can be reconstructed by gauging a certain subgroup of the global symmetries. This deforms the three-dimensional diffeomorphisms to a gauged version, and it is shown that they can be governed by a Chern-Simons theory, which unifies the spin-2 modes with the Kaluza-Klein vectors. This provides a reformulation of D-dimensional Einstein gravity, in which the physical degrees of freedom are described by the scalars of a gauged nonlinear {sigma}-model based on SL(D-2,R)/SO(D-2), while the metric appears in a purely topological Chern-Simons form.
On p -form theories with gauge invariant second order field equations
Deffayet, Cédric; Mukohyama, Shinji; Sivanesan, Vishagan
2016-04-01
We explore field theories of a single p -form with equations of motions of order strictly equal to 2 and gauge invariance. We give a general method for the classification of such theories which are extensions to the p -forms of the Galileon models for scalars. Our classification scheme allows us to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a nontrivial Galileon-like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no nontrivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd-p cases.
On p-form theories with gauge invariant second order field equations
Deffayet, Cédric; Sivanesan, Vishagan
2016-01-01
We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no non trivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd p cases.
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
Hanada, Masanori; Honma, Yoshinori; Nishimura, Jun; Shiba, Shotaro; Yoshida, Yutaka
2012-01-01
We show that the ABJM theory, which is a N=6 superconformal U(N)\\times U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that the previously proposed analytical formula needs to be corrected by an additional term at each order of the string coupling expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.
Higher Derivative Corrections To Extended Supersymmetric Theories
Braun, G A
2004-01-01
We investigate higher-derivative terms in N = 2 supersymmetric effective actions. We systematically construct such terms in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. We write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches, modulo the existence of superspace Chern-Simons-like terms. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. We then search for superspace Chern-Simons-like terms, which are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which gauge potential superfield appears explicitly. We find a class of four- derivative terms with N = 2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally on the Coulomb branch are superspace Chern- Simons-like.
Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
Sugawa, Seiji; Perry, Abigail R; Yue, Yuchen; Spielman, Ian B
2016-01-01
Because global topological properties are robust against local perturbations, understanding and manipulating the topological properties of physical systems is essential in advancing quantum science and technology. For quantum computation, topologically protected qubit operations can increase computational robustness, and for metrology the quantized Hall effect directly defines the von Klitzing constant. Fundamentally, topological order is generated by singularities called topological defects in extended spaces, and is quantified in terms of Chern numbers, each of which measures different sorts of fields traversing surfaces enclosing these topological singularities. Here, inspired by high energy theories, we describe our synthesis and characterization of a singularity present in non-Abelian gauge theories - a Yang monopole - using atomic Bose-Einstein condensates in a five-dimensional space, and quantify the monopole in terms of Chern numbers measured on enclosing manifolds. While the well-known 1st Chern numb...
Directory of Open Access Journals (Sweden)
Matthieu Noucher
2014-07-01
Full Text Available Simon Chignard est l’auteur de « L’open data, comprendre l’ouverture des données publiques » (FYP éditions, mars 2012. Dans ce livre il propose des repères pour replacer l’open data dans le contexte français et comprendre les enjeux et les limites de l’ouverture des données publiques. Il a participé dès 2010 à l’animation de l’ouverture des données publiques de Rennes Métropole, territoire pionnier en France. Consultant et formateur indépendant, il est à titre bénévole président de l’association Bug (innovation sociale et numérique et vice-président de la Cantine numérique rennaise. Il anime le blog : http://donneesouvertes.info/
Murthy, Ganpathy
2001-11-01
A microscopic Hamiltonian theory of the fractional quantum Hall effect developed by Shankar and the present author based on the fermionic Chern-Simons approach has recently been quite successful in calculating gaps and finite-tempertature properties in fractional quantum Hall states. Initially proposed as a small-q theory, it was subsequently extended by Shankar to form an algebraically consistent theory for all q in the lowest Landau level. Such a theory is amenable to a conserving approximation in which the constraints have vanishing correlators and decouple from physical response functions. Properties of the incompressible fractions are explored in this conserving approximation, including the magnetoexciton dispersions and the evolution of the small-q structure factor as ν-->12. Finally, a formalism capable of dealing with a nonuniform ground-state charge density is developed and used to show how the correct fractional value of the quasiparticle charge emerges from the theory.
Consistent chiral kinetic theory in Weyl materials: chiral magnetic plasmons
Gorbar, E V; Shovkovy, I A; Sukhachov, P O
2016-01-01
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern--Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. T...
On skew tau-functions in higher spin theory
Melnikov, D; Morozov, A
2016-01-01
Recent studies of higher spin theory in three dimensions concentrate on Wilson loops in Chern-Simons theory, which in the classical limit reduce to peculiar corner matrix elements between the highest and lowest weight states in a given representation of SL(N). Despite these "skew" tau-functions can seem very different from conventional ones, which are the matrix elements between the two highest weight states, they also satisfy the Toda recursion between different fundamental representations. Moreover, in the most popular examples they possess simple representations in terms of matrix models and Schur functions. We provide a brief introduction to this new interesting field, which, after quantization, can serve as an additional bridge between knot and integrability theories.
Exact results for Wilson loops in orbifold ABJM theory
Ouyang, Hao; Wu, Jun-Bao; Zhang, Jia-Ju
2016-08-01
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d = 3 mathcal = 4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the mathcal = 4 orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the saddle point approach and Fermi gas approach. The results for Wilson loops are in accord with the available gravity results. Supported by NSFC (11222549, 11575202), K. C. Wong Education Foundation and Youth Innovation Promotion Association of CAS (2011016)
Derivation of the Simon equation
Fedorov, P. P.
2016-09-01
The form of the empirical Simon equation describing the dependence of the phase-transition temperature on pressure is shown to be asymptotically strict when the system tends to absolute zero of temperature, and then only for crystalline phases.
F-theory and 2d (0, 2) theories
Schäfer-Nameki, Sakura; Weigand, Timo
2016-05-01
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.
On equivariant Chern-Weil forms and determinant lines
Freed, Daniel S
2016-01-01
A strong from of invariance under a group G is manifested in a family over the classifying space BG. We advocate a differential-geometric avatar of BG when G is a Lie group. Applied to G-equivariant connections on smooth principal or vector bundles, the equivariance-->families principle converts the G-equivariant extensions of curvature and Chern-Weil forms to the standard nonequivariant versions. An application of this technique yields the moment map of the determinant line of a G-equivariant Dirac operator, which in turn sheds light on some anomaly formulas in quantum field theory.
2011-01-01
Daniel Simon, PS Division Leader from 1994 to 1999, died on 2 June, 2011, at the age of 74, in Nancy. CERN owes him for a great number of contributions to the experimental areas around the PS and the existence of the Antiproton Decelerator (AD). Daniel came to CERN in 1962 from the University of Nancy. He first worked in the Nuclear Physics Apparatus (NPA) Division on the electrostatic separators for the secondary beams at the PS, a subject he also chose for his thesis. Then, as a member of the PS-Division, he designed a variety of beam lines, including those providing protons and antiprotons to ICE, the decisive experiment for CERN to launch the antiproton project, based on stochastic cooling. His contributions to the initial layout and further evolution of the experimental areas of LEAR were essential for the success of the LEAR programme. He subsequently drove the decision and worked on the conversion of LEAR into LEIR for the provision of lead-ions to the LHC. He was one of the leaders of t...
Topological Structure and Topological Tensor Current of Gauss-Bonnet-Chern Theorem
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; WU Shao-Feng; ZHANG Peng-Ming
2006-01-01
We offer an intrinsic theoretical framework to reveal the inner relationships among three theories for Euler we consider the Gauss-Bonnet-Chern (GBC) form imbedded in arbitrary higher-dimensional manifold, which suggests a Hodge dual tensor current. We show the brane structure inherent in the GBC tensor current and obtain the generalized Nambu action for the multi branes with quantized topological charge.
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.
M-Theory Brane as Giant Graviton and the Fractional Quantum Hall Effect
Huo, R
2006-01-01
A small number of M-theory branes as giant gravitons in the M-theory sector of LLM geometry is studied as a probe. The abelian way shows that the low energy effective action for M-theory brane is exactly the 2d electron subject to a vertical magnetic field. We also briefly discuss the microscopic description of M2-brane giant graviton in this geometry, in the language of a combination of D0-branes as fuzzy 2-spheres. Then we go to the well-established Noncommutative Chern-Simons theory description. After quantization, well behaved Fractional Quantum Hall Effect is demonstrated. This goes beyond the original LLM description and should be some indication of novel geometry.
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.
Finite-temperature effective boundary theory of the quantized thermal Hall effect
Nakai, Ryota; Ryu, Shinsei; Nomura, Kentaro
2016-02-01
A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two distinct types of the field theory have been proposed to describe the quantized thermal Hall effect. One of these, known as the gravitational Chern-Simons action, is a kind of topological field theory, and the other is a phenomenological theory relevant to the Strěda formula. In order to solve this problem, we derive microscopically an effective theory that accounts for the quantized thermal Hall effect. In this paper, the two-dimensional Dirac fermion under a static background gravitational field is considered in equilibrium at a finite temperature, from which an effective boundary free energy functional of the gravitational field is derived. This boundary theory is shown to explain the quantized thermal Hall conductivity and thermal Hall current in the bulk by assuming the Lorentz symmetry. The bulk effective theory is consistently determined via the boundary effective theory.
On fractional quantum Hall solitons in ABJM-like theory
Energy Technology Data Exchange (ETDEWEB)
Belhaj, Adil, E-mail: belhaj@unizar.es [Centre of Physics and Mathematics, CPM-CNESTEN, Rabat (Morocco); Lab Phys Hautes Energies, Modelisation et Simulation, Faculte des Sciences, Rabat (Morocco); Groupement National de Physique des Hautes Energies, Siege focal: FSR, Rabat (Morocco)
2011-11-24
Using D-brane physics, we study fractional quantum Hall solitons (FQHS) in ABJM-like theory in terms of type IIA dual geometries. In particular, we discuss a class of Chern-Simons (CS) quivers describing FQHS systems at low energy. These CS quivers come from R-R gauge fields interacting with D6-branes wrapped on 4-cycles, which reside within a blown up CP{sup 3} projective space. Based on the CS quiver method and mimicking the construction of del Pezzo surfaces in terms of CP{sup 2}, we first give a model which corresponds to a single layer model of FQHS system, then we propose a multi-layer system generalizing the doubled CS field theory, which is used in the study of topological defect in graphene.
F-theory and 2d (0,2) Theories
Schafer-Nameki, Sakura
2016-01-01
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 t...
Wang, Tao
2012-01-01
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter two edge-critical graph on $n$ vertices is at most $\\lfloor \\frac{n^{2}}{4} \\rfloor$ and the extremal graph is the complete bipartite graph $K_{\\lfloor \\frac{n}{2} \\rfloor, \\lceil \\frac{n}{2} \\rceil}$. In the series papers [8-10], the Murty-Simon Conjecture stated by Haynes et al is not the original conjecture, indeed, it is only for the diameter two edge-critical graphs of even order. Haynes et al proved the conjecture for the graphs whose complements have diameter three but only with even vertices. In this paper, we prove the Murty-Simon Conjecture for the graphs whose complements have diameter three, not only with even vertices but also odd ones.
Bianchi, Marco S; Mauri, Andrea; Penati, Silvia; Santambrogio, Alberto
2011-01-01
We study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using N=2 superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic N>=2 supersymmetric theories and find a vanishing result for N=6 ABJ(M) and N=8 BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Final...
DEFF Research Database (Denmark)
Foss, Kirsten; Foss, Nicolai
as a general approach to problem solving. We apply these Simonian ideas to organizational issues, specifically new organizational forms. Specifically, Simonian ideas allow us to develop a morphology of new organizational forms and to point to some design problems that characterize these forms.Keywords: Herbert...... Simon, problem-solving, new organizational forms. JEL Code: D23, D83......Two of Herbert Simon's best-known papers are "The Architecture of Complexity" and "The Structure of Ill-Structured Problems." We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...
Large-N expansion, conformal field theory and renormalization-group flows in three dimensions
Anselmi, D
2000-01-01
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy a set of non-perturbative g 1/g dualities. There is an exact relation between the beta function and the anomalous dimension of the composite boson. Non-Abelian gauge fields have a non-renormalized and quantized gauge coupling, although no Chern-Simons term is present. A problem of the naive dimensional-regularization technique for these theories is uncovered and removed with a non-local, evanescent, non-renormalized kinetic term. The models are expected to be a fruitful arena for the study of odd-dimensional conformal field theory.
Study of Planar Models in Quantum Mechanics, Field theory and Gravity
Kumar, Sarmistha
2014-01-01
Instantons, monopoles and vortices have become paradigms of topological structures in field theory and quantum mechanics, with important applications in particle physics, astrophysics, condensed matter physics and mathematics. We have discussed here the self-dual Chern-Simons theory specially in (2+1) dimensions. we start with a relevant topological quantum mechanical model (such as Landau problem consisting of two basic chiral oscillators) and extrapolate the analysis to (2+1)dimensional vector field theory. Aspects of selfdual symmetry in topologically massive gravity model were also considered using three different approaches. We have demonstrated how duality symmetric (or chiral) actions are already present in the quantum mechanical examples such as in usual harmonic oscillator. Using the chiral oscillator form, we will briefly develop the key concepts of the soldering mechanism. We have also discussed the non commutative property of such quantum models. Models involving higher order derivative of Abelian...
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
Cremonesi, Stefano
2015-01-01
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
Wu, Chaolun
2014-01-01
We show that Horava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Horava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geomet...
Electron-electron bound states in Maxwell-Chern-Simons-Proca QED{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Belich, H.; Helayel-Neto, J.A. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil)]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas]. E-mail: belich@cbpf.br; helayel@gft.ucp.br; Del Cima, O.M. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil)]. E-mail: delcima@gft.ucp.br; Ferreira, M.M. Jr. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil)]|[Maranhao Univ., Sao Luis, MA (Brazil). Dept. de Fisica]. E-mail: manojr@cbpf.br
2002-10-01
We start from a parity-breaking MCS QED{sub 3} model with spontaneous breaking of the gauge symmetry as a framework for evaluation of the electron-electron interaction potential and for attainment of numerical values for the e{sup -}e{sup -} - bound state. Three expressions (V{sub eff{down_arrow}}{sub {down_arrow}}, V{sub eff{down_arrow}}{sub {up_arrow}}, V{sub eff{down_arrow}}{sub {down_arrow}}) are obtained according to the polarization state of the scattered electrons. In an energy scale compatible with condensed matter electronic excitations, these potentials become degenerated. The resulting potential is implemented in the Schroedinger equation and the variational method is applied to carry out the electronic binding energy. The resulting binding energies in the scale of 10-100 meV and a correlation length in the scale of 10 - 30 Angstrom are possible indications that the MCS-QED{sub 3} model adopted may be suitable to address an eventual case of e{sup -}e{sup -} pairing in the presence of parity-symmetry breakdown. The data analyzed here suggest an energy scale of 10-100 meV to fix the breaking of the U(1)-symmetry. (author)
Cryptanalysis of SIMON Variants with Connections
DEFF Research Database (Denmark)
Alizadeh, Javad; Alkhzaimi, Hoda A.; Aref, Mohammad Reza
2014-01-01
SIMON is a family of 10 lightweight block ciphers published by Beaulieu et al. from the United States National Security Agency (NSA). A cipher in this family with K-bit key and N-bit block is called SIMONN/K. We present several linear characteristics for reduced-round SIMON32/64 that can be used...... the presented observations do not directly yield an attack, but provide a basis for further analysis for the specific SIMON variant. Finally, we exploit a connection between linear and differential characteristics for SIMON to construct linear characteristics for different variants of reduced-round SIMON. Our...
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.
Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
Bianchi, Marco S; Mauri, Andrea; Penati, Silvia; Santambrogio, Alberto
2011-01-01
For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scatteringa amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the N=4 SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.
Misra, A
2002-01-01
Following the work of Lima et al on the exact evaluation of the nonperturbative contribution to the superpotential from open-membrane instanton in Heterotic M-Theory, we evaluate systematically the contribution to the superpotential of a membrane instanton obtained by wrapping of a single M2 brane, once, on an isolated supersymmetric 3-cycle in a G_2-holonomy manifold. We then try to relate the results obtained to those sketched out in Harvey and Moore. We also do a heat-kernel asymptotics analysis to see whether one gets similar UV-divergent terms for (one or both of) the bosonic and fermionic determinants indicative of (partial) cancelation among them. The answer is in the affirmative, as expected by the supersymmetry of the starting membrane action. This work is a first step in understanding the large N Chern-Simons/closed type-A topological string theory duality of Gopakumar and Vafa from M theory point of view.
A Piagetian Critique of Kohlberg's 'Moral Development' and of Simon's 'Values Clarification.'
Lewis, Frank W.
The paper presents key features of Jean Piaget's theory of moral development, compares Piaget's theory with Lawrence Kohlberg's theory of moral development and Sidney Simon's theory of values clarification, and evaluates the values clarification movement in light of Piaget's theoretical and practical conclusions. The focus is twofold: first, on…
Fractional Quantum Hall Filling Factors from String Theory using Toric Geometry
Belhaj, A; Idrissi, M El; Manaut, B; Sebbar, A; Sedra, M B
2015-01-01
Using toric Cartan matrices as abelian gauge charges, we present a class of stringy fractional quantum Hall effect (FQHE) producing some recent experimental observed filling factor values. More precisely, we derive the corresponding Chern-Simons type models from M-theory compactified on four complex dimensional hyper-K\\"{a}hler manifolds X^4. These manifolds, which are viewed as target spaces of a particular N=4 sigma model in two dimensions, are identified with the cotangent bundles over intersecting 2-dimensional toric varieties V_i^2 according to toric Cartan matrices. Exploring results of string dualities, the presented FQHE can be obtained from D6-banes wrapping on such intersecting toric varieties interacting with R-R gauge fields. This string theory realization provides a geometric interpretation of the filling factors in terms of toric and Euler characteristic topological data of the compactified geometry. Concretely, explicit bilayer models are worked out in some details.
Simon Newcomb: America's Unofficial Astronomer Royal
Graham, John
2007-10-01
Bill Carter and Merri Sue Carter Mantazas; xiii + 213 pp.; ISBN 1-59113-803-5 2006; $26.95 This book introduced me to a commanding figure in American science from the late nineteenth century: Simon Newcomb. Newcomb has been called the nineteenth-century equivalent of Carl Sagan and Albert Einstein. He rose from humble beginnings to be the preeminent American astronomer of his generation. He made basic, far-reaching, and enduring contributions to positional astronomy and planetary dynamics. On the more practical side, he determined a remarkably accurate value for the velocity of light, one within 0.01% of the value accepted today. His work provided an experimental grounding for the special and general theories of relativity to be formulated by Einstein in the coming twentieth century.
The (not so) social Simon effect: a referential coding account.
Dolk, Thomas; Hommel, Bernhard; Prinz, Wolfgang; Liepelt, Roman
2013-10-01
The joint go-nogo Simon effect (social Simon effect, or joint cSE) has been considered as an index of automatic action/task co-representation. Recent findings, however, challenge extreme versions of this social co-representation account by suggesting that the (joint) cSE results from any sufficiently salient event that provides a reference for spatially coding one's own action. By manipulating the salient nature of reference-providing events in an auditory go-nogo Simon task, the present study indeed demonstrates that spatial reference events do not necessarily require social (Experiment 1) or movement features (Experiment 2) to induce action coding. As long as events attract attention in a bottom-up fashion (e.g., auditory rhythmic features; Experiment 3 and 4), events in an auditory go-nogo Simon task seem to be co-represented irrespective of the agent or object producing these events. This suggests that the cSE does not necessarily imply the co-representation of tasks. The theory of event coding provides a comprehensive account of the available evidence on the cSE: the presence of another salient event requires distinguishing the cognitive representation of one's own action from the representation of other events, which can be achieved by referential coding-the spatial coding of one's action relative to the other events.
Gauge theories and integrable lattice models
Witten, Edward
1989-08-01
Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question — previously considered in both the knot theory and statistical mechanics — are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be presented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory.
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
Cheon, Sangmo; Kim, Nakwoo
2011-01-01
We test the AdS/CFT correspondence by computing the partition function of some $\\cN=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds $Q^{1,1,1}$ or $V^{5,2}$. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to $N^{3/2}$ and the coefficient matches correctly the volume of $Q^{1,1,1}$ and $V^{5,2}$.
Anomaly cancelation in field theory and F-theory on a circle
Grimm, Thomas W.; Kapfer, Andreas
2016-05-01
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.
Anomaly Cancelation in Field Theory and F-theory on a Circle
Grimm, Thomas W
2015-01-01
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.
Supersymmetric M5 brane theories on R × CP2
Kim, Hee-Cheol; Lee, Kimyeong
2013-07-01
We propose 4 and 12 supersymmetric conformal Yang-Mills-Chern-Simons theories on R × CP2 as multiple representations of the theory on M5 branes. These theories are obtained by twisted Zk modding and dimensional reduction of the 6d (2,0) superconformal field theory on R × S5 and have a discrete coupling constant 1/{g_{{YM}^2}}=k/{4{π^2}} with natural number k. Instantons in these theories are expected to represent the Kaluza-Klein modes. For the k = 1 , 2 cases, we argue that the number of supersymmetries in our theories should be enhanced to 32 and 16, respectively. For the k = 3 case, only the 4 supersymmetric theory gets the supersymmetric enhancement to 8. For the 4 supersymmetric case, the vacuum structure becomes more complicated as there are degenerate supersymmetric vacua characterized by fuzzy spheres. We calculate the perturbative part of the SU( N ) gauge group Euclidean path integral for the index function at the symmetric phase of the 4 supersymmetric case and confirm it with the known half-BPS index. From the similar twisted Z k modding of the AdS7 × S4 geometry, we speculate that the M region is for k ≲ N 1/3 and the type IIA region is N 1/3 ≲ k ≲ N. When nonperturbative corrections are included, our theories are expected to produce the full index of the 6d (2,0) theory.
Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
Chiou, Dah-Wei; Lin, Feng-Li
2016-01-01
We have studied extensively the band crossing patterns of the bulk entanglement spectrum (BES) for various lattice Chern insulators. We find that only partitions with dual symmetry can have either stable nodal-lines or nodal-points in the BES when the system is in the topological phase of a nonzero Chern number. By deforming the Hamiltonian to lift the accidental symmetry, one can see that only nodal points are robust. They thus should bear certain topological characteristics of the BES. By studying the band crossing patterns in details we conclude that the topological characteristics of the BES are inherited from the topological order of the underlying Chern insulators and the former can have more refined topological structures. We then propose the conjecture that the sum of the vorticities in the BES in a properly chosen reduced Brillouin zone equals the Chern number of the underlying Chern insulator.
L'industrialisme de Saint-Simon
Grange, Juliette
2003-01-01
This article presents Saint-Simon's works as a philosophical contribution, with an internal logic covering all knowledge fields.; Cet article considère l'oeuvre de Saint-Simon comme une oeuvre philosophique, pourvu d'une logique interne et couvrant tous les champs du savoirs.
Bidirectional Priming Processes in the Simon Task
Metzker, Manja; Dreisbach, Gesine
2009-01-01
The Simon effect is mostly explained in terms of dual-route models, which imply unidirectional activation processes from stimulus features to response features. However, there is also evidence that these preactivated response features themselves prime corresponding stimulus features. From this perspective, the Simon effect should only occur…
Comments on the origin of dual superconformal symmetry in ABJM theory
Colgáin, E Ó
2016-01-01
Strong evidence for dual superconformal symmetry in $\\mathcal{N} = 6$ superconformal Chern-Simons theory has fueled expectations that the AdS/CFT dual geometry $AdS_4 \\times \\mathbb{C} P^3$ is self-dual under T-duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T-duality, a symmetry originally proposed by Berkovits & Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T-duality and comment on T-duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T-duality for $AdS_4 \\times \\mathbb{C} P^3$ or its TsT deformations, but leave the door open for new possibilities.
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.
The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory
Huang, Hsin-Yuan; Zhang, Lei
2017-01-01
Let {Ω} be a flat torus and {G} be the Green's function of {-Δ} on {Ω}. One intriguing mystery of {G} is how the number of its critical points is related to blowup solutions of certain PDEs. In this article we prove that for the following equation that describes a Chern-Simons model in Gauge theory: Δ u_1+1/ɛ^2e^{u_2}(1-e^{u_1})=8πδ_{p1} Δ u_2+1/ɛ^2e^{u_1}(1-e^{u_2})=8πδ_{p2} in quad Ω., quad p_1-p_2 {{ is a half period}}, if fully bubbling solutions of Liouville type exist, {G} has exactly three critical points. In addition we establish necessary conditions for the existence of fully bubbling solutions with multiple bubbles.
Topological M-theory as Unification of Form Theories of Gravity
Dijkgraaf, R; Neitzke, A; Vafa, C; Dijkgraaf, Robbert; Gukov, Sergei; Neitzke, Andrew; Vafa, Cumrun
2004-01-01
We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological action for a 3-form gauge field introduced by Hitchin. We show that by reductions of this 7-dimensional theory one can classically obtain 6-dimensional topological A and B models, the topological sector of loop quantum gravity in 4 dimensions, and Chern-Simons gravity in 3 dimensions. We also find that the 7-dimensional M-theory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on S-duality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7-dimensional theory. Finally, from the topological M-theory perspective we find hints of an intriguing holographic link between non-supersymmetric Yang-Mills in 4 dimensions and A model topological strings on twistor...
M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
Costello, Kevin
2016-01-01
The $\\Omega$-background is defined for supergravity, and a very general class of such backgrounds is constructed for 11-dimensional supergravity. 11-dimensional supergravity in a certain $\\Omega$-background is shown to be equivalent to a 5-dimensional non-commutative gauge theory of Chern-Simons type. M2 and M5 branes are expressed as 1 and 2-dimensional extended objects in the 5-dimensional gauge theory. This 5-dimensional gauge theory is shown to admit a consistent quantization with two coupling constants, despite being formally non-renormalizable. A check of a twisted version of AdS/CFT is performed relating this 5-dimensional non-commutative gauge theory to the theory on N M5 branes, wrapping an $A_{k-1}$ singularity and placed in an $\\Omega$-background. The operators on the M5 branes, in the $\\Omega$-background, are described by a certain chiral algebra which in the large N limit becomes a $W_{k+\\infty}$ algebra. This chiral algebra is recovered from the 5-dimensional gauge theory. This argument also pro...
Observations on the SIMON Block Cipher Family
DEFF Research Database (Denmark)
Kölbl, Stefan; Leander, Gregor; Tiessen, Tyge
2015-01-01
In this paper we analyse the general class of functions underlying the Simon block cipher. In particular, we derive efficiently computable and easily implementable expressions for the exact differential and linear behaviour of Simon-like round functions. Following up on this, we use those...... expressions for a computer aided approach based on SAT/SMT solvers to find both optimal differential and linear characteristics for Simon. Furthermore, we are able to find all characteristics contributing to the probability of a differential for Simon32 and give better estimates for the probability for other...... variants. Finally, we investigate a large set of Simon variants using different rotation constants with respect to their resistance against differential and linear cryptanalysis. Interestingly, the default parameters seem to be not always optimal....
DEFF Research Database (Denmark)
2013), the prize for the best orchestral work at the recently held Doneueschinger Musiktage and The Nordic Council Music Prize in 2014. Seismograf/DMT wishes to celebrate the composer Simon Steen-Andersen. We present and reflect on parts of his comprehensive career, in a Danish and an international...... Rasmus Holmboe; a reflection on the importance of the unrepeatable in Steen-Andersen’s music by composer and PhD Rune Søchting, and a contextualisation of central works by Norwegian editor and writer Ida Habbestad. Our Swedish colleague Andreas Engström writes about the new piano concerto (english....... Watch the trailer. The idea for this Focus comes from Jens Voigt-Lund. It has been realised and edited by Sanne Krogh Groth and Rasmus Holmboe, and published with financial support from Carl Nielsen Fonden. English translations by Helen Clara Hemsley. The Focus is also published in a Danish version....
Stringy Chern classes of singular toric varieties and their applications
Batyrev, Victor
2016-01-01
Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This formula is motivated by its applications to mirror symmetry for Calabi-Yau complete intersections in toric varieties. We compute stringy Chern classes and give a combinatorial interpretation of the stringy Libgober-Wood identity for arbitrary projective Q-Gorenstein toric varieties. As an application we derive a new combinatorial identity relating d-dimensional reflexive polytopes to the number 12 in dimension d>3.
Arun, K. G.; Pai, Archana
2013-01-01
Gravitational wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test general relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories such as scalar-tensor theories, dynamical Chern-Simons theory and massive graviton theories. Model independent tests are attempts to write down a parametrized gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA configuration. We also compare the expected bounds on alternative theories of gravity from ground-based and space-based detectors and find that space-based GW detectors can test GR and other theories of gravity with unprecedented accuracies. We then focus on a recent proposal to use singular value decomposition of the Fisher information matrix to improve the accuracies with which post-Newtonian theory can be tested. We extend those results to the case of space-based detector eLISA and discuss its implications.
Godayol, Pilar
2013-01-01
Simone de Beauvoir fut avec Betty Friedan une des premières théoriciennes du féminisme à arriver en Catalogne dans les années soixante. Cet article rapporte la réception de Simone de Beauvoir en catalan et plus particulièrement l’influence exercée par Le deuxième sexe. Con Betty Friedan, Simone de Beauvoir fue una de las primeras pensadoras feministas que llegaron a Cataluña en los años sesenta. Este artículo da cuenta de la recepción al catalán de Simone de Beauvoir y se fija especialment...
Supersymmetric M5 Brane Theories on R x CP2
Kim, Hee-Cheol
2012-01-01
We propose 4 and 12 supersymmetric Yang-Mills-Chern-Simons theories on $\\mathrm{R\\times CP^2}$ obtained by twisted $\\mathrm{Z}_k$ moddings and dimensional reduction of the 6d (2,0) superconformal field theories on $\\mathrm{R\\times S^5}$. These theories have a discrete coupling constant $\\frac{1}{g^2_{YM}} =\\frac{k}{4\\pi^2}$ so that instantons represent the Kaluza-Klein modes correctly. We calculate the perturbative part of the SU(N) gauge group Euclidean path integral for the index function and confirm it with the known half-BPS index. The scalar and fermionic fields have the conformal dimension prescribed by the 6d theory. From the similar twisted $Z_k$ modding of the $\\mathrm{AdS_7\\times S^4}$ geometry, we speculate that the $M$ region is for $k\\lesssim N^{1/3}$ and the type IIA region is $N^{1/3}\\lesssim k \\lesssim N$. When nonperturbative corrections are included, our theory is expected to produce the full index of the 6d (2,0) theory.
Exact relations between M2-brane theories with and without Orientifolds
Honda, Masazumi
2015-01-01
We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. We mainly focus on circular quiver superconformal Chern-Simons theory on S^3, whose gauge group is O(2N+1)x USp(2N)x ... x O(2N+1)x USp(2N). This theory is a natural generalization of N=5 ABJM theory with the gauge group O(2N+1)_{2k}x USp(2N)_{-k}. We find that the partition function of this type of theory has a simple relation to the one of the M2-brane theories without the orientifolds, whose gauge group is U(N)x ... x U(N). By using this relation, we determine an exact form of the grand partition function of the O(2N+1)_2 x USp(2N)_{-1} ABJM theory, where its supersymmetry is expected to enhance to N=6. As another interesting application, we discuss that our result gives a natural physical interpretation of a relation between grand partition functions of the U(N+1)_4 x U(N)_{-4} ABJ theory and U(N)_2 x U(N)_{-2} ABJM theory, recently conjectured by Grassi-Hatsuda-Marino. We a...
Large N Dualities In Topological String Theory
Okuda, T
2005-01-01
We investigate the phenomenon of large N duality in topological string theory from three different perspectives: worldsheets, matrix models, and melting crystals. In the first part, we utilize the technique of mirror symmetry to generalize the worldsheet derivation of the duality, originally given by Ooguri and Vafa for the A- model on the conifold, to the A-model on more general geometries. We also explain how the Landau-Ginzburg models can be used to perform the worldsheet derivation of the B-model large N dualities. In the second part, we consider a class of A-model large N dualities where the open string theory reduces through the Chern-Simons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the Calabi-Yau geometry mirror to the closed string geometry, confirming the predictions of the duality. Finally in the third part, we propose a crystal model that describes the A-model on the resolved conifold. This is a generalization of the crystal for C3. We also...
Energy Technology Data Exchange (ETDEWEB)
Hoyler, Frieder [Fachhochschule Aachen, Juelich (Germany). Strahlenschutzkursstaette
2013-09-01
The CHERNE network is promoting the cooperation between colleges and research facilities at the training of students. The article describes particular study courses in the field of radiation protection. (orig.)
Improved Linear Cryptanalysis of Reduced-Round SIMON-32 and SIMON-48
DEFF Research Database (Denmark)
Abdelraheem, Mohamed Ahmed; Alizadeh, Javad; Alkhzaimi, Hoda A.;
2015-01-01
In this paper we analyse two variants of SIMON family of light-weight block ciphers against variants of linear cryptanalysis and present the best linear cryptanalytic results on these variants of reducedround SIMON to date. We propose a time-memory trade-off method that finds differential/ linear...
Topological structure of Gauss-Bonnet-Chern theorem and (~p)-branes
Institute of Scientific and Technical Information of China (English)
Tian Miao; Zhang Xin-Hui; Duan Yi-shi
2009-01-01
By making use of the φ-mapping topological current theory,this paper shows that the Gauss-Bonnet-Chern densityof δ(φ),which means that only the zeros of φ contribute to X(M).This is the elementary fact of the Hopf theorem.Furthermore,it presents that a new topological tensor current of (~p)-branes can be derived from the Gauss-Bonnet-Chem density.Using this topological current,it obtains the generalized Nambu action for multi (~p)-branes.
Simon van der Meer (1925-2011)
2011-01-01
Simon van der Meer was a true giant of modern particle physics, though a gentle one. His contributions to accelerator science remain vital for the operation of accelerators such as the LHC today. Simon was an electrical engineer who grew up in The Hague, moving on to Delft University to study electrical engineering. After a short stint with Philips, he came to CERN in 1956, just two years after the lab opened, and remained with us until his retirement in 1990. Simon was an incredibly inventive man. When confronted with a problem, he would sink into deep reflection, rarely emerging until he had a solution. One of us, Steve Myers, remembers him as a man who did not suffer fools gladly, and who was extremely taciturn. Simon would never use two words where one would suffice. But that one word would invariably be the right one. Simon is best known for his contribution to the SPS collider project, for which he was awarded the Nobel Prize, jointly with Carlo Rubbia, in 1984. Stochastic cooling, the in...
Fractional statistics and confinement
Gaete, P; Gaete, Patricio; Wotzasek, Clovis
2004-01-01
It is shown that a pointlike composite having charge and magnetic moment displays a confining potential for the static interaction while simultaneously obeying fractional statistics in a pure gauge theory in three dimensions, without a Chern-Simons term. This result is distinct from the Maxwell-Chern-Simons theory that shows a screening nature for the potential.
Detection of Chirality and Mutations of Knots and Links
Pichai, Ramadevi
2011-01-01
In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more powerful than Jones, HOMFLYPT and Kauffman polynomials. However the classification problem of knots and links is still an open challenging problem.
Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
Park, Jaemo
2013-01-01
We work out Seiberg-like dualities for 3d $\\cN=2$ theories with SU(N) gauge group. We use the $SL(2,\\IZ)$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\\IZ)$ acts as gauging of the U(1) global symmetry. Utilizing $S=S^{-1}$ up to charge conjugation, we obtain Seiberg-like dual of SU(N) theories by gauging topological U(1) symmetry of the Seiberg-like dual of U(N) theories with the same matter content. We work out the Aharony dualities for SU(N) gauge theory with $N_f$ fundamental/anti-fundamnetal flavors, with/without one adjoint matter with the superpotential. We also work out the Giveon-Kutasov dualities for SU(N) gauge theory with Chern-Simons term and with $N_f$ fundamental/anti-fundamental flavors. For all the proposed dualities, we give various evidences such as chiral ring matching and the superconformal index computations. For all dualities proposed, we find the perfect matchings.
John F. Simon, jr. / John F. jun. Simon ; interv. Tilman Baumgärtel
Simon, John F. jun.
2006-01-01
Ameerika kunstnikust-programmeerijast Jon F. Simon juuniorist (sünd. 1963), tema loomingust, vestlus kunstnikuga 19. 12. 1999. a. tema ateljees. J. F. Simon jun.-i teosed on tarkvara. Monitoril tekkinud kujutisi on kunstnik eksponeerinud nimetuse "Panels" all. Kunstniku joonistusprogrammist, arvutiprogrammist "Every Icon", mis asub Internetis, tööst "Combination", võrgutööst "Alter Stars" (1995-1998) ja muust
Bergshoeff, E.; Salam, Abdus; Sezgin, E.
1987-01-01
We consider the superconformal extension of R2 actions in 6 and 10 dimensions. We show that the fields of the conformal multiplet alone admit a one parameter family of R2 actions of the form Ï†[R2ÂµÎ½ab + Î±(R2ÂµÎ½ab - 4R2Âµa + R2)]. In d=6 we give the supersymmetric action for Î± = 0, while for Î±
Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.
2017-03-01
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern-Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields, taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also by oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. This finding suggests an efficient means of extracting the chiral shift parameter from the measurement of the plasma frequencies in Weyl materials.
Hamiltonian theory of the FQHE edge: Collective modes
Nguyen, Hoang; Joglekar, Yogesh; Murthy, Ganpathy
2003-03-01
We study the collective modes of the fractional quantum Hall edge states using the Hamiltonian formalism [1]. While most theoretical approaches start with an effective bosonic theory [2] in which all fermions are integrated out (an exception is the approach based on Chern-Simons theory [3]), the Hamiltonian theory treats the composite fermions as fully interacting. We obtain the gapless edge-modes using a conserving approximation which respects the constraints [4]. The implications of our study to the tunneling experiments into the edge of a fractional quantum Hall system [5] are discussed. [1] R.Shankar and G.Murthy, Phys.Rev.Lett. 79, 4437 (1997). [2] X.-G.Wen, Phys.Rev.Lett. 64, 2206 (1990); D.-H.Lee and X.-G.Wen, cond-mat/9809160; A.Lopez and E.Fradkin, Phys.Rev.B 59, 15323 (1999); U. Zulicke and A.H.MacDonald, Phys.Rev.B 60, 1837 (1999); V.J.Goldman and E.V.Tsiper, Phys.Rev.Lett. 86, 5841 (2001); S.S.Mandal and J.K.Jain, Phys.Rev.Lett. 89, 096801 (2002). [3] L.S.Levitov, A.V.Shytov, and B.I.Halperin, Phys. Rev. B 64, 075322 (2001). [4] N. Read, Phys.Rev.B 58, 16262 (1998); G. Murthy, Phys.Rev.B 64, 195310 (2001). [5] A.M.Chang et.al., Phys.Rev.Lett. 86, 143 (2000).
Matrix models and stochastic growth in Donaldson-Thomas theory
Energy Technology Data Exchange (ETDEWEB)
Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)
2012-10-15
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J.; Tierz, Miguel
2012-10-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J
2010-01-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating ...
A Chern-Weil Isomorphism for the Equivariant Brauer Group
Bouwknegt, Peter; Ratnam, Rishni
2011-01-01
In this paper we construct a Chern-Weil isomorphism for the equivariant Brauer group of R^n-actions on a principal torus bundle, where the target for this isomorphism is a "dimensionally reduced" Cech cohomology group. From this point of view, the usual forgetful functor takes the form of a connecting homomorphism in a long exact sequence in dimensionally reduced cohomology.
Two-dimensional Chern semimetals on the Lieb lattice
Palumbo, Giandomenico; Meichanetzidis, Konstantinos
2015-12-01
In this work we propose a simple model that supports Chern semimetals. These gapless topological phases share several properties with the Chern insulators like a well-defined Chern number associated with each band, topologically protected edge states and topological phase transitions that occur when the bands touch each, with linear dispersion around the contact points. The tight-binding model, defined on the Lieb lattice with intra-unit-cell and suitable nearest-neighbor hopping terms between three different species of spinless fermions, supports a single Dirac-like point. The dispersion relation around this point is fully relativistic and the 3 ×3 matrices in the corresponding effective Hamiltonian satisfy the Duffin-Kemmer-Petiau algebra. We show the robustness of the topologically protected edge states by employing the entanglement spectrum. Moreover, we prove that the Chern number of the lowest band is robust with respect to weak disorder. For its simplicity, our model can be naturally implemented in real physical systems like cold atoms in optical lattices.
Montonen, Claus
1995-01-01
Lectures presented at the VI Mexican School of Particles and Fields, Villahermosa, 3-7 October, 1994. Contents: 1. Introduction 2. The Symmetry Group Approach to the Quantum Mechanics of Identical Particles 3. How Come Anyons? 4. The Transmutation of Statistics into a Topological Interaction 5. The Chern-Simons Action and Anyon Statistics 6. Nonrelativistic Chern-Simons-(Maxwell) Field Theory 7. Epilogue
Exotic twisted equivariant cohomology of loop spaces,twisted Bismut-Chern character and T-duality
Han, Fei
2014-01-01
We define completed periodic {\\em exotic twisted $\\mathbb{T}$-equivariant cohomology} for loop spaces of smooth manifolds. We then show that the twisted Bismut-Chern character, defined on the twisted K-theory of the smooth manifold, twisted by a gerbe with connection, takes values in the completed periodic exotic twisted $\\mathbb{T}$-equivariant cohomology of the loop space of the smooth manifold. We establish a localisation theorem for the completed periodic exotic twisted $\\mathbb{T}$-equivariant cohomology for loop spaces and apply it to establish T-duality in a background flux in type II String Theory from a loop space perspective.
An Interview with AbdouMaliq Simone
Burga, Hector Fernando
2009-01-01
AbdouMaliq Simone is an urbanist and professor of sociology at Goldsmiths College, University of London. Since 1977 he has many jobs in different cities across Africa and Southeast Asia, in the fields of education, housing, social welfare, community development, local government and economic development. His best known publications are In Whose Image: Political Islam and Urban Practices in the Sudan and For the City Yet to Come: Urban change in Four African Cities. A forthcoming book is entit...
Complete intersections K-theory and Chern classes
Mandal, S S
1996-01-01
Throughout this abstruct A will denote a noetherian commutative ring of dimension n. The paper has two parts. Among the interesting results in Part-1 are the following: 1) {\\it suppose that f_1, f_2, \\ldots, f_r (with r \\leq n) is a regular sequence in A and suppose Q is a projective A-module of rank r that maps onto the ideal (f_1, f_2, \\ldots, f_{r-1},f_r^{(r-1)!}). Then [Q]=[Q_0 \\oplus A] in K_0(A) for some projective A-module~Q_0 of rank r-1.} 2) The set F_0K_0(A) = \\{[A/I] \\in K_0(A): I~ is~ a~ locally~ complete ~intersection~ ideal~ in~ A~ of~ height~n \\} is a {\\it subgroup} of K_0(A). We also show that if A is a reduced affine algebra over a field k then F_0K_0(A) {\\it is indeed the Zero Cycle Subgroup of} K_0(A) {\\it that is generated by smooth maximal ideals} \\Cal M {\\it of height} n. 3){\\it let A be such that whenever I is a locally complete intersection ideal of height n with [A/I]=0 then I is the image of a projective A-module of rank n. Then for any locally complete intersection ideal J of height...
(3+1)D Anomalous Twisted Gauge Theories with Global Symmetry
Ye, Peng
2016-01-01
In (3+1)D twisted gauge theories, global symmetry may be imposed on topological currents $\\star\\frac{1}{2\\pi}db^I$ in a hydrodynamical way ($I=1,2,\\cdots$, $\\{b^I\\}$ is a set of Kalb-Ramond gauge fields). This methodology has been applied before in the Chern-Simons theory of fractional quantum Hall liquids. We find that, in some twisted gauge theories (with discrete Abelian gauge group $G_g$), implementing a global symmetry (denoted by $G_s$) is always inconsistent. There are two consequences. First, the symmetry-enriched topological order (SET) of the ground state is anomalous, which cannot exist in (3+1)D system alone. It can exist as a boundary of 4+1D topological phases. Second, if $G_s$ is fully gauged, the resulting new gauge theory has gauge anomaly. A (4+1)D topological phase is required to cancel this anomaly. We elaborate this phenomenon via a concrete example.
Application of abelian holonomy formalism to the elementary theory of numbers
Abe, Yasuhiro
2012-05-01
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on S1 × S1 × R. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of Fp = Z/pZ, where p is an odd prime number. This enables us to calculate "scattering amplitudes" of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of "scattering" for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be useful for studies on quantum aspects of topology and number theory.
The spider genera Euthycaelus Simon and Schismatothele Karsch (Mygalomorphae, Theraphosidae).
Guadanucci, José Paulo Leite; Weinmann, Dirk
2014-05-13
The genus Euthycaelus Simon 1889 is diagnosed based on the examination of type-material and additional material from Venezuela and Colombia. The genus now includes: Euthycaelus colonicus Simon 1889, E. norae sp. nov., E. amandae sp. nov.; Euthycaelus steini Simon 1889 is transferred to Psalistops comb. nov. The genus Schismatothele Karsch 1879 is considered a senior synonym of Hemiercus Simon 1903. Schismatothele includes S. lineata Karsch 1879, S. inflata (Simon 1889) comb. nov., S. modesta (Simon 1889) comb. nov, and S. benedettii Panzera et al. 2011. Hemiercus proximus Mello-Leitão 1923, from Cubatão, São Paulo, Brazil, is transferred to Acanthoscurria proxima (Mello-Leitão 1923) comb. nov. Hemiercus kastoni Caporiacco 1955 is considered a species inquirenda pending the examination of the type material.
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J; Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of $q$-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for $U(N)$ Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold ...
Topological quantum field theory: 20 years later
DEFF Research Database (Denmark)
Reshetikhin, Nicolai
2008-01-01
This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory.......This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory....
Flat Chern band in a two-dimensional organometallic framework.
Liu, Zheng; Wang, Zheng-Fei; Mei, Jia-Wei; Wu, Yong-Shi; Liu, Feng
2013-03-01
By combining exotic band dispersion with nontrivial band topology, an interesting type of band structure, namely, the flat Chern band, has recently been proposed to spawn high-temperature fractional quantum Hall states. Despite the proposal of several theoretical lattice models, however, it remains doubtful whether such a "romance of flatland" could exist in a real material. Here, we present a first-principles design of a two-dimensional indium-phenylene organometallic framework that realizes a nearly flat Chern band right around the Fermi level by combining lattice geometry, spin-orbit coupling, and ferromagnetism. An effective four-band model is constructed to reproduce the first-principles results. Our design, in addition, provides a general strategy to synthesize topologically nontrivial materials by virtue of organic chemistry and nanotechnology.
Connes-Chern character for manifolds with boundary and eta cochains
Lesch, Matthias; Pflaum, Markus J
2009-01-01
We represent the Connes-Chern character of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off parameter. Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a cocycle whose expression involves higher eta cochains and their b-analogues. The corresponding formulae for the pairing with relative K-theory classes retain information about the boundary, and thus have geometric implications. In particular, they lead to a generalization of the Atiyah-Patodi-Singer odd-index theorem, from trivialized flat bundles to any pair of K-equivalent vector bundles.
Review of Raffaele Simone and Francesca Masini: Word classes: Nature, typology and representations
DEFF Research Database (Denmark)
Shibuya, Yoshikata; Jensen, Kim Ebensgaard
2016-01-01
Review of Raffaele Simone and Francesca Masini (eds.). Word classes: Nature, typology and representations. Current Issues in Linguistic Theory [CILT] 332. Amsterdam/ Philadelphia: John Benjamins Publishing Company, 2014, 293 + vii pp., ISBN: 1978-90-272-4851-0. Hardback and E-book 99.00 EUR / 149...