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Sample records for chern-simons gauge theory

  1. Gauge dependence in Chern-Simons theory

    CERN Document Server

    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 \

  2. Frobenius-Chern-Simons gauge theory

    Science.gov (United States)

    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) .

  3. Frobenius-Chern-Simons gauge theory

    CERN Document Server

    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...

  4. String theory duals of Lifshitz-Chern-Simons gauge theories

    CERN Document Server

    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.

  5. Topics In Gauge Theory (effective Action, Quantum Electrodynamics, Chern Simons)

    CERN Document Server

    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...

  6. Gauge invariance and finite temperature effective actions of Chern-Simons gauge theories with fermions

    CERN Document Server

    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.

  7. Gauge and supersymmetry invariance of N = 2 boundary Chern-Simons theory

    Science.gov (United States)

    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.

  8. 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.)

  9. Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory

    Institute of Scientific and Technical Information of China (English)

    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.

  10. Torsion as a Gauge Field in a Lorentz-Chern-Simons Theory

    CERN Document Server

    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.

  11. Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields

    CERN Document Server

    Kim, Hyojoong

    2012-01-01

    The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established yet, due to technical problems in both analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested that the counting of chiral operators can be used to find the eigenvalue distribution of quiver matrix models. In this paper we apply this method to some vector-like or chiral-like quiver theories, including the triangular quivers with generic Chern-Simons levels which are dual to in-homogeneous Sasaki-Einstein manifolds $Y^{p,k}(\\mathbb{CP}^2)$. The result is consistent with AdS/CFT and the volume formula. We discuss the implication of our analysis.

  12. Chern-Simons theory with finite gauge group

    Science.gov (United States)

    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.

  13. Observables, skein relations, and tetrahedra in Chern-Simons gauge theory

    Science.gov (United States)

    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.

  14. From Doubled Chern-Simons-Maxwell Lattice Gauge Theory to Extensions of the Toric Code

    CERN Document Server

    Olesen, T Z; Wiese, U -J

    2015-01-01

    We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group $\\mathbb{R}$, each local Hilbert space is analogous to the one of a charged "particle" moving in the link-pair group space $\\mathbb{R}^2$ in a constant "magnetic" background field. In the compact case, the link-pair group space is a torus $U(1)^2$ threaded by $k$ units of quantized "magnetic" flux, with $k$ being the level of the Chern-Simons theory. The holonomies of the torus $U(1)^2$ give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry...

  15. 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...

  16. Induced spin from the ISO(2,1) gauge theory with the gravitational Chern-Simons term

    CERN Document Server

    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\

  17. On Fractional Quantum Hall Solitons and Chern-Simons Quiver Gauge Theories

    CERN Document Server

    Belhaj, Adil

    2011-01-01

    We investigate a class of hierarchical multiple layers of fractional quantum Hall solitons (FQHS) systems from Chern-Simons quivers embedded in M-theory on the cotangent on a 2-dimensional complex toric variety \\bf V^2, which is dual to type IIA superstring on a 3-dimensional complex manifolds \\bf {CP}^1\\times V^2 fibered over a real line \\mathbb{R}. Based on M-theory/Type IIA duality, FQHS systems can be derived from wrapped D4-branes on 2-cycles in \\bf {CP}^1\\times V^2 type IIA geometry. In this realization, the magnetic source can be identified with gauge fields obtained from the decomposition of the R-R 3-form on a generic combination of 2-cycles. Using type IIA D-brane flux data, we compute the filling factors for models relying on \\bf {CP}^2 and the zeroth Hirzebruch surface.

  18. Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group

    CERN Document Server

    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...

  19. 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...

  20. 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...

  1. Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group

    Science.gov (United States)

    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.

  2. Self-dual Chern-Simons theories

    CERN Document Server

    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....

  3. Instanton Counting and Chern-Simons Theory

    Energy Technology Data Exchange (ETDEWEB)

    Kashani-Poor, Amir-Kian

    2003-02-06

    The instanton partition function of N = 2, D = 4 SU(2) gauge theory is obtained by taking the field theory limit of the topological open string partition function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the open string side is obtained by geometric transition from local IP{sup 1} x IP{sup 1} which is used in the geometric engineering of the SU(2) theory. The partition function obtained from the Chern-Simons theory agrees with the closed topological string partition function of local IP{sup 1} x IP{sup 1} proposed recently by Nekrasov. We also obtain the partition functions for local F{sub 1} and F{sub 2} CY3-folds and show that the topological string amplitudes of all three local Hirzebruch surfaces give rise to the same field theory limit. It is shown that a generalization of the topological closed string partition function whose field theory limit is the generalization of the instanton partition function, proposed by Nekrasov, can be determined easily from the Chern-Simons theory.

  4. Level/rank Duality and Chern-Simons-Matter Theories

    CERN Document Server

    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.

  5. Hidden singularities and closed timelike curves in a proposed dual for Lifshitz-Chern-Simons gauge theories

    CERN Document Server

    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.

  6. 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.

  7. 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.

  8. Maxwell-Chern-Simons theory and an ambiguity in Chern-Simons perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    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.).

  9. The moduli spaces of $3d$ ${\\cal N} \\ge 2$ Chern-Simons gauge theories and their Hilbert series

    CERN Document Server

    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.

  10. Chern-Simons theory in SIM(1) superspace

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  11. Topological obstructions in Lagrangian field theories, with an application to 3D Chern-Simons gauge theory

    CERN Document Server

    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.

  12. Topological obstructions in Lagrangian field theories, with an application to 3D Chern-Simons gauge theory

    Science.gov (United States)

    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.

  13. Abelian Chern-Simons theory, Stokes' Theorem, and generalized connections

    CERN Document Server

    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.

  14. Lecture notes on Chern-Simons-Witten theory

    CERN Document Server

    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

  15. Chern-Simons Theory on Supermanifolds

    CERN Document Server

    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.

  16. W∞ Algebras from Noncommutative Chern Simons Theory

    Science.gov (United States)

    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.

  17. A Lie based 4-dimensional higher Chern-Simons theory

    CERN Document Server

    Zucchini, Roberto

    2015-01-01

    We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.

  18. 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...

  19. Embedded graph invariants in Chern-Simons theory

    OpenAIRE

    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 ...

  20. 4-d semistrict higher Chern-Simons theory I

    CERN Document Server

    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.

  1. Schwinger-Dyson functional in Chern-Simons theory

    CERN Document Server

    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.

  2. Schwinger-Dyson functional in Chern-Simons theory

    Science.gov (United States)

    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.

  3. Vector and Spinor Decomposition of SU(2) Gauge Potential, Their Equivalence, and Knot Structure in SU(2) Chern-Simons Theory

    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.

  4. Maxwell Chern Simons Theory in a Geometric Representation

    CERN Document Server

    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

  5. Topological entanglement negativity in Chern-Simons theories

    CERN Document Server

    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).

  6. Topological entanglement negativity in Chern-Simons theories

    Science.gov (United States)

    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].

  7. Baryons, monopoles and dualities in Chern-Simons-matter theories

    Energy Technology Data Exchange (ETDEWEB)

    Aharony, Ofer [Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot, 7610001 (Israel)

    2016-02-15

    There is significant evidence for a duality between (non-supersymmetric) U(N) Chern-Simons theories at level k coupled to fermions, and U(k) Chern-Simons theories at level N coupled to scalars. Most of the evidence comes from the large N ’t Hooft limit, where many details of the duality (such as whether the gauge group is U(N) or SU(N), the precise level of the U(1) factor, and order one shifts in the level) are not important. The main evidence for the validity of the duality at finite N comes from adding masses and flowing to pure Chern-Simons theories related by level-rank duality, and from flowing to the non-supersymmetric duality from supersymmetric dualities, whose finite N validity is well-established. In this note we clarify the implications of these flows for the precise form of the duality; in particular we argue that in its simplest form the duality maps SU(N) theories to U(k) theories, though there is also another version relating U(N) to U(k). This precise form strongly affects the mapping under the duality of baryon and monopole operators, and we show, following arguments by Radičević, that their mapping is consistent with our claims. We also discuss the implications of our results for the additional duality between these Chern-Simons matter theories and (the UV completion of) high-spin gravity theories on AdS{sub 4}. The latter theories should contain heavy particles carrying electric and/or magnetic charges under their U(1) gauge symmetry.

  8. Higher-spin Chern-Simons theories in odd dimensions

    Energy Technology Data Exchange (ETDEWEB)

    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}.

  9. Combinatorial quantization of the Hamiltonian Chern-Simons theory, 2

    CERN Document Server

    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...

  10. W-Infinity Algebras from Noncommutative Chern-Simons Theory

    CERN Document Server

    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.

  11. Gauge Symmetries and Holographic Anomalies of Chern-Simons and Transgression AdS Gravity

    CERN Document Server

    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.

  12. Chern-Simons functional under gauge transformations on flat bundles

    Science.gov (United States)

    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.

  13. Matroid theory and Chern-Simons

    Science.gov (United States)

    Nieto, J. A.; Marín, M. C.

    2000-12-01

    It is shown that matroid theory may provide a natural mathematical framework for a duality symmetries not only for quantum Yang-Mills physics, but also for M-theory. Our discussion is focused in an action consisting purely of the Chern-Simons term, but in principle the main ideas can be applied beyond such an action. In our treatment the theorem due to Thistlethwaite, which gives a relationship between the Tutte polynomial for graphs and Jones polynomial for alternating knots and links, plays a central role. Before addressing this question we briefly mention some important aspects of matroid theory and we point out a connection between the Fano matroid and D=11 supergravity. Our approach also seems to be related to loop solutions of quantum gravity based in an Ashtekar formalism.

  14. Eta-invariants and anomalies in U(1)-Chern-Simons theory

    CERN Document Server

    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.

  15. Kinetic derivation of generalized phase space Chern-Simons theory

    CERN Document Server

    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.

  16. 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.

  17. Link Invariants from Classical Chern-Simons Theory

    CERN Document Server

    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.

  18. 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.

  19. Extended higher cup-product Chern-Simons theories

    CERN Document Server

    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...

  20. Spinor Decomposition of SU(2) Gauge Potential and Spinor Structures of Chern-Simons and Chern Density

    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.

  1. Spinor Decomposition of SU(2) Gauge Potential and Spinor Structures of Chern-Simons and Chern Density

    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.

  2. Gauged Baby Skyrme Model with Chern-Simons term

    CERN Document Server

    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, ...

  3. Chern-Simons theory on a lattice and a new description of 3-manifolds invariants

    CERN Document Server

    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.

  4. Quaternion based generalization of Chern-Simons theories in arbitrary dimensions

    CERN Document Server

    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.

  5. Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups

    CERN Document Server

    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 $N_f \\leq N-2$).

  6. Extended higher cup-product Chern-Simons theories

    Science.gov (United States)

    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.

  7. Batalin-Tyutin quantization of the Chern-Simons-Proca theory

    CERN Document Server

    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.

  8. Chern-Simons-like Gravity Theories

    NARCIS (Netherlands)

    Bergshoeff, Eric A.; Hohm, Olaf; Merbis, Wout; Routh, Alasdair J.; Townsend, Paul K.

    2014-01-01

    A wide class of three-dimensional gravity models can be put into "Chern-Simons-like" form. We perform a Hamiltonian analysis of the general model and then specialise to Einstein-Cartan Gravity, General Massive Gravity, the recently proposed Zwei-Dreibein Gravity and a further parity violating

  9. Perturbative expansion of Chern-Simons theory

    OpenAIRE

    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.

  10. Dynamical Chern-Simons Theory in the Brillouin Zone

    CERN Document Server

    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.

  11. Deformation of surfaces, integrable systems, and Chern-Simons theory

    Science.gov (United States)

    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.

  12. Explicit connection between conformal field theory and 2+1 Chern-Simons theory

    CERN Document Server

    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.

  13. Z Extremization in Chiral-Like Chern Simons Theories

    CERN Document Server

    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.

  14. Topological boundary conditions in abelian Chern-Simons theory

    Energy Technology Data Exchange (ETDEWEB)

    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.

  15. Remarks on the solutions of the Maxwell- Chern-Simons theories

    CERN Document Server

    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.

  16. Uncertainty Relations and Quantum Effects of Constraints in Chern-Simons Theory

    CERN Document Server

    Nakamura, M

    2013-01-01

    It is well known that Chern-Simons Theories are in the constrained systems and their total Hamiltonians become identically zero, because of their gauge invariance. While treating the constraints quantum mechanially, it will be expected taht there remain the quantum fluctuations due to the uncertainty principle. Using the projection operator method (POM) and the theory of dynamical constraints, such fluctuation terms are systematically derived in the case of Abelian Chern-Simons theory. It is shown that these terms produce the effective mass in the complex scalar fields coupled to the CS fields.

  17. The A-polynomial in Chern-Simons theory

    DEFF Research Database (Denmark)

    Malusà, Alessandro

    One of the most amusing aspects of mathematical physics is the great variety of areas of mathematics it relates to, and builds bridges between. The world of TQFT’s, and in particular Chern-Simons, relates to algebraic geometry via the theory of moduli spaces: one example of this is given by the A......-polynomial. This knot invariant is obtained from the algebraic geometry of character varieties, and takes the meaning of the equation of a constraint central in Chern-Simons theory. In my poster I wish to expose the construction of this invariant, and highlight its strong ties with mathematical physics....

  18. Disorder operators in Chern-Simons-fermion theories

    Energy Technology Data Exchange (ETDEWEB)

    Radičević, Ðorđe [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)

    2016-03-18

    Building on the recent progress in solving Chern-Simons-matter theories in the planar limit, we compute the scaling dimensions of a large class of disorder (“monopole”) operators in U(N){sub k} Chern-Simons-fermion theories at all ’t Hooft couplings. We find that the lowest-dimension operator of this sort has dimension (2/3)k{sup 3/2}. We comment on the implications of these results to analyzing maps of fermionic disorder operators under 3D bosonization.

  19. Aspects of monopole operators in N=6 Chern-Simons theory

    CERN Document Server

    Kim, Seok

    2009-01-01

    We study local operators of U(N)xU(N) N=6 Chern-Simons-matter theory including a class of magnetic monopole operators. To take into account the interaction of monopoles and basic fields for large Chern-Simons level k, we consider the appropriate perturbation theory in 1/k which reliably describes small excitations around protected chiral operators. We also compute the superconformal index for the simplest monopole operators and show that it agrees with the recent result obtained from localization. For this agreement, it is crucial that excitations of gauge fields and some matter scalars mix, which is described classically by odd dimensional self-duality equations.

  20. Quantum modularity and complex Chern-Simons theory

    CERN Document Server

    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 $\\zeta^k=1$.

  1. Fermionic impurities in Chern-Simons-matter theories

    Science.gov (United States)

    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.

  2. Fermionic impurities in Chern-Simons-matter theories

    CERN Document Server

    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.

  3. New Phase Transitions in Chern-Simons Matter Theory

    CERN Document Server

    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...

  4. Knots in $SU\\left(M|N\\right) $ Chern-Simons Field Theory

    OpenAIRE

    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) $.

  5. Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D

    CERN Document Server

    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.

  6. Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity

    Science.gov (United States)

    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.

  7. Embedded graph invariants in Chern-Simons theory

    Science.gov (United States)

    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.

  8. Embedded graph invariants in Chern-Simons theory

    CERN Document Server

    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.

  9. Visible and hidden sectors in a model with Maxwell and Chern-Simons gauge dynamics

    Science.gov (United States)

    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.

  10. Visible and hidden sectors in a model with Maxwell and Chern-Simons gauge dynamics

    CERN Document Server

    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.

  11. 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].

  12. Chern-Simons theory, Stokes' Theorem, and the Duflo map

    CERN Document Server

    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.

  13. Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field arXiv

    CERN Document Server

    Figueroa, Daniel G.

    Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction between a $shift$-symmetric field and some $U(1)$ gauge sector, $a(x)\\tilde{F}_{\\mu\

  14. Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity

    CERN Document Server

    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...

  15. Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm

    Science.gov (United States)

    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.

  16. Super-Chern-Simons Theory as Superstring Theory

    CERN Document Server

    Grassi, P A

    2004-01-01

    Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with bosonic and fermionic strings. Here we present a common geometrical setting to develop systematically the prescription for amplitude computations. The geometrical origin of these difficulties is the theory of integration of superforms. We provide a translation between the theory of supermanifolds and topological strings with supertarget space. We show how in this formulation one can naturally construct picture changing operators to be inserted in the correlation functions to soak up the zero modes of commuting ghost and we derive the amplitude prescriptions from the coupling with an extended topological gravity on the worldsheet. As an application we consider a simple model on R^(3|2) leading to super-Chern-Simons theory.

  17. 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.

  18. Dual superconformal symmetry of N = 6 Chern-Simons theory

    OpenAIRE

    Huang, Yu-tin(School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.); Arthur E. Lipstein

    2010-01-01

    We demonstrate that the four and six-point tree-level amplitudes of N = 6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP^3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some impli...

  19. Entanglement from Topology in Chern-Simons Theory

    CERN Document Server

    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...

  20. Dimensionally compactified Chern-Simon theory in 5D as a gravitation theory in 4D

    CERN Document Server

    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.

  1. Chern-Simons theory for Heisenberg spins on the Kagome Lattice

    Science.gov (United States)

    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 .

  2. Charged rotating black holes in Einstein--Maxwell--Chern-Simons theory with negative cosmological constant

    CERN Document Server

    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...

  3. Supersymmetric Yang-Mills theory as higher Chern-Simons theory

    Science.gov (United States)

    Sämann, Christian; Wolf, Martin

    2017-07-01

    We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.

  4. Gravitational and gauge couplings in Chern-Simons fractional spin gravity

    Energy Technology Data Exchange (ETDEWEB)

    Boulanger, Nicolas [Mécanique et Gravitation, Université de Mons - UMONS,20 Place du Parc, 7000 Mons, Belgique (Belgium); Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS,Université François Rabelais,Parc de Grandmont, 37200 Tours (France); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Valenzuela, Mauricio [Facultad de Ingeniería y Tecnología, Universidad San Sebastían,General Lagos 1163, Valdivia 5110693 (Chile)

    2016-01-28

    We propose an extension of Vasiliev’s supertrace operation for the enveloping algebra of Wigner’s deformed oscillator algebra to the fractional spin algebra given in http://arxiv.org/abs/1312.5700. We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern-Simons theory for Blencowe-Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2ℓ+1) or gl(ℓ|ℓ+1) and various real forms thereof.

  5. Chern-Simons theory for frustrated quantum magnets

    Science.gov (United States)

    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.

  6. Transgression forms as source for topological gravity and Chern-Simons-Higgs theories

    CERN Document Server

    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...

  7. L∞-algebra models and higher Chern-Simons theories

    Science.gov (United States)

    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.

  8. Chern Simons bosonization along RG flows

    National Research Council Canada - National Science Library

    Minwalla, Shiraz; Yokoyama, Shuichi

    2016-01-01

    It has previously been conjectured that the theory of free fundamental scalars minimally coupled to a Chern Simons gauge field is dual to the theory of critical fundamental fermions minimally coupled...

  9. Framing and localization in Chern-Simons theories with matter

    Energy Technology Data Exchange (ETDEWEB)

    Bianchi, Marco S. [Center for Research in String Theory - School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Griguolo, Luca [Dipartimento di Fisica e Scienze della Terra, Università di Parma andINFN Gruppo Collegato di Parma,Viale G.P. Usberti 7/A, 43100 Parma (Italy); Leoni, Matias [Physics Department, FCEyN-UBA & IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina); Mauri, Andrea [Dipartimento di Fisica, Università degli studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Penati, Silvia [Dipartimento di Fisica, Università degli studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Seminara, Domenico [Dipartimento di Fisica, Università di Firenze and INFN Sezione di Firenze,via G. Sansone 1, 50019 Sesto Fiorentino (Italy)

    2016-06-22

    Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.

  10. 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.

  11. Instability of Chern-Simons Theory with Fermions at Large N

    CERN Document Server

    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.

  12. Transgressions and Holographic Conformal Anomalies for Chern-Simons Gravities

    CERN Document Server

    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.

  13. String Theory Origin of Dyonic N=8 Supergravity and Its Chern-Simons Duals.

    Science.gov (United States)

    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.

  14. Wave function of the Universe and Chern-Simons Perturbation Theory

    CERN Document Server

    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.

  15. 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....

  16. Chern-Simons-Higgs theory with visible and hidden sectors and its N = 2 SUSY extension

    Science.gov (United States)

    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.

  17. Perturbative Aspects of the Chern-Simons Topological Quantum Field Theory

    Science.gov (United States)

    Bar-Natan, Dror-Dror

    We investigate the Feynman-diagram perturbative expansion of the Chern-Simons topological quantum field theory. After introducing the theory, we compute the on -loop expectation value for knots and links, recovering Gauss' linking number formula for links and the self-linking number of a framed knot. The self-linking formula is shown to suffer from an anomaly proportional to the total torsion of the knot, whose definition requires 'framing' the knot. This explains the appearance of framings. In an appendix, we use these results to characterize the total torsion of a curve as the only parametrization independent quantity of vanishing scaling dimension having 'local' variation, explaining why no further anomalies are expected. We then treat rigorously the two loop expectation value of a knot, finding it to be finite and invariant under isotopy. We identify the resulting knot invariant to essentially be the second coefficient of the Conway polynomial, in agreement with Witten's earlier non-perturbative computation. We give 'formal' (namely, algebraic with missing analytical details) proofs that the perturbative expansion gives manifold and link invariants and suggest that a slight generalization of the Feynman rules of the Chern-Simons theory might still give knot invariants, possibly new. We discuss the relation between perturbation theory and the Vassiliev knot invariants, solving a related algebraic problem posed by Birman and Lin. We compute the stationary phase approximation to the Chern-Simons path integral with compact and non -compact gauge group, explaining the appearance of framings of 3-manifolds and the so called 'shift in k', and finding the result in the non-compact case not to be a simple analytic continuation of the result in the compact case. Finally we outline our expectation for the behavior of the theory beyond the one- and two-loop rigorous results.

  18. Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit

    CERN Document Server

    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.

  19. Superconformal Chern-Simons-matter theories in N =4 superspace

    Science.gov (United States)

    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.

  20. 3d N = 1 Chern-Simons-matter theory and localization

    Science.gov (United States)

    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.

  1. Non-Abelian vortices in Chern-Simons theories and their induced effective theory

    CERN Document Server

    Aldrovandi, L G

    2007-01-01

    Non-Abelian vortices for a supersymmetric {\\cal N}=2 Chern-Simons-Higgs theory are explicitly constructed. We introduce N Higgs fields in the fundamental representation of the U(N) gauge group in order to have a color-flavor SU(N) group remaining unbroken in the asymmetric phase. Bogomol'nyi-like first order equations are found and rotationally symmetric solutions are proposed. These solutions are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. The low energy effective action for the orientational moduli results to be the one-dimensional supersymmetric {\\cal N}=2 CP^{N-1} model. We analyze the quantum mechanics of this effective theory in the N=2 case.

  2. 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.

  3. Chern-Simons theory and Wilson loops in the Brillouin zone

    Science.gov (United States)

    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.

  4. Kauffman Knot Invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts Model

    CERN Document Server

    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.

  5. Effective action of 6D F-Theory with U(1) factors: Rational sections make Chern-Simons terms jump

    CERN Document Server

    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.

  6. Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity

    CERN Document Server

    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.

  7. Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity

    Science.gov (United States)

    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.

  8. On supersymmetric Chern-Simons-type theories in five dimensions

    CERN Document Server

    Kuzenko, Sergei M

    2014-01-01

    We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor multiplet is described in superspace for the first time.

  9. Quantum Hairs and Isolated Horizon Entropy from Chern-Simons Theory

    CERN Document Server

    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...

  10. 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.)

  11. Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories

    CERN Document Server

    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.

  12. Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace

    CERN Document Server

    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.

  13. A Chern-Simons pandemic

    Science.gov (United States)

    Montero, Miguel; Uranga, Angel M.; Valenzuela, Irene

    2017-07-01

    In this paper we study the consistency of generalized global symmetries in theories of quantum gravity, in particular string theory. Such global symmetries arise in theories with ( p + 1)-form gauge fields, and for spacetime dimension d ≤ p + 3 there are obstructions to their breaking even by quantum effects of charged objects. In 4d theories with a 2-form gauge field (or with an axion scalar), these fields endow Schwarzschild black holes with quantum hair, a global charge leading to usual trouble with remnants. We describe precise mechanisms, and examples from string compactifications and holographic pairs, in which these problems are evaded by either gauging or breaking the global symmetry, via (suitable versions of) Stuckelberg or 4-form couplings. We argue that even in the absence of such couplings, the generic solution in string theory is the breaking of the global symmetries by cubic Chern-Simons terms involving different antisymmetric tensor fields. We conjecture that any theory with (standard or higher-degree antisymmetric tensor) gauge fields is in the Swampland unless its effective action includes such Chern-Simons terms. This conjecture implies that many familiar theories, like QED (even including the charged particles required by the Weak Gravity Conjecture) or N=8 supergravity in four dimensions, are inconsistent in quantum gravity unless they are completed by these Chern-Simons terms.

  14. 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...

  15. SL(2,C) Chern-Simons Theory and Quantum Gravity with a Cosmological Constant

    Science.gov (United States)

    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.

  16. The path integral quantization and the construction of the S-matrix in the abelian and non-abelian Chern-Simons theories

    CERN Document Server

    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-...

  17. A Vector Non-abelian Chern-Simons Duality

    CERN Document Server

    García-Compéan, H; Ramírez, C

    2002-01-01

    Abelian Chern-Simons gauge theory it is known to possess a `S-self-dual' action where its coupling constant k is inverted i.e. k goes to 1/k. Here a vector non-abelian duality it is found in the pure non-abelian Chern-Simons action at the classical level. The procedure is given explicitly for the gauge group SU(2), but it is valid for any compact Lie group. The dimensional reduction of the dual Chern-Simons action to two-dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.

  18. Twisted Chern-Simons supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Castellani, L. [Dipartimento di Scienze e Innovazione Tecnologica, Univ. del Piemonte Orientale, Alessandria (Italy); INFN Gruppo collegato di Alessandria (Italy)

    2014-09-11

    We present a noncommutative version of D = 5 Chern-Simons supergravity, where noncommutativity is encoded in a *-product associated to an abelian Drinfeld twist. The theory is invariant under diffeomorphisms, and under the *-gauge supergroup SU(2,2 vertical stroke 4), including Lorentz and N = 4 local supersymmetries. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  19. D2-brane Chern-Simons theories: F-maximization = a-maximization

    CERN Document Server

    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.

  20. 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)

  1. Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory

    CERN Document Server

    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.

  2. Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector

    CERN Document Server

    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.

  3. Chern-Simons-Higgs Theory with Visible and Hidden Sectors and its ${\\cal N}=2$ SUSY Extension

    CERN Document Server

    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.

  4. Chern-Simons actions and their gaugings in 4D, N=1 superspace

    Energy Technology Data Exchange (ETDEWEB)

    Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843-4242 (United States)

    2016-06-17

    We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra g. The resulting non-abelian tensor hierarchy can be interpreted via a g-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.

  5. The Chern-Simons Number as a Dynamical Variable

    CERN Document Server

    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.

  6. Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.

    Science.gov (United States)

    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.

  7. Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory

    Science.gov (United States)

    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.

  8. Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants

    CERN Document Server

    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...

  9. Split Chern-Simons theory in the BV-BFV formalism

    CERN Document Server

    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.

  10. Light States in Chern-Simons Theory Coupled to Fundamental Matter

    CERN Document Server

    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.

  11. Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

    CERN Document Server

    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

  12. Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

    Science.gov (United States)

    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.

  13. F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories

    CERN Document Server

    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.

  14. The Quantum Hall Effect in Supersymmetric Chern-Simons Theories

    CERN Document Server

    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.

  15. Black hole entropy in the Chern-Simons-like theories of gravity and Lorentz-diffeomorphism Noether charge

    Science.gov (United States)

    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.

  16. Black hole entropy in the Chern-Simons-like theories of gravity and Lorentz-diffeomorphism Noether charge

    CERN Document Server

    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.

  17. Aspects of screening and confinement in a topologically massive $U{\\left( 1 \\right)_{\\cal W}} \\times U{(1)_{\\cal Y}}$ Chern-Simons-Higgs theory

    CERN Document Server

    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.

  18. 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.

  19. Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories

    CERN Document Server

    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

  20. Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories

    Science.gov (United States)

    Mariño, Marcos

    2011-11-01

    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 N3/2 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.

  1. Mimetic discretization of the Abelian Chern-Simons theory and link invariants

    CERN Document Server

    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.

  2. Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories

    Science.gov (United States)

    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.

  3. A profusion of $1/2$ BPS Wilson loops in $\\mathcal{N}=4$ Chern-Simons-matter theories

    CERN Document Server

    Cooke, Michael; Trancanelli, Diego

    2015-01-01

    We initiate the study of $1/2$ BPS Wilson loops in $\\mathcal{N}=4$ Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels $k$, $-k$ and $0$, and focus on loops preserving one of the two $SU(2)$ subgroups of the $R$-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermultiplets have Wilson loops preserving another set of supercharges). We expect this classical pairwise degeneracy to be lifted by quantum corrections. In the case with nodes with vanishing Chern-Simons terms connected by twisted hypermultiplets, we find that the usual $1/4$ BPS Wilson loops are automatically enlarged to $1/2$ BPS, as happens also in 3-dimensional Yang-Mills theory. When the nodes with vanishing Chern-Simons levels are connected by untwisted hypermultiplets, we do not find any Wilson loops coupling to those nodes which are c...

  4. A geometric discretisation scheme applied to the Abelian Chern-Simons theory

    CERN Document Server

    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

  5. 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.

  6. 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)

  7. Duality, Quantum Vortices and Anyons in Maxwell-Chern-Simons-Higgs Theories

    CERN Document Server

    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...

  8. Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity

    CERN Document Server

    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.

  9. Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles

    CERN Document Server

    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 ...

  10. 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.

  11. Heavy operators in superconformal Chern-Simons theory

    Science.gov (United States)

    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.

  12. Multiple Chern-Simons fields on a torus

    CERN Document Server

    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.

  13. Construction of novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories

    CERN Document Server

    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.

  14. Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity

    CERN Document Server

    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.

  15. Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

    CERN Document Server

    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.

  16. Maxwell-Chern-Simons Casimir Effect

    CERN Document Server

    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.

  17. Extension of the Chern-Simons Theory: Conservation Laws, Lagrange Structures, and Stability

    Science.gov (United States)

    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.

  18. Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

    Science.gov (United States)

    Moriyama, Sanefumi; Nakayama, Shota; Nosaka, Tomoki

    2017-08-01

    In the so-called (2, 2) theory, which is the U( N)4 circular quiver superconformal Chern-Simons theory with levels ( k, 0, - k, 0), it was known that the instanton effects are described by the free energy of topological strings whose Gopakumar-Vafa invariants coincide with those of the local D 5 del Pezzo geometry. By considering two types of one-parameter rank deformations U( N)×U( N + M)×U( N + 2 M)×U( N + M) and U( N + M)×U( N)×U( N + M)×U( N), we classify the known diagonal BPS indices by degrees. Together with other two types of one-parameter deformations, we further propose the topological string expression when both of the above two deformations are turned on.

  19. Extension of the Chern-Simons Theory: Conservation Laws, Lagrange Structures, and Stability

    Science.gov (United States)

    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.

  20. Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

    CERN Document Server

    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.

  1. All Chern-Simons invariants of 4D, N = 1 gauged superform hierarchies

    Science.gov (United States)

    Becker, Katrin; Becker, Melanie; Linch, William D.; Randall, Stephen; Robbins, Daniel

    2017-04-01

    We give a geometric description of supersymmetric gravity/(non-)abelian p-form hierarchies in superspaces with 4D, N = 1 super-Poincaré invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, N = 1 graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/ BF -type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of p-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF -type and cubic Chern-Simons actions. As an application, we compute the quartic invariant ˜ AdAdAdA + . . . relevant, for example, to seven-dimensional supergravity compactifications.

  2. The sky is the limit: free boundary conditions in AdS$_3$ Chern-Simons theory

    CERN Document Server

    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.

  3. Hydrodynamics in 1+1 dimensions from Maxwell-Chern-Simons theory in AdS_3

    CERN Document Server

    Chang, Han-Chih; Kaminski, Matthias

    2015-01-01

    In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string theory constructions, and we found exact solutions in the low frequency, low momentum limit (omega, k << T, the hydrodynamic limit). Our results are translated into correlation functions of vector operators in the dual strongly coupled 1+1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T, via the holographic correspondence. The applicability of the hydrodynamic limit is discussed, together with the comparison between an exact field theoretic computation and the found holographic correlation functions in the conformal case.

  4. Thermodynamics of Relativistic Fermions with Chern-Simons Coupling

    CERN Document Server

    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.

  5. Canonical Chern-Simons gravity

    Science.gov (United States)

    Sarkar, Souvik; Vaz, Cenalo

    2017-07-01

    We study the canonical description of the axisymmetric vacuum in 2 +1 -dimensional gravity, treating Einstein's gravity as a Chern-Simons gauge theory on a manifold with the restriction that the dreibein is invertible. Our treatment is in the spirit of Kuchař's description of the Schwarzschild black hole in 3 +1 dimensions, where the mass and angular momentum are expressed in terms of the canonical variables and a series of canonical transformations that turn the curvature coordinates and their conjugate momenta into new canonical variables is performed. In their final form, the constraints are seen to require that the momenta conjugate to the Killing time and curvature radius vanish, and what remains is the mass, the angular momentum, and their conjugate momenta, which we derive. The Wheeler-DeWitt equation is trivial and describes time independent systems with wave functions described only by the total mass and total angular momentum.

  6. 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.

  7. Chern-Simons term in the 4-dimensional SU(2) Higgs model Rev

    CERN Document Server

    Karsch, Frithjof; Neuhaus, T; Plache, B; Wiese, U J

    1992-01-01

    Using a variation of Lueschers geometric charge definition for SU(2) lattice gauge theory, we have managed to give a geometric expression for it's Chern-Simons ter. From this definition we have checked the periodic structure. we determined the Chern-Simons density for symmetric and asymmetric lattices near the critical region in the SU(2) Higgs model. The data indicate that tunneling is increased at high temperature.

  8. On superconformal Chern-Simons-matter theories in N=4 superspace

    CERN Document Server

    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...

  9. Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems

    CERN Document Server

    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...

  10. Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories

    Science.gov (United States)

    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.

  11. ‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern-Simons theory

    Science.gov (United States)

    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.

  12. Quantum Computation and Non-Abelian Statistics in Chern-Simons-Higgs Theory

    CERN Document Server

    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...

  13. Chern-Simons Supersymmetric Branes

    CERN Document Server

    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.

  14. Topological R\\'enyi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual

    CERN Document Server

    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.

  15. Exact Chern-Simons / Topological String duality

    CERN Document Server

    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.

  16. Chern-Simons gravity in four dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Morales, Ivan; Neves, Bruno; Piguet, Olivier [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Vicosa, MG (Brazil); Oporto, Zui [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Vicosa, MG (Brazil); Universidad Mayor de San Andres, Carrera de Fisica, La Paz (Bolivia, Plurinational State of)

    2017-02-15

    Five-dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to general relativity with cosmological constant. We consider the zero modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and ΛCDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions. (orig.)

  17. Novel Bogomol'nyi-Prasad-Sommerfield Wilson Loops in Three-dimensional Quiver Super Chern-Simons-matter Theories

    CERN Document Server

    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.

  18. N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations

    CERN Document Server

    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.

  19. Holographic Chern-Simons Defects

    CERN Document Server

    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.

  20. Chern-Simons Invariants of Torus Knots and Links

    CERN Document Server

    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.

  1. 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.)

  2. Seiberg duality for Chern-Simons quivers and D-brane mutations

    Science.gov (United States)

    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.

  3. Seiberg duality for Chern-Simons quivers and D-brane mutations

    CERN Document Server

    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.

  4. SL (2, C) Chern-Simons theory, a non-planar graph operator, and 4D quantum gravity with a cosmological constant: Semiclassical geometry

    Science.gov (United States)

    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.

  5. The quantum 1/2 BPS Wilson loop in ${\\cal N}=4$ Chern-Simons-matter theories

    CERN Document Server

    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.

  6. Higher Derivative CP(N) Model and Quantization of the Induced Chern-Simons Term

    CERN Document Server

    Itoh, T; Itoh, Taichi; Oh, Phillial

    2001-01-01

    We consider higher derivative CP(N) model in 2+1 dimensions with the Wess-Zumino-Witten term and the topological current density squared term. We quantize the theory by using the auxiliary gauge field formulation in the path integral method and prove that the extended model remains renormalizable in the large N limit. We also find that the Maxwell-Chern-Simons theory is dynamically induced in the large N effective action and the coefficient of the Chern-Simons term must be quantized.

  7. Chern-Simons production during preheating in hybrid inflation models

    CERN Document Server

    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...

  8. Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

    Science.gov (United States)

    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.

  9. 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...

  10. Faddeev-Senjanovic quantization of SU(n) N=2 supersymmetric gauge field system with a non-Abelian Chern-Simons topological term and its fractional spin

    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.

  11. Non-Abelian Chern-Simons Vortices

    CERN Document Server

    Lozano, G S; Moreno, E F; Schaposnik, F A

    2007-01-01

    We consider the bosonic sector of a ${\\cal N} = 2$ supersymmetric Chern-Simons-Higgs theory in 2 + 1 dimensions. The gauge group is $U(1)\\times SU(N)$ and has $N_f$ flavors of fundamental matter fields. The model supports non-Abelian (axially symmetric) vortices when $N_f \\geq N$, which have internal (orientational) moduli. When $N_f > N$, the solutions acquire additional collective coordinates parameterizing their transverse size. We solve the BPS equations numerically and obtain local ($N_f = N$) and semi-local ($N_f > N$) string solutions. A $CP^{N-1}$ low-energy effective action for the orientational moduli is obtained in both cases. In the semilocal case there is an additional term in the effective action induced by the transverse size moduli. We find such term in the limit of large transverse size, where exact solutions can be obtained analytically.

  12. 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.)

  13. Anomalous spin of the Chern-Simons-Georgi-Glashow model

    CERN Document Server

    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.

  14. Action Principles for Transgression and Chern-Simons AdS Gravities

    CERN Document Server

    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...

  15. On Chern-Simons Quivers and Toric Geometry

    CERN Document Server

    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.

  16. Holography of Wrapped M5-branes and Chern-Simons theory

    OpenAIRE

    Gang, Dongmin; Kim, Nakwoo; Lee, Sangmin

    2014-01-01

    We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d–3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern–Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N3 scaling with precise coefficients.

  17. The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity

    Science.gov (United States)

    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.

  18. The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity

    CERN Document Server

    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. ...

  19. Role of Ambiguities and Gauge Invariance in the Calculation of the Radiatively Induced Chern-Simons Shift in Extended Q.E.D.

    CERN Document Server

    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...

  20. Anomalies, Chern-Simons Terms and Black Hole Entropy

    CERN Document Server

    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.

  1. Real-time Chern-Simons term for hypermagnetic fields

    OpenAIRE

    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 ...

  2. Exact Slope and Interpolating Functions in N=6 Supersymmetric Chern-Simons Theory

    Science.gov (United States)

    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).

  3. The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory

    DEFF Research Database (Denmark)

    Andersen, Jørgen Ellegaard; Gammelgaard, Niels Leth

    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......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......-Simons theory, both for compact and complex gauge groups....

  4. SIM(1)-VSR Maxwell-Chern-Simons electrodynamics

    Science.gov (United States)

    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.

  5. SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics

    CERN Document Server

    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.

  6. Lecture notes on Chern-Simons (super-)gravities

    CERN Document Server

    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...

  7. Dual equivalence between Self-Dual and Maxwell-Chern-Simons models coupled to dynamical U(1) charged matter

    CERN Document Server

    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.

  8. The Chern-Simons invariant as the natural time variable for classical and quantum cosmology

    CERN Document Server

    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 \

  9. Lorentz-diffeomorphism quasi-local conserved charges and Virasoro algebra in Chern-Simons-like theories of gravity

    Science.gov (United States)

    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.

  10. The Chern-Simons diffusion rate in improved holographic QCD

    NARCIS (Netherlands)

    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

  11. Chern-Simons Dynamics and the Quantum Hall Effect

    CERN Document Server

    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.

  12. 3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction

    CERN Document Server

    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.

  13. Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity

    CERN Document Server

    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.

  14. Self-dual vortices in Chern-Simons hydrodynamics

    CERN Document Server

    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

  15. Fractional Quantum Hall Effect via Holography Chern-Simons, Edge States, and Hierarchy

    CERN Document Server

    Fujita, Mitsutoshi; Ryu, Shinsei; Takayanagi, Tadashi

    2009-01-01

    We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in N=6 Chern-Simons theory. We show that D4-branes wrapped on CP^1 or D8-branes wrapped on CP^3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)_k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on C^2/Z_n.

  16. SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry

    CERN Document Server

    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 ...

  17. 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.

  18. AdS Chern-Simons Gravity induces Conformal Gravity

    CERN Document Server

    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.

  19. Covariant charges in Chern-Simons AdS sub 3 gravity

    CERN Document Server

    Allemandi, G; Raiteri, M

    2003-01-01

    We try to give hereafter an answer to some open questions about the definition of conserved quantities in Chern-Simons theory, with particular reference to Chern-Simons AdS sub 3 gravity. Our attention is focused on the problem of global covariance and gauge invariance of the variation of Noether charges. A theory which satisfies the principle of covariance on each step of its construction is developed, starting from a gauge invariant Chern-Simons Lagrangian and using a recipe developed by Allemandi et al (2002 Class. Quantum Grav. 19 2633-55, 237-58) to calculate the variation of conserved quantities. The problem of giving a mathematical well-defined expression for the infinitesimal generators of symmetries is pointed out and it is shown that the generalized Kosmann lift of spacetime vector fields leads to the expected numerical values for the conserved quantities when the solution corresponds to the BTZ black hole. The fist law of black-hole mechanics for the BTZ solution is then proved and the transition b...

  20. Covariant Charges in Chern-Simons AdS_3 Gravity

    CERN Document Server

    Allemandi, G; Raiteri, M

    2003-01-01

    We try to give hereafter an answer to some open questions about the definition of conserved quantities in Chern-Simons theory, with particular reference to Chern-Simons AdS_3 Gravity. Our attention is focused on the problem of global covariance and gauge invariance of the variation of Noether charges. A theory which satisfies the principle of covariance on each step of its construction is developed, starting from a gauge invariant Chern-Simons Lagrangian and using a recipe developed in gr-qc/0110104 and gr-qc/0107074 to calculate the variation of conserved quantities. The problem to give a mathematical well-defined expression for the infinitesimal generators of symmetries is pointed out and it is shown that the generalized Kosmann lift of spacetime vector fields leads to the expected numerical values for the conserved quantities when the solution corresponds to the BTZ black hole. The fist law of black holes mechanics for the BTZ solution is then proved and the transition between the variation of conserved qu...

  1. Real-time Chern-Simons term for hypermagnetic fields

    CERN Document Server

    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.

  2. Dirac matrices for Chern-Simons gravity

    Science.gov (United States)

    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.

  3. 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.

  4. Derivative expansion and the induced Chern-Simons term in N=1, d=3 superspace

    CERN Document Server

    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.

  5. Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3

    CERN Document Server

    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.

  6. Phase string effect and mutual Chern-Simons theory of Hubbard mo del%Hubbard模型中的相位弦效应与交互Chern-Simons理论∗

    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.

  7. On higher holonomy invariants in higher gauge theory I

    CERN Document Server

    Zucchini, Roberto

    2015-01-01

    This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of surface knots of arbitrary genus and determine its covariance properties under 1--gauge transformation and change of base data.

  8. Loop Representation of charged particles interacting with Maxwell and Chern-Simons fields

    CERN Document Server

    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.

  9. Pure Yang-mills, Noncommutative Chern-simons And Noncommutative Quantum Mechanics: A Hamiltonian Approach

    CERN Document Server

    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...

  10. On effective Chern-Simons Term induced by a Local CPT-Violating Coupling using $\\gamma_5$ in Dimensional Regularization

    CERN Document Server

    Ferrari, Ruggero

    2015-01-01

    We resume a long-standing, yet not forgotten, debate on whether a Chern-Simons birefringence can be generated by a local term $b_\\mu\\bar\\psi\\gamma^\\mu \\gamma_5\\psi$ in the Lagrangian (where $b_\\mu$ are constants). In the present paper we implement a new way of managing $\\gamma_5$ in dimensional regularization. Gauge invariance in the underlying theory (QED) is enforced by this choice of defining divergent amplitudes. We investigate the singular behavior of the vector meson two-point-function around the $m^2=0$ and $p^2=0$ point. We find that the coefficient of the effective Chern-Simons can be finite or zero. It depends on how one takes the limits: they cannot be interchanged due to the associate change of symmetry. For $m^2=0$ we evaluate also the self-mass of the photon at the second orderin $b_\\mu$. We find zero.

  11. Generalized Higher Gauge Theory

    CERN Document Server

    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.

  12. Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.

    Science.gov (United States)

    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.

  13. Topological gauge theories and group cohomology

    Science.gov (United States)

    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.

  14. A New Look at Chern-Simons on Circle Bundles I: The Caloron Correspondence

    CERN Document Server

    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. ...

  15. Integrable Lattice Models From Gauge Theory

    CERN Document Server

    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.)

  16. The effects of Chern-Simons gravity on bodies orbiting the Earth

    CERN Document Server

    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.

  17. 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.

  18. Topological resolution of gauge theory singularities

    CERN Document Server

    Saracco, Fabio; Torroba, Gonzalo

    2013-01-01

    Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high energy metric (that would exhibit the singularity) and a regular singularity-free low energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

  19. 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.

  20. Enhancement of hidden symmetries and Chern-Simons couplings

    CERN Document Server

    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.

  1. Edge Currents and Vertex Operators for Chern-Simons Gravity

    CERN Document Server

    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...

  2. Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity

    CERN Document Server

    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.

  3. Self-Dual Chern-Simons Solitons and Generalized Heisenberg Ferromagnet Models

    CERN Document Server

    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.

  4. Entropy for gravitational Chern-Simons terms by squashed cone method

    CERN Document Server

    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 ...

  5. Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators

    CERN Document Server

    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...

  6. 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)

  7. 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)

  8. Chern-Simons terms from thermal circles and anomalies

    CERN Document Server

    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.

  9. 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.

  10. 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.

  11. Induced magnetic moment in noncommutative Chern-Simons scalar QED

    CERN Document Server

    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.

  12. 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.

  13. Chern-Simons modified gravity and closed time-like curves

    CERN Document Server

    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.

  14. Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

    CERN Document Server

    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.

  15. Perturbations of Schwarzschild black holes in Dynamical Chern-Simons modified gravity

    CERN Document Server

    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.

  16. Testing Chern-Simons modified gravity with orbiting superconductive gravity gradiometers --- The non-dynamical formulation

    CERN Document Server

    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.

  17. The gauge theory of the de Sitter group and Ashtekar formulation

    CERN Document Server

    Nieto, J A; Socorro, J

    1994-01-01

    By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the field-strengths, of the Chern-Simons type, from which the Ashtekar formulation is derived.

  18. On higher holonomy invariants in higher gauge theory II

    CERN Document Server

    Zucchini, Roberto

    2015-01-01

    This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module such to yield surface knot invariants upon application to 2-holonomies. We show further that the properties of the trace are best described using the theory quandle crossed modules.

  19. Extremal Black Holes in Dynamical Chern-Simons Gravity

    CERN Document Server

    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...

  20. Effective Superpotential and the Renormalization Group Equation in a Supersymmetric Chern-Simons-Matter Model in the Superfield Formalism

    CERN Document Server

    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 $\\...

  1. 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.

  2. Self-dual Maxwell-Chern-Simons solitons from a Lorentz-violating model

    CERN Document Server

    Casana, Rodolfo

    2013-01-01

    Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view. In particular we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.

  3. Self-dual Maxwell-Chern-Simons solitons from a Lorentz-violating model

    Science.gov (United States)

    Casana, Rodolfo; Sourrouille, Lucas

    2013-10-01

    Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view. In particular, we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.

  4. Toric Fano varieties and Chern-Simons quivers

    CERN Document Server

    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.

  5. Chern-Simons Supergravity in D=3 and Maxwell superalgebras

    CERN Document Server

    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.

  6. Generalized self-dual Chern-Simons vortices

    OpenAIRE

    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.

  7. Scattering amplitudes of massive N =2 gauge theories in three dimensions

    Science.gov (United States)

    Agarwal, Abhishek; Lipstein, Arthur E.; Young, Donovan

    2014-02-01

    We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with N =2 supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the scattering matrices of these theories. We then compute various 3 and 4-point on-shell tree-level amplitudes in these theories. For the mass-deformed Chern-Simons theory, odd-point amplitudes vanish and we find that all of the 4-point amplitudes can be encoded elegantly in superamplitudes. For the Yang-Mills-Chern-Simons theory, we obtain all of the 4-point tree-level amplitudes using a combination of perturbative techniques and algebraic constraints and we comment on difficulties related to computing amplitudes with external gauge fields using Feynman diagrams. Finally, we propose a Britto-Cachazo-Feng-Witten recursion relation for mass-deformed theories in three dimensions and discuss the applicability of this proposal to mass-deformed N =2 theories.

  8. Gauge invariance and the Pauli-Villars regulator in Lorentz- and CPT-violating electrodynamics

    Science.gov (United States)

    Altschul, B.

    2004-11-01

    We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentz- and CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the nonperturbative theory appears to generate a definite value. However, the CPT-even radiative corrections in this same formulation of the theory generally break gauge invariance. We show that gauge invariance may yet be preserved through the use of a Pauli-Villars regulator, and, contrary to earlier expectations, this regulator does not necessarily give rise to a vanishing Chern-Simons term. Instead, two possible values of the Chern-Simons coefficient are allowed, one zero and one nonzero. This formulation of the theory therefore allows the coefficient to vanish naturally, in agreement with experimental observations.

  9. Diphoton signal via Chern-Simons interaction in a warped geometry scenario

    Science.gov (United States)

    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.

  10. Dense Chern-Simons Matter with Fermions at Large N

    CERN Document Server

    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 ...

  11. Dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model

    Energy Technology Data Exchange (ETDEWEB)

    Belich, H. Jr.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); E-mails: belich@cbpf.br; helayel@cbpf.br; Ferreira, M.M. Jr. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); Maranhao Univ., Sao Luiz, MA (Brazil). Dept. de Fisica]. E-mail: manojr@cbpf.br; Orlando, M.T.D. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); Espirito Santo Univ., Vitoria, ES (Brazil). Dept. de Fisica e Quimica; E-mail: orlando@cce.ufes.br

    2003-01-01

    Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional to D = 1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, {nu}{sup {mu}}. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of {nu}{sup {mu}} . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitary of the gauge sector is assured without any restriction , while the scalar sector is unitary only in the space-like case. (author)

  12. N=2-Maxwell-Chern-Simons Model with Anomalous Magnetic Moment Coupling via Dimensional Reduction

    CERN Document Server

    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.

  13. Higgs-and Skyrme-Chern-Simons densities in all dimensions

    Science.gov (United States)

    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.

  14. 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.

  15. The Initial Value Formulation of Dynamical Chern-Simons Gravity

    CERN Document Server

    Delsate, Térence; Witek, Helvi

    2014-01-01

    We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but the full field equations are in no sense hyperbolic. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

  16. Resolution of Chern--Simons--Higgs Vortex Equations

    CERN Document Server

    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.

  17. 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.).

  18. Ward identities and gauge flow for M-theory in N =3 superspace

    Science.gov (United States)

    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).

  19. The Chern-Simons diffusion rate in improved holographic QCD

    National Research Council Canada - National Science Library

    Gürsoy, U; Iatrakis, I; Kiritsis, E; Nitti, F; O’Bannon, A

    2013-01-01

    ... ], with F the YM field strength. The Chern-Simons diffusion rate is a crucial ingredient for many CP-odd phenomena, including the chiral magnetic effect in the quark-gluon plasma. We compute Γ...

  20. Scattering amplitude and bosonization duality in general Chern-Simons vector models

    Science.gov (United States)

    Yokoyama, Shuichi

    2016-09-01

    We present the exact large N calculus of four point functions in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine the two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, an unusual crossing relation and a non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to the Chern-Simons theory interacting with free fermions.

  1. Adiabatic Limit and the Slow Motion of Vortices in a Chern-Simons-Schrödinger System

    Science.gov (United States)

    Demoulini, Sophia; Stuart, David

    2009-09-01

    We study a nonlinear system of partial differential equations in which a complex field (the Higgs field) evolves according to a nonlinear Schrödinger equation, coupled to an electromagnetic field whose time evolution is determined by a Chern-Simons term in the action. In two space dimensions, the Chern-Simons dynamics is a Galileo invariant evolution for A, which is an interesting alternative to the Lorentz invariant Maxwell evolution, and is finding increasing numbers of applications in two dimensional condensed matter field theory. The system we study, introduced by Manton, is a special case (for constant external magnetic field, and a point interaction) of the effective field theory of Zhang, Hansson and Kivelson arising in studies of the fractional quantum Hall effect. From the mathematical perspective the system is a natural gauge invariant generalization of the nonlinear Schrödinger equation, which is also Galileo invariant and admits a self-dual structure with a resulting large space of topological solitons (the moduli space of self-dual Ginzburg-Landau vortices). We prove a theorem describing the adiabatic approximation of this system by a Hamiltonian system on the moduli space. The approximation holds for values of the Higgs self-coupling constant λ close to the self-dual (Bogomolny) value of 1. The viability of the approximation scheme depends upon the fact that self-dual vortices form a symplectic submanifold of the phase space (modulo gauge invariance). The theorem provides a rigorous description of slow vortex dynamics in the near self-dual limit.

  2. Remarks on 2+1 Self-dual Chern-Simons Gravity

    CERN Document Server

    García-Compéan, H; Ramírez, C; Sabido, M

    2000-01-01

    We study 2+1 Chern-Simons gravity at the classical level action. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti)`self-duality' of the `internal' Lorentzian indices. The relation to a genuine four-dimensional (anti) self-dual topological theories greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally non-abelian vector field ``dual'' action is also obtained.

  3. Remarks on 2+1 Self-dual Chern-Simons Gravity

    OpenAIRE

    Garcia-Compean, H.; Obregon, O.; Ramirez, C.; Sabido, M.

    1999-01-01

    We study 2+1 Chern-Simons gravity at the classical action level. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti) self-duality of the ``internal'' Lorentzian indices. The relation to a genuine four-dimensional (anti)self-dual topological theory greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally a non-abelian vector field ``dual'' action is also obtained.

  4. Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications

    CERN Document Server

    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.

  5. Charged Rotating AdS Black Holes with Chern-Simons coupling

    CERN Document Server

    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.

  6. Toward semistrict higher gauge theory

    CERN Document Server

    Zucchini, Roberto

    2011-01-01

    We work out a formulation of higher gauge theory, whose symmetry is encoded in a semistrict Lie 2-algebra v and which we call semistrict. We view v as a 2-term L-infinity algebra, a special case of strong homotopy Lie algebra generalizing an ordinary Lie algebra by allowing the Lie bracket to have a non trivial Jacobiator. Fields are v-valued and gauge transformations are special Aut(v)-valued maps organized as an ordinary group and acting on them. The global behaviour of fields is controlled by appropriate gauge transformation 1-cocycles. Using the BV quantization method in the AKSZ geometrical version, we write down a 3-dimensional semistrict higher BF gauge theory generalizing ordinary BF theory, carry out its gauge fixing and obtain as end result a semistrict higher topological gauge field theory of the Witten type. We also introduce a related 4-dimensional semistrict higher Chern--Simons gauge theory. We discuss merits and weaknesses of our formulation in relations to other approaches.

  7. Chern-Simons (super)gravity

    CERN Document Server

    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...

  8. Gravitational waves from extreme mass-ratio inspirals in Dynamical Chern-Simons gravity

    CERN Document Server

    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...

  9. Gravitational waves from extreme mass-ratio inspirals in dynamical Chern-Simons gravity

    Science.gov (United States)

    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.

  10. The Chern-Simons term in a dual Josephson junction

    CERN Document Server

    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...

  11. Vortex Solutions in the Chern-Simons Stueckelberg Model

    CERN Document Server

    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...

  12. On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models

    CERN Document Server

    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...

  13. On the higher-spin spectrum in large N Chern-Simons vector models

    Science.gov (United States)

    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.

  14. N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories

    CERN Document Server

    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.

  15. QCD axion from a higher dimensional gauge field theory.

    Science.gov (United States)

    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.

  16. The Maxwell-Chern-Simons gravity, and its cosmological implications

    Science.gov (United States)

    Haghani, Zahra; Harko, Tiberiu; Shahidi, Shahab

    2017-08-01

    We consider the cosmological implications of a gravitational theory containing two vector fields coupled via a generalized Chern-Simons term. One of the vector fields is the usual Maxwell field, while the other is a constrained vector field with constant norm included in the action via a Lagrange multiplier. The theory admits a de Sitter type solution, with healthy cosmological perturbations. We also show that there are seven degrees of freedom that propagate on top of de Sitter space-time, consisting of two tensor polarizations, four degrees of freedom related to the two vector fields, and a scalar degree of freedom that makes one of the vector fields massive. We investigate the cosmological evolution of Bianchi type I space-time, by assuming that the matter content of the Universe can be described by the stiff and dust. The cosmological evolution of the Bianchi type I Universe strongly depends on the initial conditions of the physical quantities, as well as on the model parameters. The mean anisotropy parameter, and the deceleration parameter, are also studied, and we show that independently of the matter equation of state the cosmological evolution of the Bianchi type I Universe always ends in an isotropic de Sitter type phase.

  17. Fifty Years of Yang-Mills Theory and my Contribution to it

    CERN Document Server

    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.

  18. Vortices in generalized Abelian Chern-Simons-Higgs model

    CERN Document Server

    Casana, Rodolfo

    2015-01-01

    We study a generalization of abelian Chern-Simons-Higgs model by introducing nonstandard kinetic terms. We will obtain a generic form of Bogomolnyi equations by minimizing the energy functional of the model. This generic form of Bogomolnyi equations produce an infinity number of soliton solutions. As a particular limit of these generic Bogomolnyi equations, we obtain the Bogomolnyi equations of the abelian Maxwell-Higgs model and the abelian Chern-Simons Higgs model. Finally, novel soliton solutions emerge from these generic Bogomolnyi equations. We analyze these solutions from theoretical and numerical point of view.

  19. Maxwell-Chern-Simons Hydrodynamics for the Chiral Magnetic Effect

    CERN Document Server

    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.

  20. Supersymmetric Chern-Simons terms in ten dimensions

    NARCIS (Netherlands)

    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 α (Lorentz) and β (Yang-Mills), we obtain the complete O(α) supersymmetrization. Furthermore, we present the leading O(α2) and O(αβ) corrections requi

  1. Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets

    NARCIS (Netherlands)

    Claus, P.; Wit, B. de; Faux, M.; Termonia, P.

    1996-01-01

    The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained

  2. Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory BTZ solution with torsion

    CERN Document Server

    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}

  3. Extremal black holes in dynamical Chern-Simons gravity

    Science.gov (United States)

    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.

  4. Topologically Massive Gauge Theory: Wu-Yang Type Solutions

    CERN Document Server

    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...

  5. Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature arXiv

    CERN Document Server

    Figueroa, Daniel G.

    We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, with the use of both analytical estimates and real-time classical numerical simulations. We investigate the random walk of the Chern-Simons number $N_{\\rm CS} \\propto \\int d^4x F_{\\mu\

  6. A test of bosonization at the level of four-point functions in Chern-Simons vector models

    CERN Document Server

    Bedhotiya, Akshay

    2015-01-01

    We study four-point functions in Chern-Simons vector models in the large $N$ limit. We compute the four-point function of the scalar primary to all orders in the `t Hooft coupling $\\lambda=N/k$ in $U(N)_k$ Chern-Simons theory coupled to a fundamental fermion, in both the critical and non-critical theory, for a particular case of the external momenta. These theories cover the entire 3-parameter "quasi-boson" and 2-parameter "quasi-fermion" families of 3-dimensional quantum field theories with a slightly-broken higher spin symmetry. Our results are consistent with the celebrated bosonization duality, as we explicitly verify by calculating four-point functions in the free critical and non-critical bosonic theories.

  7. 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.)

  8. Remarks on the Taub-NUT solution in Chern-Simons modified gravity

    Science.gov (United States)

    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.

  9. Light-Front Dynamics Of Massive Vector Chern-Simons Gravity

    CERN Document Server

    Aragone, C; Khoudeir, A

    1993-01-01

    We present a second order gravity action which consists of ordinary Einstein action augmented by a first-order, vector like, Chern-Simons quasi topological term. This theory is ghost-free and propagates a pure spin-2 mode. It is diffeomorphism invariant, although its local Lorentz invariance has been spontaneuosly broken. We perform the light-front (LF) analysis for both the linearized system and the exact curved model. In constrast to the 2+1 canonical analysis, in the quasi LF coordinates the differential constraints can be solved. Its solution is presented here.

  10. Vanishing magnetic mass in QED$_{3}$ with a Chern-Simons term

    OpenAIRE

    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.

  11. The Chern-Simons Source as a Conformal Family and Its Vertex Operators

    CERN Document Server

    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...

  12. Dimensional Reduction of a Lorentz- and CPT-violating Chern-Simons Model

    CERN Document Server

    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...

  13. Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity

    CERN Document Server

    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.

  14. Classification and properties of symmetry-enriched topological phases: Chern-Simons approach with applications to Z2 spin liquids

    Science.gov (United States)

    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.

  15. Two gravitationally Chern-Simons terms are too many

    CERN Document Server

    Aragone, C; Khoudeir, A; Arias, Pio J.

    1993-01-01

    It is shown that topological massive gravity augmented by the triadic gravitational Chern-Simons first order term is a curved a pure spin-2 action. This model contains two massive spin-2 excitations. However, since its light-front energy is not semidefinite positive, this double CS-action does not have any physical relevance.In other words, topological massive gravity cannot be spontaneously broken down by the presence of the triadic CS term.

  16. Higgs- and Skyrme-Chern-Simons densities in all dimensions

    CERN Document Server

    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.

  17. Causality aspects of the dynamical Chern-Simons modified gravity

    Science.gov (United States)

    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.

  18. $CP^N$ Model With a Chern-Simons Term

    CERN Document Server

    Ferretti, G

    1992-01-01

    The $CP^N$ model in three euclidean dimensions is studied in the presence of a Chern-Simons term using the $1/N$ expansion. The $\\beta$-function for the CS coefficient $\\theta$ is found to be zero to order $1/N$ in the unbroken phase by an explicit calculation. It is argued to be zero to all orders. Some remarks on the $\\theta$ dependence of the critical exponents are also made.

  19. Generalized Gauge Theories and Weinberg-Salam Model with Dirac-Kähler Fermions

    CERN Document Server

    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.

  20. 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.

  1. Phase space structure of non-abelian Chern-Simons particles

    CERN Document Server

    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}.

  2. Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories

    CERN Document Server

    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...

  3. Superstring theories as low-energy limit of supergroup gauge theories

    CERN Document Server

    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.

  4. Diphoton excess via Chern-Simons interaction in a warped geometry scenario

    CERN Document Server

    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.

  5. On S-duality in (2+1)-Chern-Simons Supergravity

    CERN Document Server

    García-Compéan, H; Ramírez, C; Sabido, M

    2001-01-01

    Strong/weak coupling duality in Chern-Simons supergravity is studied. It is argued that this duality can be regarded as an example of superduality. The use of supergroup techniques for the description of Chern-Simons supergravity greatly facilitates the analysis.

  6. On the dual equivalence of the Born-Infeld-Chern-Simons model coupled to dynamical U(1) charged matter

    CERN Document Server

    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.

  7. Undergraduate Lecture Notes in Topological Quantum Field Theory

    OpenAIRE

    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

  8. Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators

    Science.gov (United States)

    Alekseev, Anton; Naef, Florian; Xu, Xiaomeng; Zhu, Chenchang

    2017-09-01

    Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern-Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as p= where F is the curvature 2-form and is an invariant scalar product on the corresponding Lie algebra g. The descent for p gives rise to an element ω =ω _3+ω _2+ω _1+ω _0 of mixed degree. The 3-form part ω _3 is the Chern-Simons form. The 2-form part ω _2 is known as the Wess-Zumino action in physics. The 1-form component ω _1 is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components ω _1 and ω _0 . Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara-Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara-Vergne equation F is mapped to ω _1=C(F) . Furthermore, the component ω _0 is related to the associator Φ corresponding to F. It is surprising that while F and Φ satisfy the highly nonlinear twist and pentagon equations, the elements ω _1 and ω _0 solve the linear descent equation.

  9. Gauge theories and integrable lattice models

    Science.gov (United States)

    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.

  10. Possible altitudinal, latitudinal and directional dependence of relativistic Sagnac effect in Chern-Simons modified gravity

    CERN Document Server

    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.

  11. Remarks on the Taub-NUT solution in Chern-Simons modified gravity

    CERN Document Server

    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.

  12. Renormalization group improvement and dynamical breaking of symmetry in a supersymmetric Chern-Simons-matter model

    Science.gov (United States)

    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.

  13. The gravity dual of supersymmetric gauge theories on a squashed three-sphere

    Energy Technology Data Exchange (ETDEWEB)

    Martelli, Dario [Department of Mathematics, King' s College, London, The Strand, London WC2R 2LS (United Kingdom); Passias, Achilleas, E-mail: achilleas.passias@kcl.ac.uk [Department of Mathematics, King' s College, London, The Strand, London WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)

    2012-11-21

    We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a U(1) Multiplication-Sign U(1)-invariant squashed three-sphere, with a non-trivial background gauge field. This is described by a supersymmetric solution of four-dimensional N=2 gauged supergravity with a non-trivial instanton for the graviphoton field. The particular gauge theory in turn determines the lift to a solution of eleven-dimensional supergravity. We compute the partition function for a class of Chern-Simons quiver gauge theories on both sides of the duality, in the large N limit, finding precise agreement for the functional dependence on the squashing parameter. This constitutes an exact check of the gauge/gravity correspondence in a non-conformally invariant setting.

  14. Chern-Simons states in spin-network quantum gravity

    CERN Document Server

    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.

  15. Generalized self-dual Maxwell-Chern-Simons-Higgs model

    CERN Document Server

    Bazeia, D; da Hora, E; Menezes, R

    2012-01-01

    We present a consistent BPS framework for a generalized Maxwell-Chern-Simons-Higgs model. The overall model, including its self-dual potential, depends on three different functions, h(|{\\phi}|,N), w(|{\\phi}|) and G(|{\\phi}|), which are functions of the scalar fields only. The BPS energy is proportional to the magnetic flux when w(|{\\phi}|) and G(|{\\phi}|) are related to each other by a differential constraint. We present an explicit non-standard model and its topologically non-trivial static configurations, which are described by the usual radially symmetric profile. Finally, we note that the non-standard results behave in a similar way as their standard counterparts, as expected, reinforcing the consistence of the overall construction.

  16. Generalized self-dual Maxwell-Chern-Simons-Higgs model

    Science.gov (United States)

    Bazeia, D.; Casana, R.; da Hora, E.; Menezes, R.

    2012-06-01

    We present a consistent Bogomol’nyi-Prasad-Sommerfield (BPS) framework for a generalized Maxwell-Chern-Simons-Higgs model. The overall model, including its self-dual potential, depends on three different functions, h(|ϕ|,N), w(|ϕ|), and G(|ϕ|), which are functions of the scalar fields only. The BPS energy is proportional to the magnetic flux when w(|ϕ|) and G(|ϕ|) are related to each other by a differential constraint. We present an explicit nonstandard model and its topologically nontrivial static configurations, which are described by the usual radially symmetric profile. Finally, we note that the nonstandard results behave in a similar way as their standard counterparts, as expected, reinforcing the consistence of the overall construction.

  17. Adiabatic pumping of Chern-Simons axion coupling.

    Science.gov (United States)

    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.

  18. Heterotic Moduli Stabilization with Fractional Chern-Simons Invariants

    Energy Technology Data Exchange (ETDEWEB)

    Gukov, S

    2003-11-07

    We show that fractional flux from Wilson lines can stabilize the moduli of heterotic string compactifications on Calabi-Yau threefolds. We observe that the Wilson lines used in GUT symmetry breaking naturally induce a fractional flux. When combined with a hidden-sector gaugino condensate, this generates a potential for the complex structure moduli, Kaehler moduli, and dilaton. This potential has a supersymmetric AdS minimum at moderately weak coupling and large volume. Notably, the necessary ingredients for this construction are often present in realistic models. We explore the type IIA dual phenomenon, which involves Wilson lines in D6-branes wrapping a three-cycle in a Calabi-Yau, and comment on the nature of the fractional instantons which change the Chern-Simons invariant.

  19. Translational Chern-Simons Action and New Planar Particle Dynamics

    CERN Document Server

    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 $r>r_0$.

  20. Noncommutative ${\\cal N}=2$ Chern-Simons-matter model

    CERN Document Server

    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.

  1. Higher Spin Lifshitz Theories and the KdV-Hierarchy

    CERN Document Server

    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.

  2. On p -form theories with gauge invariant second order field equations

    Science.gov (United States)

    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.

  3. On p-form theories with gauge invariant second order field equations

    CERN Document Server

    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.

  4. Testing Chern-Simons modified gravity with gravitational-wave detections of extreme-mass-ratio binaries

    Science.gov (United States)

    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

  5. New Holographic Dark Energy in Chern-Simons Gravity and Cosmography

    Science.gov (United States)

    Debnath, Ujjal

    2014-12-01

    We have considered a five-dimensional 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 with barotropic EoS and new holographic dark energy. We will study the dynamic formulation of Chern-Simons gravity, where the coupling constant is promoted to a scalar field with potential. We have studied the implications of replacing the Einstein-Hilbert action by the Chern-Simons action on the cosmological evolution for a 5D FRW metric. The deceleration parameter shows that our considered model cannot cross the phantom divide. Also the natures of the cosmography parameters are examined in Chern-Simons gravity.

  6. Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity

    Energy Technology Data Exchange (ETDEWEB)

    Barnich, Glenn [Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Giribet, Gastón [Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Leston, Mauricio [Instituto de Astronomía y Física del Espacio IAFE-CONICET, Ciudad Universitaria, Pabellón IAFE, C.C. 67 Suc. 28, 1428 Buenos Aires (Argentina)

    2015-07-15

    We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity.

  7. Chern-Simons improved Hamiltonians for strings in three space dimensions

    Science.gov (United States)

    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.

  8. Contributions to the UY(1 ) Chern-Simons term and the evolution of fermionic asymmetries and hypermagnetic fields

    Science.gov (United States)

    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.

  9. Signature of range observable in non-dynamical Chern-Simons modified gravity and the measurements with satellite-satellite tracking missions. Theoretical Studies

    CERN Document Server

    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...

  10. Phase diagram of 4D field theories with chiral anomaly from holography

    CERN Document Server

    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.

  11. Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity

    Science.gov (United States)

    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.

  12. Some cosmological solutions in Einstein-Chern-Simons gravity

    CERN Document Server

    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...

  13. Chern-Simons diffusion rate across different phase transitions

    CERN Document Server

    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...

  14. The Topological Theory of the Milnor Invariant $\\bar{\\mu}(1,2,3)$

    CERN Document Server

    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.

  15. Randall-Sundrum brane Universe as a ground state for Chern-Simons gravity

    Science.gov (United States)

    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.

  16. Analytic solution for Gauged Dirac-Weyl equation in $(2+1)$-dimensions

    CERN Document Server

    Ardenghi, Juan Sebastián; Sourrouille, Lucas

    2016-01-01

    A gauged Dirac-Weyl equation in (2+1)-dimension is considered. This equation describe relativistic matter. In particular we are interested in matter interacting with a Chern-Simons gauge fields. We show that exact self-dual solutions are admitted. These solutions are the same as those supported by nonrelativistic matter interacting with a Chern-Simons gauge field.

  17. Dyon of a non-Abelian Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions

    CERN Document Server

    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.

  18. 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.

  19. On the causality aspects of the dynamical Chern-Simons modified gravity

    CERN Document Server

    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.

  20. BPS Maxwell-Chern-Simons-like vortices in a Lorentz-violating framework

    CERN Document Server

    Casana, R; Da Hora, E; Neves, A B F

    2013-01-01

    We have analyzed Maxwell-Chern-Simons-Higgs BPS vortices in a Lorentz-violating CPT-odd context. The Lorentz violation induces profiles with a conical behavior at the origin. For some combination of the coefficients for Lorentz violation there always exists a sufficiently large winding number for which the magnetic field flips its sign.

  1. Chern-Simons matrix model coherent states and relation to Laughlin wavefunctions

    CERN Document Server

    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.

  2. Dirac Branes and Anomalies/Chern-Simons terms in any D

    CERN Document Server

    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...

  3. 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.

  4. M-theory in the Omega-background and 5-dimensional non-commutative gauge theory

    CERN Document Server

    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...

  5. Electrically charged finite energy solutions of an SO(5) and an SU(3) Higgs-Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions

    Science.gov (United States)

    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.

  6. Electrically charged finite energy solutions of an $SO(5)$ and an $SU(3)$ Higgs-Chern-Simons--Yang-Mills-Higgs systems in $3+1$ dimensions

    CERN Document Server

    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...

  7. Topological field theories on manifolds with Wu structures

    Science.gov (United States)

    Monnier, Samuel

    We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4ℓ + 3 endowed with a Wu structure of degree 2ℓ + 2. After analyzing 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 3-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 state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the ℓ = 1 case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with (2, 0) supersymmetry, as will be discussed elsewhere.

  8. Gauge-invariant functional measure for gauge fields on CP2

    Science.gov (United States)

    Nair, V. P.

    2013-11-01

    We introduce a general parametrization for non-Abelian gauge fields on the four-dimensional space CP2. The volume element for the gauge-orbit space or the space of physical configurations is then investigated. The leading divergence in this volume element is obtained in terms of a higher dimensional Wess-Zumino-Witten action, which has previously been studied in the context of Kähler-Chern-Simons theories. This term, it is argued, implies that one needs to introduce a dimensional parameter to specify the integration measure, a step which is a nonperturbative version of the well-known dimensional transmutation in four-dimensional gauge theories.

  9. Comments on twisted indices in 3d supersymmetric gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Closset, Cyril [Simons Center for Geometry and PhysicsState University of New York, Stony Brook, NY 11794 (United States); Kim, Heeyeon [Perimeter Institute for Theoretical Physics31 Caroline Street North, Waterloo, N2L 2Y5, Ontario (Canada)

    2016-08-09

    We study three-dimensional N=2 supersymmetric gauge theories on Σ{sub g}×S{sup 1} with a topological twist along Σ{sub g}, a genus-g Riemann surface. The twisted supersymmetric index at genus g and the correlation functions of half-BPS loop operators on S{sup 1} can be computed exactly by supersymmetric localization. For g=1, this gives a simple UV computation of the 3d Witten index. Twisted indices provide us with a clean derivation of the quantum algebra of supersymmetric Wilson loops, for any Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe equations for the theory on ℝ{sup 2}×S{sup 1}. This also provides a powerful and simple tool to study 3d N=2 Seiberg dualities. Finally, we study A- and B-twisted indices for N=4 supersymmetric gauge theories, which turns out to be very useful for quantitative studies of three-dimensional mirror symmetry. We also briefly comment on a relation between the S{sup 2}×S{sup 1} twisted indices and the Hilbert series of N=4 moduli spaces.

  10. The superspace geometry of gravitational Chern-Simons forms and their couplings to linear multiplets a review

    CERN Document Server

    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.

  11. Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality

    CERN Document Server

    Bhattacharyya, Arpan; Hung, Ling-Yan

    2016-01-01

    In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor $T$ and current density $J$, there is a mixed contribution to the relative entropy bi-linear in $T$ and $J$, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.

  12. On the Contributions to the $\\bf U_Y(1)$ Chern-Simons Term and the Evolution of Fermionic Asymmetries and Hypermagnetic Fields

    CERN Document Server

    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...

  13. Secular Gravity Gradients in Non-Dynamical Chern-Simons Modified Gravity for Satellite Gradiometry Measurements

    CERN Document Server

    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.

  14. Vortex dynamics in self-dual Chern-Simons Higgs systems

    CERN Document Server

    Kim, Y; Kim, Yoonbai; Lee, Kimyeong

    1994-01-01

    We consider vortex dynamics in self-dual Chern-Simons Higgs systems. We show that the naive Aharanov-Bohm phase is the inverse of the statistical phase expected from the vortex spin, and that the self-dual configurations of vortices are degenerate in energy but not in angular momentum. We also use the path integral formalism to derive the dual formulation of Chern-Simons Higgs systems in which vortices appear as charged particles. We argue that besides the electromagnetic interaction, there is an additional interaction between vortices, the so-called Magnus force, and that these forces can be put together into a single `dual electromagnetic' interaction. This dual electromagnetic interaction leads to the right Aharanov-Bohm phase. We also derive and study the effective action for slowly moving vortices, which contains terms both linear and quadratic in the vortex velocity.

  15. 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.

  16. Chern-Simons functions on toric Calabi-Yau threefolds and virtual motives

    CERN Document Server

    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.

  17. The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory

    Science.gov (United States)

    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.

  18. Kitaev Lattice Models as a Hopf Algebra Gauge Theory

    Science.gov (United States)

    Meusburger, Catherine

    2017-07-01

    We prove that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to the combinatorial quantisation of Chern-Simons theory for the Drinfeld double D( H). This shows that Kitaev models are a special case of the older and more general combinatorial models. This equivalence is an analogue of the relation between Turaev-Viro and Reshetikhin-Turaev TQFTs and relates them to the quantisation of moduli spaces of flat connections. We show that the topological invariants of the two models, the algebra of operators acting on the protected space of the Kitaev model and the quantum moduli algebra from the combinatorial quantisation formalism, are isomorphic. This is established in a gauge theoretical picture, in which both models appear as Hopf algebra valued lattice gauge theories. We first prove that the triangle operators of a Kitaev model form a module algebra over a Hopf algebra of gauge transformations and that this module algebra is isomorphic to the lattice algebra in the combinatorial formalism. Both algebras can be viewed as the algebra of functions on gauge fields in a Hopf algebra gauge theory. The isomorphism between them induces an algebra isomorphism between their subalgebras of invariants, which are interpreted as gauge invariant functions or observables. It also relates the curvatures in the two models, which are given as holonomies around the faces of the lattice. This yields an isomorphism between the subalgebras obtained by projecting out curvatures, which can be viewed as the algebras of functions on flat gauge fields and are the topological invariants of the two models.

  19. (3+1)D Anomalous Twisted Gauge Theories with Global Symmetry

    CERN Document Server

    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.

  20. Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group

    CERN Document Server

    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.

  1. Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories.

    Science.gov (United States)

    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.

  2. Topological field theories on manifolds with Wu structures

    CERN Document Server

    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...

  3. Chern-Simons interactions in AdS$_3$ and the current conformal block

    CERN Document Server

    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.

  4. A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity

    Science.gov (United States)

    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.

  5. Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits

    Directory of Open Access Journals (Sweden)

    J. Niederle

    2010-01-01

    Full Text Available Two Maxwell-Chern-Simons (MCS models in the (1 + 3-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.

  6. The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere

    Energy Technology Data Exchange (ETDEWEB)

    Martelli, Dario, E-mail: dario.martelli@kcl.ac.uk [Department of Mathematics, King' s College, London, The Strand, London WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)

    2013-01-01

    We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, with a non-trivial background gauge field. This is described by a 1/2 BPS Euclidean solution of four-dimensional N=2 gauged supergravity, consisting of a Taub-NUT-AdS metric with a non-trivial instanton for the graviphoton field. The holographic free energy of this solution agrees precisely with the large N limit of the free energy obtained from the localized partition function of a class of Chern-Simons quiver gauge theories. We also discuss a different supersymmetric solution, whose boundary is a biaxially squashed Lens space S{sup 3}/Z{sub 2} with a topologically non-trivial background gauge field. This metric is of Eguchi-Hanson-AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S{sup 2} cycle.

  7. Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level

    Science.gov (United States)

    Wang, Chong; Cooper, Nigel R.; Halperin, Bertrand I.; Stern, Ady

    2017-07-01

    It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the interaction strength; thus, one can ignore mixing between Landau levels. This symmetry is explicit in the description of a half-filled Landau level recently introduced by Son, using Dirac fermions, but it was thought to be absent in the older fermion-Chern-Simons approach, developed by Halperin, Lee, and Read (HLR) and subsequent authors. We show here, however, that when properly evaluated, the HLR theory gives results for long-wavelength low-energy physical properties—including the Hall conductance in the presence of impurities and the positions of minima in the magnetoroton spectra for fractional quantized Hall states close to half-filling—that are identical to predictions of the Dirac formulation. In fact, the HLR theory predicts an emergent particle-hole symmetry near half-filling, even when the cyclotron energy is finite.

  8. Chern-Simons couplings at order O (α'2)

    Science.gov (United States)

    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.

  9. Gauge theory and little gauge theory

    CERN Document Server

    Koizumi, Kozo

    2016-01-01

    The gauge theory is the most important type of the field theory, in which the interactions of the elementary particles are described by the exchange of the gauge bosons.In this article, the gauge theory is reexamined as geometry of the vector space, and a new concept of "little gauge theory" is introduced. A key peculiarity of the little gauge theory is that the theory is able to give a restriction for form of the connection field. Based on the little gauge theory, Cartan geometry, a charged boson and the Dirac fermion field theory are investigated. In particular, the Dirac fermion field theory leads to an extension of Sogami's covariant derivative. And it is interpreted that Higgs bosons are included in new fields introduced in this article.

  10. Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons $QED_{3}$?

    CERN Document Server

    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.

  11. Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3)

    Science.gov (United 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.

  12. Possible latitude effects of Chern-Simons gravity on quantum interference

    CERN Document Server

    Okawara, Hiroki; Asada, Hideki

    2013-01-01

    It has been recently suggested that possible effects of Chern-Simons gravity on a quantum interferometer are dependent on the latitude and direction of the interferometer on Earth in orbital motion around Sun. Continuing work initiated in the earlier publication [Okawara, Yamada and Asada, Phys. Rev. Lett. 109, 231101 (2012)], we perform numerical calculations of time variation in the induced phase shifts for nonequatorial cases. We show that the maximum phase shift at any latitude might occur at 6, 0 (and 12), and 18 hours (in local time) of each day, when the normal vector to the interferometer is vertical, eastbound and northbound, respectively. If two identical interferometers were located at different latitudes, the difference between two phase shifts that are measured at the same local time would be $O(\\sin \\delta\\varphi)$ for a small latitude difference $\\delta\\varphi$. It might thus become maximally $\\sim 20$ percents for $\\delta\\varphi \\sim 10$ degrees, for instance.

  13. Maxwell-Chern-Simons vortices in a CPT-odd Lorentz-violating Higgs Electrodynamics

    CERN Document Server

    Casana, R; da Hora, E; Neves, A B F

    2014-01-01

    We have studied BPS vortices in a CPT-odd and Lorentz-violating Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating parameter induces a pronounced behavior at origin (for the magnetic/electric fields and energy density) which is absent in the MCSH vortices. For some combination of the Lorentz-violating coefficients there always exist a sufficiently large winding number $n_{0}$ such that for all $% |n|\\geq |n_{0}|$ the magnetic field flips its signal, yielding two well defined regions with opposite magnetic flux. However, the total magnetic flux remains quantized and proportional to the winding number.

  14. Maxwell-Chern-Simons vortices in a CPT-odd Lorentz-violating Higgs electrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Casana, R.; Ferreira, M.M.; Hora, E. da; Neves, A.B.F. [Universidade Federal do Maranhao, Departamento de Fisica, Sao Luis, Maranhao (Brazil)

    2014-09-15

    We study BPS vortices in a CPT-odd and Lorentz-violating Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating parameter induces a pronounced behavior at origin (for the magnetic/electric fields and energy density) which is absent in the MCSH vortices. For some combination of the Lorentz-violating coefficients there always exists a sufficiently large winding number n{sub 0} such that for all vertical stroke n vertical stroke ≥ vertical stroke n{sub 0} vertical stroke the magnetic field flips sign, yielding two well-defined regions with opposite magnetic flux. However, the total magnetic flux remains quantized and proportional to the winding number. (orig.)

  15. Maxwell-Chern-Simons vortices in a CPT-odd Lorentz-violating Higgs electrodynamics

    Science.gov (United States)

    Casana, R.; Ferreira, M. M.; da Hora, E.; Neves, A. B. F.

    2014-09-01

    We have studied BPS vortices in a CPT-odd and Lorentz-violating Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating parameter induces a pronounced behavior at origin (for the magnetic/electric fields and energy density) which is absent in the MCSH vortices. For some combination of the Lorentz-violating coefficients there always exist a sufficiently large winding number $n_{0}$ such that for all $% |n|\\geq |n_{0}|$ the magnetic field flips its signal, yielding two well defined regions with opposite magnetic flux. However, the total magnetic flux remains quantized and proportional to the winding number.

  16. Primordial massive gravitational waves from Einstein-Chern-Simons-Weyl gravity

    Energy Technology Data Exchange (ETDEWEB)

    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.

  17. Finite action principle for Chern-Simons AdS gravity

    CERN Document Server

    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.

  18. Thermodynamics in dynamical Chern-Simons modified gravity with canonical scalar field

    Science.gov (United States)

    Rani, Shamaila; Nawaz, Tanzeela; Jawad, Abdul

    2016-09-01

    We take the scalar field dark energy model possessing a non-canonical kinetic term in the framework of modified Chern-Simon gravity. We assume the flat FRW universe model and interacting scenario between dark matter and non-canonical dark energy part. Under this scenario, we check the stability of the model using squared speed of sound which represents the stable behavior for a specific choice of model parameters. We also discuss the validity of generalized second law of thermodynamics by assuming the usual entropy and its corrected forms (logarithmic and power law) at the apparent horizon. This law satisfied for all cases versus redshift parameter at the present as well as later epoch.

  19. The geometry and physics of Abelian gauge groups in F-theory

    Energy Technology Data Exchange (ETDEWEB)

    Keitel, Jan

    2015-07-14

    In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

  20. On Gauge Invariant Descriptions of Gluon Polarization

    CERN Document Server

    Guo, Zhi-Qiang

    2012-01-01

    We propose methods to construct gauge invariant decompositions of nucleon spin, especially gauge invariant descriptions of gluon polarization. We show that gauge invariant decompositions of nucleon spin can be derived naturally from the conserved current of a generalized Lorentzian transformation by Noether theorem. We also examine the problem of gauge dependence with a gauge invariant extension of the Chern-Simons current.

  1. Discrete gauge theories

    NARCIS (Netherlands)

    de Wild Propitius, M.D.F.; Bais, F.A.

    1999-01-01

    In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha

  2. Stochastic quantization of topological field theory: generalized Langevin equation with memory kernel

    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)

  3. Self-dual soliton solutions in a Chern-Simons-CP(1) model with a nonstandard kinetic term

    Science.gov (United States)

    Casana, Rodolfo; Sourrouille, Lucas

    2014-07-01

    A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomol'nyi equations. The Bogomol'nyi-Prasad-Sommerfield (BPS) energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The self-dual equations are solved analytically and verified numerically.

  4. Phases of the Dirac determinant, Abelian Chern-Simons terms and Berry's phases in the field theoretic description of graphene

    CERN Document Server

    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.

  5. Effects of the UY(1 ) Chern-Simons term and its baryonic contribution on matter asymmetries and hypermagnetic fields

    Science.gov (United States)

    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.

  6. Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

    Science.gov (United States)

    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.

  7. Searching for a Connection Between Matroid Theory and String Theory

    CERN Document Server

    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.

  8. Supergravity from Gauge Theory

    CERN Document Server

    Berkowitz, Evan

    2016-01-01

    Gauge/gravity duality is the conjecture that string theories have dual descriptions as gauge theories. Weakly-coupled gravity is dual to strongly-coupled gauge theories, ideal for lattice calculations. I will show precision lattice calculations that confirm large-N continuum D0-brane quantum mechanics correctly reproduces the leading-order supergravity prediction for a black hole's internal energy---the first leading-order test of the duality---and constrains stringy corrections.

  9. Cosmological Analysis of Dynamical Chern-Simons Modified Gravity via Dark Energy Scenario

    Directory of Open Access Journals (Sweden)

    Abdul Jawad

    2015-01-01

    Full Text Available The purpose of this paper is to study the cosmological evolution of the universe in the framework of dynamical Chern-Simons modified gravity. We take pilgrim dark energy model with Hubble and event horizons in interacting scenario with cold dark matter. For this scenario, we discuss cosmological parameters such as Hubble and equation of state and cosmological plane like ωϑ-ωϑ′ and squared speed of sound. It is found that Hubble parameter approaches the ranges 75-0.5+0.5 (for u=2 and (74, 74.30 (for u=1,-1,-2 for Hubble horizon pilgrim dark energy. It implies the ranges 74.80-0.005+0.005 (for u=2 and (73.4, 74 (for u=-2 for event horizon pilgrim dark energy. The equation of state parameter provides consistent ranges with different observational schemes. Also, ωϑ-ωϑ′ planes lie in the range (ωϑ=-1.13-0.25+0.24,ωϑ′<1.32. The squared speed of sound shows stability for all present models in the present scenario. We would like to mention here that our results of various cosmological parameters show consistency with different observational data like Planck, WP, BAO, H0, SNLS, and WMAP.

  10. Field theory representation of mixed gauge-gravity symmetry-protected topological invariants, group cohomology and beyond

    Science.gov (United States)

    Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang

    The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689

  11. Invariants from classical field theory

    CERN Document Server

    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.

  12. Basis Tensor Gauge Theory

    CERN Document Server

    Chung, Daniel J H

    2016-01-01

    We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.

  13. Gauge theories and holisms

    Science.gov (United States)

    Healey, Richard

    Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum "particles", it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis of a supposed gravitational analog to the Aharonov-Bohm effect. By contrast with electromagnetism in the original Aharonov-Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of nongravitational interactions is associated with holism depends on what counts as the relevant part-whole relation. Loop representations of quantized gauge theories of nongravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields.

  14. Self-dual soliton solutions in a Chern-Simons-CP(1) model with a nonstandard kinetic term

    CERN Document Server

    Casana, Rodolfo

    2013-01-01

    A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomol'nyi equations. The BPS energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The magnetic flux is a finite quantity proportional to the potential coupling constant and to the effective radius of the topological defect. The self-dual equations are solved analytically and verified numerically.

  15. G2 gauge theories

    CERN Document Server

    Maas, Axel

    2012-01-01

    QCD can be formulated using any gauge group. One particular interesting choice is to replace SU(3) by the exceptional group G2. Conceptually, this group is the simplest group with a trivial center. It thus permits to study the conjectured relevance of center degrees of freedom for QCD. Practically, since all its representation are real, it is possible to perform lattice simulations for this theory also at finite baryon densities. It is thus an excellent environment to test methods and to investigate general properties of gauge theories at finite densities. We review the status of our understanding of gauge theories with the gauge group G2, including Yang-Mills theory, Yang-Mills-Higgs theory, and QCD both in the vacuum and in the phase diagram.

  16. Higher spin gauge theories

    CERN Document Server

    Henneaux, Marc; Vasiliev, Mikhail A

    2017-01-01

    Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at an international workshop in Singapore in November 2015 where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories i...

  17. Global Anomalies and Effective Field Theory

    CERN Document Server

    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.

  18. Knot Invariants from Classical Field Theories

    CERN Document Server

    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.

  19. Viscous conformal gauge theories

    DEFF Research Database (Denmark)

    Toniato, Arianna; Sannino, Francesco; Rischke, Dirk H.

    2017-01-01

    We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories.......We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories....

  20. Digital lattice gauge theories

    CERN Document Server

    Zohar, Erez; Reznik, Benni; Cirac, J Ignacio

    2016-01-01

    We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms...

  1. Criticality and novel quantum liquid phases in Ginzburg-Landau theories with compact and non-compact gauge fields

    Energy Technology Data Exchange (ETDEWEB)

    Smiseth, Jo

    2005-07-01

    The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)

  2. Self-Dual Configurations in a Generalized Abelian Chern-Simons-Higgs Model with Explicit Breaking of the Lorentz Covariance

    Directory of Open Access Journals (Sweden)

    Rodolfo Casana

    2016-01-01

    Full Text Available We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions, ω1(|ϕ| and ω(|ϕ|, which split the kinetic term of the Higgs field, |Dμϕ|2→ω1(|ϕ||D0ϕ|2-ω(|ϕ||Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether ω(|ϕ|∝β|ϕ|2β-2 with β≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ω1(|ϕ| which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual |ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.

  3. Gauge Theories of Gravitation

    CERN Document Server

    Blagojević, Milutin

    2012-01-01

    During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge field theory of the Weyl-Cartan-Yang-Mills type. The resulting theory, the Poincar\\'e gauge theory of gravity, encompasses Einstein's gravitational theory as well as the teleparallel theory of gravity as subcases. In general, the spacetime structure is enriched by Cartan's torsion and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. The present reprint volume contains articles from the most prominent proponents of the theory and is supplemented by detailed commentaries of the editors. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\\'e gauge theory and its generalizations are explored and specific topi...

  4. 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.

  5. Gauge field theories

    CERN Document Server

    Frampton, Paul H

    2008-01-01

    This third edition on the classic Gauge Field Theories is an ideal reference for researchers starting work with the Large Hadron Collider and the future International Linear Collider. This latest title continues to offer an up to date reference containing revised chapters on electroweak interactions and model building including a completely new chapter on conformality. Within this essential reference logical organization of the material on gauge invariance, quantization, and renormalization is also discussed providing necessary reading for Cosmologists and Particle Astrophysicists

  6. Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

    CERN Document Server

    Alvarez, Gustavo; Kniehl, Bernd A; Kondrashuk, Igor; Parra-Ferrada, Ivan

    2016-01-01

    We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We ...

  7. 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.

  8. 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.)

  9. Finite quantum gauge theories

    Science.gov (United States)

    Modesto, Leonardo; Piva, Marco; Rachwał, Lesław

    2016-07-01

    We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).

  10. Geometric symmetries and topological terms in F-theory and field theory

    Energy Technology Data Exchange (ETDEWEB)

    Kapfer, Andreas

    2016-08-25

    In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory. The first part treats settings of supersymmetry breaking in five dimensions. We focus on an N=4 to N=2 breaking in gauged supergravity. For certain classes of embedding tensors we can analyze the theory around the vacuum to a great extent. Importantly, one-loop corrections to Chern-Simons terms are generically induced which are independent of the supersymmetry-breaking scale. We investigate concrete examples of consistent truncations of supergravity and M-theory which show this N=4 to N=2 breaking pattern in five dimensions. In particular, we analyze necessary conditions for these consistent truncations to be used as effective theories for phenomenology by demanding consistency of the scale-independent corrections to Chern-Simons couplings. The second part is devoted to the study of anomalies and large gauge transformations in circle-reduced gauge theories and F-theory. We consider four- and six-dimensional matter-coupled gauge theories on the circle and classify all large gauge transformations that preserve the boundary conditions of the matter fields. Enforcing that they act consistently on one-loop Chern-Simons couplings in three and five dimensions explicitly yields all higher-dimensional gauge anomaly cancelation conditions. In the context of F-theory compactifications we identify the classified large gauge transformations along the circle with arithmetic structures on elliptically fibered Calabi-Yau manifolds via the dual M-theory setting. Integer Abelian large gauge transformations correspond to free basis shifts in the Mordell-Weil lattice of rational sections while special fractional non-Abelian large gauge transformations are matched to torsional shifts in the Mordell-Weil group. For integer non-Abelian large gauge transformations we

  11. Higher Spin Lifshitz Theory and Integrable Systems

    CERN Document Server

    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.

  12. The a-function for N=2 supersymmetric gauge theories in three dimensions

    CERN Document Server

    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.

  13. Hot Conformal Gauge Theories

    DEFF Research Database (Denmark)

    Mojaza, Matin; Pica, Claudio; Sannino, Francesco

    2010-01-01

    We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in s.......e. they are independent on the specific matter representation.......We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged...... in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We...

  14. Digital lattice gauge theories

    Science.gov (United States)

    Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

    2017-02-01

    We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

  15. Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

    Science.gov (United States)

    Bartolo, Nicola; Orlando, Giorgio

    2017-07-01

    Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f(phi). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass MCS. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra langle γ γ ζ rangle for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f(phi) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.

  16. Lattice gauge theories

    Science.gov (United States)

    Weisz, Peter; Majumdar, Pushan

    2012-03-01

    Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.

  17. Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes

    CERN Document Server

    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.

  18. The Doublet Extension of Tensor Gauge Potentials and a Reassessment of the Non-Abelian Topological Mass Mechanism

    CERN Document Server

    Cantcheff, M Botta

    2011-01-01

    A well-defined local gauge structure for non-Abelian two-form gauge fields was introduced some years ago. This was achieved by introducing doublet group representations and doublet-assembled connections. We provide a summarized version of this formalism, in order to recall its features and applications. We also build up doublet-extended gauge-invariant actions for bosonic and fermionic matter, and discuss the appearance of novel topological quantities in these doublet-type gauge models. A partner action for higher spin fields appears in the doublet version of the fermionic matter sector. As an application of the formalism, a Chern-Simons and an Yang-Mills action in four dimensions may both be rigorously defined. We carry out this task and show that, in this doublet framework, their combination constitutes a consistent (power-counting renormalizable and unitary) non-Abelian generalization of the Cremmer-Scherk-Kalb-Ramond theory with topological mass.

  19. Algebraic aspects of gauge theories

    Science.gov (United States)

    Zharinov, V. V.

    2014-08-01

    Gauge theories are primary tools in modern elementary particle physics. The generally recognized mathematical foundations of these theories are in differential geometry, namely, in the theory of connections in a principal fiber bundle. We propose another approach to the mathematical description of gauge theories based on a combination of algebraic and geometric methods.

  20. Charged BPS vortices and reversal of the magnetic flux in a Maxwell-Higgs type model without the Chern-Simons term

    Energy Technology Data Exchange (ETDEWEB)

    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)

  1. Hot Conformal Gauge Theories

    CERN Document Server

    Mojaza, Matin; Sannino, Francesco

    2010-01-01

    We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We show that the reduced free energy changes sign, at the second, fifth and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as signal of an instability of the system then we infer a critical number of flavors. Surprisingly this number, if computed to the order g^2, agrees with previous predictions for the lower boundary o...

  2. A massive renormalizable abelian gauge theory in 2+1 dimensions

    CERN Document Server

    Dilkes, F A; Dilkes, F A; McKeon, D G C

    1995-01-01

    The standard formulation of a massive Abelian vector field in 2+1 dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stückelberg mass term. In this latter model, we still have a massive vector field, but now the interaction with a charged spinor field is renormalizable (as opposed to super renormalizable). By choosing an appropriate gauge fixing term, the Stückelberg auxiliary scalar field decouples from the vector field. The one-loop spinor self energy is computed using operator regularization, a technique which respects the three dimensional character of the antisymmetric tensor \\epsilon_{\\alpha\\beta\\gamma}. This method is used to evaluate the vector self energy to two-loop order; it is found to vanish showing that the beta function is zero to two-loop order. The canonical structure of the model is examined using the Dirac constraint formalism.

  3. Light-Front quantization of field theory

    CERN Document Server

    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.

  4. 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)

  5. 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)

  6. The tensor hierarchy of 8-dimensional field theories

    Science.gov (United States)

    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.

  7. The tensor hierarchy of 8-dimensional field theories

    CERN Document Server

    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.

  8. The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter

    CERN Document Server

    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.

  9. Ponzano-Regge model revisited: I. Gauge fixing, observables and interacting spinning particles

    Energy Technology Data Exchange (ETDEWEB)

    Freidel, Laurent [Perimeter Institute for Theoretical Physics, 35 King street North, Waterloo N2J 2G9, Ontario (Canada); Louapre, David [Laboratoire de Physique, UMR 5672 du CNRS, Ecole Normale Superieure de Lyon, 46 allee d' ltalie, 69364 Lyon Cedex 07 (France)

    2004-12-21

    We show how to properly gauge fix all the symmetries of the Ponzano-Regge model for 3D quantum gravity. This amounts to doing explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the presence of interacting quantum spinning particles. We introduce a notion of operators whose expectation value gives rise to either gauge fixing, introduction of time, or insertion of particles, according to the choice. We give the link between the spin foam quantization and the Hamiltonian quantization. We finally show the link between the Ponzano-Regge model and the quantization of Chern-Simons theory based on the double quantum group of SU(2)

  10. On the gauge invariant and topological nature of the localization determining the Quantum Hall Effect plateaus

    CERN Document Server

    Cabo-Montes de Oca, Alejandro

    2002-01-01

    It is shown how the electromagnetic response of 2DEG under Quantum Hall Effect regime, characterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge-reservoirs that stabilize the Hall conductivity plateaus. The results determine the basic dynamical origin of the singular properties of localization under the occurrence of the Quantum Hall Effect obtained in the pioneering works of Laughlin and of Joynt and Prange, by means of a gauge invariance argument and a purely electronic analysis, respectively. The common intuitive picture of electrons moving along the equipotential lines gets an analytical realization through the Chern-Simons current and charge densities.

  11. Introduction to Supersymmetric Gauge Theories

    CERN Document Server

    Piguet, O

    1997-01-01

    In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to account for the lack of exact supersymmetry in the actual world of elementary particles.

  12. Gauge Mediation in String Theory

    OpenAIRE

    Kawano, Teruhiko; Ooguri, Hirosi; Ookouchi, Yutaka

    2007-01-01

    We show that a large class of phenomenologically viable models for gauge mediation of supersymmetry breaking based on meta-stable vacua can be realized in local Calabi–Yau compactifications of string theory.

  13. 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)

  14. Higher Derivative Corrections To Extended Supersymmetric Theories

    CERN Document Server

    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.

  15. Gauge fields emerging from time-reversal symmetry breaking for spin-5/2 fermions in a honeycomb lattice

    Energy Technology Data Exchange (ETDEWEB)

    Szirmai, G.; Szirmai, E. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest (Hungary); Zamora, A. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); Lewenstein, M. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); ICREA-Institucio Catalana de Recerca i Estudis Avancats, Lluis Companys 23, E-08010 Barcelona (Spain)

    2011-07-15

    We propose an experimentally feasible setup with ultracold alkaline-earth-metal atoms to simulate the dynamics of U(1) lattice gauge theories in 2 + 1 dimensions with a Chern-Simons term. To this end we consider the ground-state properties of spin-5/2 alkaline-earth-metal fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin-liquid state with 2{pi}/3 flux per plaquette, which violates time-reversal invariance. We demonstrate that due to the breaking of time-reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge-field dynamics. We discuss also properties of the lowest energy competing orders.

  16. Gauge Theories of Vector Particles

    Science.gov (United States)

    Glashow, S. L.; Gell-Mann, M.

    1961-04-24

    The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.

  17. Brane charges and Chern Simons invariants of hyperbolic spaces, with cosmological applications

    Science.gov (United States)

    Bytsenko, Andrei A.; Elizalde, Emilio

    2006-05-01

    We discuss methods of K-theory associated with hyperbolic orbifolds and valid for the description of Chern morphisms and brane charges. Such methods of K-theory are applied to compute D-brane charges, which are identified with elements of Grothendick K-groups, and for manifolds with horizons, spaces that naturally arise as the near-horizon of black brane geometries. In de Sitter spaces, these solutions break supersymmetry, and do not describe universes with zero cosmological constant. Here we pay attention to real hyperbolic spaces, and we examine associated Chern classes and brane charges using methods of K-theory and spectral theory of differential operators related to real hyperbolic spaces. An argument in favour of hyperbolic geometries in the treatment of the contributions to the vacuum persistence amplitude in QFT is given. All those are to be viewed as the proper mathematical structures underlying QFT with relevant backgrounds and boundary conditions in string cosmology. Invited contribution to the 7th Int. Workshop on Quantum Field Theory under the Influence of External Conditions, QFEXT'05 (Barcelona, 5 9 Sept. 2005).

  18. Gauge Theories with Lorentz-symmetry Violation and Electrically Charged Vortices in the Planar Regime

    CERN Document Server

    Belich, H

    2004-01-01

    We deal with a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to D=1+2. The new planar model obtained is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background $v^{\\mu}$) that imposes the Lorentz violation to the reduced model. The vortex solutions for the reduced model in a superconductor environment are investigated. The Aharonov-Casher Effect in layered superconductors, that shows interference of particles with a magnetic moment moving around a line charge, is studied. Our vortex solution presents electrical charge which generates a screened electrical field, and simulate the same phase shift caused by a charged wire.

  19. Quantum principal bundles and corresponding gauge theories

    CERN Document Server

    Durdevic, M

    1995-01-01

    A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.

  20. Gauge theory loop operators and Liouville theory

    Energy Technology Data Exchange (ETDEWEB)

    Drukker, Nadav [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Gomis, Jaume; Okuda, Takuda [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Teschner, Joerg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2009-10-15

    We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S{sup 4} - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)

  1. Mathematical aspects of quantum field theories

    CERN Document Server

    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...

  2. Gravity: a gauge theory perspective

    CERN Document Server

    Nester, James M

    2016-01-01

    The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether's two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincar\\'e group. The dynamical potentials of the Poincar\\'e gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed,...

  3. Gauge Theories, Tessellations & Riemann Surfaces

    CERN Document Server

    He, Yang-Hui

    2014-01-01

    We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.

  4. Gauge theories, tessellations & Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom); Loon, Mark van [Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom)

    2014-06-10

    We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.

  5. From Gauging Nonrelativistic Translations to N-Body Dynamics

    CERN Document Server

    Lukierski, J; Zakrzewski, W J

    2001-01-01

    We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge-invariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d\\times (d+1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d=2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic 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. We describe the effective interaction of the d=2 N-particle problem and discuss its classical solution for N=2. The phase space Hamilt...

  6. Self-duality and F theory

    CERN Document Server

    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.

  7. Three-family particle physics models from global F-theory compactifications

    Energy Technology Data Exchange (ETDEWEB)

    Cvetič, Mirjam [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104-6396 (United States); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Peña, Damián Kaloni Mayorga [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34151, Trieste (Italy); Oehlmann, Paul-Konstantin; Reuter, Jonas [Bethe Center for Theoretical Physics, Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany)

    2015-08-17

    We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations X with the choice of base ℙ{sup 3}. We observe that the F-theory conditions on the G{sub 4}-flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent G{sub 4}-flux. For this purpose we compute the vertical cohomology H{sub V}{sup (2,2)}(X) in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the expressions found for the G{sub 4}-flux allow for a cancellation of D3-brane tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that our G{sub 4}-flux solutions are adequately quantized.

  8. The inaction approach to gauge theories

    CERN Document Server

    Pivovarov, Grigorii

    2012-01-01

    The inaction approach introduced previously for phi^4 is generalized to gauge theories. It combines the advantages of the effective field theory and causal approaches to quantum fields. Also, it suggests ways to generalizing gauge theories.

  9. SO(d, d; Z) Transformation Property for Gauge Fluxes and Ramond-Ramond Fields in Noncommutative Geometry

    Institute of Scientific and Technical Information of China (English)

    WANG Pei

    2002-01-01

    In this paper we study the spinor constructions of gauge fluxes and Ramond Ramond fields on noncommu-tative tori Td up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern Simons Lagrangian in toroidal compactification as a product of spinors.

  10. Geometric Formulation of Gauge Theory of Gravity

    Institute of Scientific and Technical Information of China (English)

    WUNing; ZHANGDa-Hua; RUANTu-Nan

    2003-01-01

    DitTerential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence between quantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gauge theory of gravity is studied.

  11. Gauge symmetry enhancement in Hamiltonian formalism

    CERN Document Server

    Hong, S T; Lee, T H; Oh, P; Oh, Phillial

    2003-01-01

    We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of out model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.

  12. New N=5,6, 3D gauged supergravities and holography

    Energy Technology Data Exchange (ETDEWEB)

    Chatrabhuti, Auttakit; Karndumri, Parinya [String Theory and Supergravity Group, Department of Physics,Faculty of Science, Chulalongkorn University,254 Phayathai Road, Pathumwan, Bangkok 10330 (Thailand); Thailand Center of Excellence in Physics, CHE, Ministry of Education,Bangkok 10400 (Thailand); Ngamwatthanakul, Boonpithak [String Theory and Supergravity Group, Department of Physics,Faculty of Science, Chulalongkorn University,254 Phayathai Road, Pathumwan, Bangkok 10330 (Thailand)

    2014-01-29

    We study N=5 gauged supergravity in three dimensions with compact, non-compact and non-semisimple gauge groups. The theory under consideration is of Chern-Simons type with USp(4,k)/USp(4)×USp(k) scalar manifold. We classify possible semisimple gauge groups of the k=2,4 cases and identify some of their critical points. A number of supersymmetric AdS{sub 3} critical points are found, and holographic RG flows interpolating between these critical points are also investigated. As one of our main results, we consider a non-semisimple gauge group SO(5)⋉T{sup 10} for the theory with USp(4,4)/USp(4)×USp(4) scalar manifold. The resulting theory describes N=5 gauged supergravity in four dimensions reduced on S{sup 1}/ℤ{sub 2} and admits a maximally supersymmetric AdS{sub 3} critical point with Osp(5|2,ℝ)×Sp(2,ℝ) superconformal symmetry. We end the paper with the construction of SO(6)⋉T{sup 15} gauged supergravity with N=6 supersymmetry. The theory admits a half-supersymmetric domain wall as a vacuum solution and may be obtained from an S{sup 1}/ℤ{sub 2} reduction of N=6 gauged supergravity in four dimensions.

  13. Entwinement in discretely gauged theories

    Science.gov (United States)

    Balasubramanian, V.; Bernamonti, A.; Craps, B.; De Jonckheere, T.; Galli, F.

    2016-12-01

    We develop the notion of "entwinement" to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an S N gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS3 at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M = 0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.

  14. Entwinement in discretely gauged theories

    CERN Document Server

    Balasubramanian, V; Craps, B; De Jonckheere, T; Galli, F

    2016-01-01

    We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an $S_N$ gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS$_3$ at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the...

  15. Differential renormalization of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)

    1998-10-01

    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

  16. Noncommutative Gauge Theories: Model for Hodge theory

    CERN Document Server

    Upadhyay, Sudhaker

    2013-01-01

    The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.

  17. An introduction to gauge theories

    CERN Document Server

    Cabibbo, Nicola; Benhar, Omar

    2017-01-01

    Written by three of the world's leading experts on particle physics and the standard model, including an award-winning former director general of CERN, this book provides a completely up-to-date account of gauge theories. Starting from Feynman’s path integrals, Feynman rules are derived, gauge fixing and Faddeev-Popov ghosts are discussed, and renormalization group equations are derived. Several important applications to quantum electrodynamics and quantum chromodynamics (QCD) are discussed, including the one-loop derivation of asymptotic freedom for QCD.

  18. Gauge theory and variational principles

    CERN Document Server

    Bleecker, David

    2005-01-01

    This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field

  19. The role of the anomaly cancellation mechanism in the evaluation of the radiatively induced Chern-Simons term in extended QED

    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.)

  20. Introduction to lattice gauge theory

    Science.gov (United States)

    Gupta, R.

    The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics.