Massive gravitational waves in Chern-Simons modified gravity
Myung, Yun Soo; Moon, Taeyoon(Institute of Basic Science and Department of Computer Simulation, Inje University, Gimhae, 621-749, Korea)
2014-01-01
We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for $\\theta=x/\\mu$ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman-Penrose formalism, the number of polarization modes is one in addition to an unspecified $\\Psi_4$, implying thre...
Massive gravitational waves in Chern-Simons modified gravity
We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for θ=x/μ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman–Penrose formalism, the number of polarization modes is one in addition to an unspecified Ψ4, implying three degrees of freedom for θ=x/μ. This compares with two for a canonical embedding of θ=t/μ. Also, if one introduces the Ricci tensor formalism to describe a massive graviton arising from the nCS modified gravity, one finds one massive mode after making second-order wave equations, which is compared to five found from the parity-even Einstein–Weyl gravity
Ricci dark energy in Chern-Simons modified gravity
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρx ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
Ricci dark energy in Chern-Simons modified gravity
Silva, J.G.; Santos, A.F. [Universidade Federal de Mato Grosso (UFMT), Campo Grande, MT (Brazil)
2013-07-01
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρ{sub x} ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, M. Jamil; Ali, Sarfraz
2016-04-01
This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.
Membrane paradigm of black holes in Chern-Simons modified gravity
Zhao, Tian-Yi
2015-01-01
The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.
Membrane paradigm of black holes in Chern-Simons modified gravity
Zhao, Tian-Yi; Wang, Towe
2016-06-01
The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.
Dirichlet boundary-value problem for Chern-Simons modified gravity
Chern-Simons modified gravity comprises the Einstein-Hilbert action and a higher-derivative interaction containing the Chern-Pontryagin density. We derive the analog of the Gibbons-Hawking-York boundary term required to render the Dirichlet boundary-value problem well defined. It turns out to be a boundary Chern-Simons action for the extrinsic curvature. We address applications to black hole thermodynamics.
On the Chern-Simons State in General Relativity and Modified Gravity Theories
The Chern-Simons state is one solution to quantum constraints of gravity in the context of general relativity (GR) theory if we use Ashtekar's variables and if one orders the constraints with the triads to the left. Six years ago Krasnov introduced a certain class of modified gravity theories by replacing the cosmological constant by a cosmological function of the curvature. If this function is a constant we come back to GR. In this note we review how the Chern-Simons state is one solution to the constraints of GR and we state the problem to face if we wish a generalized Chern-Simons state for the modified Krasnov's theories
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.
Chern-Simons modified gravity and closed time-like curves
Porfirio, P J; Nascimento, J R; Petrov, A Yu; Ricardo, J; Santos, A F
2016-01-01
We verify the consistency of the G\\"odel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.
Pasqua, Antonio [University of Trieste, Department of Physics, Trieste (Italy); Rocha, Roldao da [Universidade Federal do ABC, Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil); International School for Advanced Studies (SISSA), Trieste (Italy); Chattopadhyay, Surajit [Bengal Pailan Park, Pailan College of Management and Technology, Kolkata (India)
2015-02-01
Dark energy models are here investigated and studied in the framework of the Chern-Simons modified gravity model. We bring into focus the holographic dark energy model with Granda-Oliveros cut-off, the modified holographic Ricci dark energy model and a model with higher derivatives of the Hubble parameter. The relevant expressions of the scale factor a(t) for a Friedmann-Robertson-Walker Universe are derived and studied, and, in this context, the evolution of the scale factor is shown to be similar to the one displayed by the modified Chaplygin gas in two of the above models. (orig.)
Does a black hole rotate in Chern-Simons modified gravity?
Konno, Kohkichi; Tanda, Satoshi
2007-01-01
Rotating black hole solutions in the (3+1)-dimensional Chern-Simons modified gravity theory are discussed by taking account of perturbation around the Schwarzschild solution. The zenith-angle dependence of a metric function related to the frame-dragging effect is determined from a constraint equation independently of a choice of the embedding coordinate. We find that at least within the framework of the first-order perturbation method, the black hole cannot rotate for finite black hole mass if the embedding coordinate is taken to be a timelike vector. However, the rotation can be permitted in the limit of $M/r \\to 0$ (where $M$ is the black hole mass and $r$ is the radius). For a spacelike vector, the rotation can also be permitted for any value of the black hole mass.
Thermodynamics in dynamical Chern-Simons modified gravity with canonical scalar field
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.
Chern-Simons-like Gravity Theories
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 generalisation combining the latter two.
Vacuum instability in Chern-Simons gravity
Dyda, Sergei; Flanagan, Éanna É.; Kamionkowski, Marc
2012-12-01
We explore perturbations about a Friedmann-Robertson-Walker background with a nonvanishing cosmological Chern-Simons scalar field in Chern-Simons gravity. At large momenta one of the two circularly polarized tensor modes becomes ghostlike. We argue that nevertheless the theory does not exhibit classical runaway solutions, except possibly in the relativistic nonlinear regime. However, the ghost modes cause the vacuum state to be quantum mechanically unstable, with a decay rate that is naively infinite. The decay rate can be made finite only if one interprets the theory as an effective quantum field theory valid up to some momentum cutoff Λ, which violates Lorentz invariance. By demanding that the energy density in photons created by vacuum decay over the lifetime of the Universe not violate observational bounds, we derive strong constraints on the two dimensional parameter space of the theory, consisting of the cutoff Λ and the Chern-Simons mass.
Having great accuracy in the range and range rate measurements, the GRACE mission and the planed GRACE follow on mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the satellite-to-satellite tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of χ cm for each free flight of these SST missions, here χ is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale MCS = (4ℎc)/(χa) of the non-dynamical Chern-Simons gravity could be constrained to be larger than 1.9 x 10.9 eV. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that MCS ≥ 5 x 10-7 eV is expected. (orig.)
Qiang, Li-E [Chang' an University, Department of Geophysics, College of Geology Engineering and Geomatics, Xi' an (China); Xu, Peng [Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Beijing (China)
2015-08-15
Having great accuracy in the range and range rate measurements, the GRACE mission and the planed GRACE follow on mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the satellite-to-satellite tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of χ cm for each free flight of these SST missions, here χ is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale M{sub CS} = (4ℎc)/(χa) of the non-dynamical Chern-Simons gravity could be constrained to be larger than 1.9 x 10.9 eV. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that M{sub CS} ≥ 5 x 10{sup -7} eV is expected. (orig.)
Vacuum Instability in Chern-Simons Gravity
Dyda, Sergei; Kamionkowski, Marc
2012-01-01
We explore perturbations about a Friedmann-Robertson-Walker background in Chern-Simons gravity. At large momenta one of the two circularly polarized tensor modes becomes ghostlike. We argue that nevertheless the theory does not exhibit classical runaway solutions, except possibly in the relativistic nonlinear regime. However, the ghost modes cause the vacuum state to be quantum mechanically unstable, with a decay rate that is naively infinite. The decay rate can be made finite only if one interprets the theory as an effective quantum field theory valid up to some momentum cutoff, which violates Lorentz invariance. By demanding that the energy density in photons created by vacuum decay over the lifetime of the Universe not violate observational bounds, we derive strong constraints on the two dimensional parameter space of the theory, consisting of the cutoff and the Chern-Simons mass.
Hamiltonian analysis of Einstein-Chern-Simons gravity
Avilés, L.; Salgado, P.
2016-06-01
In this work we consider the construction of the Hamiltonian action for the transgressions field theory. The subspace separation method for Chern-Simons Hamiltonian is built and used to find the Hamiltonian for five-dimensional Einstein-Chern-Simons gravity. It is then shown that the Hamiltonian for Einstein gravity arises in the limit where the scale parameter l approaches zero.
Boundary Dynamics of Higher Dimensional Chern-Simons Gravity
Gegenberg, J.; Kunstatter, G.
2000-01-01
We review the relevance to the black hole entropy problem of boundary dynamics in Chern-Simons gravity. We then describe a recent derivation of the action induced on the four dimensional boundary in a five dimensional Chern-Simons gravity theory with gauge invariant, anti-deSitter boundary conditions.
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...
Even-dimensional topological gravity from Chern-Simons gravity
Merino, N.; Perez, Alfredo; Salgado, P.(Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile)
2009-01-01
It is shown that the topological action for gravity in 2n-dimensions can be obtained from the 2n+1-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a 2n+1-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field $\\phi^{a}$, which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associat...
AdS Chern-Simons gravity induces conformal gravity
Aros, Rodrigo; Díaz, Danilo E.
2014-04-01
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 the dimensional reduction of a five-dimensional Chern-Simons action for a suitable (gauge-fixed, tractorlike) five-dimensional anti-de Sitter connection. The gauge-fixing and dimensional reduction program readily admits a generalization to higher dimensions for the case of certain conformal gravities obtained by contractions of the Weyl tensor.
AdS Chern-Simons Gravity induces Conformal Gravity
Aros, Rodrigo
2013-01-01
The leitmotif of this paper is the question of whether four- and higher even-dimensional Conformal Gravities do have a Chern-Simons pedigree. We show that Weyl gravity can be obtained as dimensional reduction of a five-dimensional Chern-Simons action for a suitable (gauged-fixed, tractor-like) five-dimensional AdS connection. The gauge-fixing and dimensional reduction program admits a readily generalization to higher dimensions for the case of certain conformal gravities obtained by contractions of the Weyl tensor.
Euler Chern Simons Gravity from Lovelock Born Infeld Gravity
Izaurieta, Fernando; Rodriguez, Eduardo; Salgado, Patricio
2004-01-01
In the context of a gauge theoretical formulation, higher dimensional gravity invariant under the AdS group is dimensionally reduced to Euler-Chern-Simons gravity. The dimensional reduction procedure of Grignani-Nardelli [Phys. Lett. B 300, 38 (1993)] is generalized so as to permit reducing D-dimensional Lanczos Lovelock gravity to d=D-1 dimensions.
Extremal Black Holes in Dynamical Chern-Simons Gravity
McNees, Robert; Yunes, Nicolás
2015-01-01
Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity (GR). Such solutions are often difficult to find in beyond-GR theories due to the inclusion of additional fields that couple to the metric non-linearly and non-minimally. In this paper, we consider rotating black hole solutions in one such theory, dynamical Chern-Simons gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dynamical Chern-Simons gravity as an effective field theory and thus work in the decoupling limit, where corrections are treated as small perturbations from general relativity. We perturb about the maximally-rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct sol...
Stellar equilibrium in Einstein-Chern-Simons gravity
Quinzacara, Cristian
2016-01-01
We consider a spherically symmetric internal solution within the context of Einstein-Chern-Simons gravity and derive a generalized five-dimensional Tolman-Oppenheimer-Volkoff (TOV) equation. It is shown that the generalized TOV equation leads, in a certain limit, to the standard five-dimensional TOV equation
Parametrized Post-Newtonian Expansion of Chern-Simons Gravity
Alexander, Stephon
2007-01-01
We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in Chern-Simons gravity with a perfect fluid source. In particular, we study the mapping of this solution to the parameterized post-Newtonian formalism to 1 PN order in the metric. We find that the PPN parameters of Chern-Simons gravity are identical to those of general relativity, with the exception of the inclusion of a new term that is proportional to the Chern-Simons coupling parameter and the curl of the PPN vector potentials. We also find that the new term is naturally enhanced by the non-linearity of spacetime and we provide a physical interpretation for it. By mapping this correction to the gravito-electro-magnetic framework, we study the corrections that this new term introduces to the acceleration of point particles and the frame-dragging effect in gyroscopic precession. We find that the Chern-Simons correction to these classical predictions could be used by current and future experiments to place bounds o...
Accelerated FRW solutions in Chern-Simons gravity
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.)
Standard general relativity from Chern-Simons gravity
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.
The Chern-Simons one-form and gravity on a fuzzy space
The one-dimensional NxN-matrix Chern-Simons action is given, for large N and for slowly varying fields, by the (2k+1)-dimensional Chern-Simons action SCS, where the gauge fields in SCS parametrize the different ways in which the large N limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern-Simons action at finite N and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold
On the Boundary Dynamics of Chern-Simons Gravity
Arcioni, Giovanni; Blau, Matthias; O'Loughlin, Martin
2002-01-01
We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, f...
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...
On the boundary dynamics of Chern-Simons gravity
We study Chern-Simons theory with a complex GC or a real GxG gauge group on a manifold with boundary - this includes lorentzian and euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a GC/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature. (author)
On the Boundary Dynamics of Chern-Simons Gravity
Arcioni, G; O'Loughlin, M H; Arcioni, Giovanni; Blau, Matthias; Loughlin, Martin O'
2003-01-01
We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS_3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature.
New post-Newtonian parameter to test Chern-Simons gravity.
Alexander, Stephon; Yunes, Nicolas
2007-12-14
We study Chern-Simons (CS) gravity in the parametrized post-Newtonian (PPN) framework through a weak-field solution of the modified field equations. We find that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional to the CS coupling and the curl of the PPN vector potential. This new term leads to a modification of frame dragging and gyroscopic precession and we provide an estimate of its size. This correction might be used in experiments, such as Gravity Probe B, to bound CS gravity and test string theory. PMID:18233434
Static solutions in Einstein-Chern-Simons gravity
Crisóstomo, J.; Gomez, F.; Mella, P.; Quinzacara, C.; Salgado, P.
2016-06-01
In this paper we study static solutions with more general symmetries than the spherical symmetry of the five-dimensional Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field ha with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with ha. It is found that exist (i) a negative tangential pressure zone around low-mass distributions (μ < μ1) when the coupling constant α is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies μ < μ2 (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field ha plays the role of a cosmological constant.
Static solutions in Einstein-Chern-Simons gravity
Crisóstomo, Juan; Quinzacara, Cristian; Salgado, Patricio
2016-01-01
In this paper we study static solutions with more general symmetries than the spherical symmetry of the so called Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field $h^a$ with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with $h^a$ . It is found that exist (i) a negative tangential pressure zone around low-mass distributions ($\\mu < \\mu_1$) when the coupling constant $\\alpha$ is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies $\\mu < \\mu_2$ ; (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field $h^a$ plays the role of a cosmological constant.
Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity
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
Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity
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.
Barnich, Glenn; Giribet, Gaston; Leston, Mauricio
2015-01-01
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.
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups. PMID:22540458
Edge Currents and Vertex Operators for Chern-Simons Gravity
Bimonte, G; Stern, A
1993-01-01
We apply elementary canonical methods for the quantization of 2+1 dimensional gravity, where the dynamics is given by E. Witten's $ISO(2,1)$ Chern-Simons action. As in a previous work, our approach does not involve choice of gauge or clever manipulations of functional integrals. Instead, we just require the Gauss law constraint for gravity to be first class and also to be everywhere differentiable. When the spatial slice is a disc, the gravitational fields can either be unconstrained or constrained at the boundary of the disc. The unconstrained fields correspond to edge currents which carry a representation of the $ISO(2,1)$ Kac-Moody algebra. Unitary representations for such an algebra have been found using the method of induced representations. In the case of constrained fields, we can classify all possible boundary conditions. For several different boundary conditions, the field content of the theory reduces precisely to that of 1+1 dimensional gravity theories. We extend the above formalism to include sou...
Canizares, Priscilla; Sopuerta, Carlos F
2012-01-01
[abridged] The detection of gravitational waves from extreme-mass-ratio (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA or eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by General Relativity and even to test whether General Relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. In this paper, we explore to what extent EMRI observations with LISA or eLISA/NGO might be able to distinguish between G...
Some cosmological solutions in Einstein-Chern-Simons gravity
Avilés, Luis; Quinzacara, Cristian; Salgado, Patricio
2016-01-01
In this paper we find new solutions for the so called Einstein-Chern-Simons Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84 (2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in the first case we find some solutions of the five-dimensional ChS-FRW field equations when the $h^a$ field is a perfect fluid that obeys a barotropic equation of state; (ii) in the second case we study the solutions, for the cases $\\gamma =1/2,\\ 3/4$, when the $h^a$ field is a five dimensional politropic fluid that obeys the equation $P^{(h)}=\\omega ^{(h)}\\rho ^{(h)\\gamma }$; (iii) in the third case we find the scale factor and the state parameter $\\omega (t)$ when the $h^a$ field is a variable modified Chaplygin gas. We consider also a space-time metric which contains as a subspace to the usual four-dimensional FRW and then we study the same three cases considered in the five-dimensional, namely when (i) the $h^a$ field is a perfect fluid, (ii) the $h^a$ field is a five dimensiona...
The Hamiltonian Form of Three-Dimensional Chern-Simons-like Gravity Models
Bergshoeff, Eric A; 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 generalisation combining the latter two.
Gauge Symmetries and Holographic Anomalies of Chern-Simons and Transgression AdS Gravity
Mora, Pablo
2014-01-01
We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravities. Those anomalies are either gauge anomalies associated to the AdS gauge group of the theory or diffeomorphism anomalies, with each kind related to the other. As a result of using suitable action principles por Chern-Simons AdS gravities, coming from Transgression forms, we obtain finite results without the need for further regularization. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories. The Wess-Zumino consistency condition ensures that anomalies of the generic form computed here should appear for these and other theories.
Triad representation of the Chern-Simons state in quantum gravity
Paternoga, R; Paternoga, Robert; Graham, Robert
2000-01-01
We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed to the real triad representation by means of a suitably generalized Fourier transformation, yielding a complex integral representation for the corresponding state in the triad variables. It is found that topologically inequivalent choices for the complex integration contour give rise to linearly independent wavefunctionals in the triad representation, which all arise from the one Chern-Simons state in the Ashtekar variables. For a suitable choice of the normalization factor, these states turn out to be gauge-invariant under arbitrary, even topologically non-trivial gauge-transformations. Explicit analytical expressions for the wavefunctionals in the triad representation can be obtained in several interesting asymptotic parameter regimes, and the associated...
2D Gravity on $AdS_2$ with Chern-Simons Corrections
Alishahiha, Mohsen; Mosaffa, Amir E
2009-01-01
We study 2D Maxwell-dilaton gravity with higher order corrections given by the Chern-Simons term. The model admits three distinctive $AdS_2$ vacuum solutions. By making use of the entropy function formalism we find the entropy of the solutions which is corrected due to the presence of the Chern-Simons term. We observe that the form of the correction depends not only on the coefficient of the Chern-Simons term, but also on the sign of the electric charge; pointing toward the chiral nature of the dual CFT. Using the asymptotic symmetry of the theory as well as requiring a consistent picture we can find the central charge and the level of U(1) current. Upon uplifting the solutions to three dimensions we get purely geometric solutions which will be either $AdS_3$ or warped $AdS_3$ with an identification.
Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity
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.
3D gravity with torsion as a Chern-Simons gauge theory
Blagojevic, M; Vasilic, M.
2003-01-01
We show that topological 3D gravity with torsion can be formulated as a Chern-Simons gauge theory, provided a specific parameter, known as the effective cosmological constant, is negative. In that case, the boundary dynamics of the theory corresponding to anti-de Sitter boundary conditions is described by a conformal field theory with two different central charges.
Generalised Chern-Simons actions for 3d gravity and κ-Poincare symmetry
We consider Chern-Simons theories for the Poincare, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern-Simons formulation of 3d gravity. We determine conditions under which κ-Poincare symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern-Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincare symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern-Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction
Action Principles for Transgression and Chern-Simons AdS Gravities
Mora, Pablo
2014-01-01
Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times. In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge...
On the Hamiltonian Analysis of Spin-3 Chern-Simons-Like Theories of Gravity
Setare, M R
2016-01-01
In this paper, we consider spin-3 Chern-Simons-like theories of gravity as extended theories of spin-3 gravity in (2+1)- dimension. In order to determine the number of local degrees of freedom we present the Hamiltonian formulation of these theories. We extract the Hamiltonian density, then we find primary and secondary constraints of these theories. Then we obtain the Poisson brackets of the primary and the secondary constraints. After that we count the number of local degrees of freedom of spin-3 Chern-Simons-like theories of gravity. We apply this method on spin-3 Einstein-Cartan gravity and spin-3 topologically massive gravity. According to the our results the spin-3 Einstein-Cartan gravity and the spin-3 topologically massive gravity have respectively zero and one bulk local degree of freedom.
SL(2,C) Chern-Simons Theory and Quantum Gravity with a Cosmological Constant
Haggard, Hal; Han, Muxin; Kaminski, Wojciech; Riello, Aldo
2015-04-01
We show a relation between 4-dimensional quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in 3-dimensions with knotted graph defects. In particular, we study the expectation value of a non-planar Wilson graph operator in SL(2,C) Chern-Simons theory on S3. We analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. We find that a class of flat connections in the graph complement manifold are in correspondence with the geometries of constant curvature 4-simplices. We show that the asymptotic behavior of the amplitude contains an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. This work was supported by the U.S. National Science Foundation, the European Marie Curie actions, and the Perimeter Institute.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
We investigate the two-dimensional version of the Chern-Simons action derived from the recently proposed even-dimensional generalized Chern-Simons action. We show that the two-dimensional topological gravity emerges if we choose the Clifford algebra as a nonstandard gauge symmetry algebra required from the generalized Chern-Simons action. We find a ''hidden order parameter'' which differentiates the gravity phase and nongravity phase
Quadratic gravity in (2+1)D with a topological Chern-Simons term
Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chern-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity. (author)
The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second-order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of projector-like operators for the degrees of freedom, rather than for the spin modes of the fields. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes becomes more immediate. Our conclusion is that the only tachyon- and ghost-free model is the Einstein-Hilbert action added up by the Chern-Simons term with a timelike vector of the type vμ=(μ,0-vector). Spectral consistency imposes that the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to ordinary gauge theories whenever conditions for the suppression of tachyons and ghosts are imposed.
Stability of the Schwarzschild black hole in f(R) gravity with the dynamical Chern-Simons term
We perform the stability analysis of the Schwarzschild black hole in f(R) gravity with the parity-violating Chern-Simons (CS) term coupled to a dynamical scalar field θ. For this purpose, we transform the f(R) gravity into the scalar-tensor theory by introducing a scalaron φ, providing the dynamical CS modified gravity with two scalars. The perturbation equation for the scalar θ is coupled to the odd-parity metric perturbation equation, providing a system of two coupled second-order equations, while the scalaron is coupled to the even-parity perturbation equation. This implies that the CS coupling affects the Regge-Wheeler equation, while f(R) gravity does not affect the Zerilli equation. It turns out that the Schwarzschild black hole is stable against the external perturbations if the scalaron is free from the tachyon.
Light-Front Dynamics Of Massive Vector Chern-Simons Gravity
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.
Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.
Yagi, Kent; Yunes, Nicolás; Tanaka, Takahiro
2012-12-21
Dynamical Chern-Simons gravity cannot be strongly constrained with current experiments because it reduces to general relativity in the weak-field limit. This theory, however, introduces modifications in the nonlinear, dynamical regime, and thus it could be greatly constrained with gravitational waves from the late inspiral of black-hole binaries. We complete the first self-consistent calculation of such gravitational waves in this theory. For favorable spin orientations, advanced ground-based detectors may improve existing solar system constraints by 6 orders of magnitude. PMID:23368447
Gravitational and gauge couplings in Chern-Simons fractional spin gravity
Boulanger, Nicolas; Valenzuela, Mauricio
2015-01-01
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 arXiv:1312.5700. The resulting three-dimensional Chern-Simons theory unifies the Blencowe-Vasiliev higher spin gravity with fractional spin fields and internal gauge potentials. For integer or half-integer fractional spins, infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2l+1) or gl(l|l+1) and various real forms thereof. We derive the relation between gravitational and internal gauge couplings.
From Lorentz-Chern-Simons to Massive Gravity in 2+1 Dimensions
del Pino, Simón; Toloza, Adolfo; Zanelli, Jorge
2015-01-01
We propose a generalization of Chiral Gravity, which follows from considering a Chern-Simons action for the spin connection with anti-symmetric contorsion. The theory corresponds to Topologically Massive Gravity at the chiral point non-minimally coupled to an additional scalar mode that gathers the torsion degree of freedom. In this setup, the effective cosmological constant (the inverse of the curvature radius of maximally symmetric solutions) is either negative or zero, and it enters as an integration constant associated to the value of the contorsion at infinity. We explain how this is not in conflict with the Zamolodchikov's $c$-theorem holding in the dual boundary theory. In fact, we conjecture that the theory formulated about three-dimensional Anti-de Sitter space is dual to a two-dimensional conformal field theory whose right- and left-moving central charges are given by $c_{R}=24k$ and $c_{L}=0$, respectively, being $k$ the level of the Chern-Simons action. We study the classical theory both at the li...
Self-Dual Chern-Simons Solitons in (2+1)-Dimensional Einstein Gravity
Cangemi, D; Cangemi, Daniel; Lee, Choonkyu
1992-01-01
We consider here a generalization of the Abelian Higgs model in curved space, by adding a Chern--Simons term. The static equations are self-dual provided we choose a suitable potential. The solutions give a self-dual Maxwell--Chern--Simons soliton that possesses a mass and a spin.
Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity
In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms
Primordial massive gravitational waves from Einstein-Chern-Simons-Weyl gravity
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 m2 → 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
Gravitational and gauge couplings in Chern-Simons fractional spin gravity
Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio
2016-01-01
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 arXiv: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(2 ℓ + 1) or gl( ℓ| ℓ + 1) and various real forms thereof.
BPS-kink and more global solutions of the Chern-Simons (super)gravity term
We study the supersymmetry of the Kaluza-Klein reduced gravitational Chern-Simons term in two dimensions and propose supergravity transformations that allow for some supersymmetry of the kink solution. (author)
The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach
As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.
Setare, M R
2015-01-01
The Chern-Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the conserved charges is problematic. In this paper we overcome to these problems by considering the concept of total variation and the Lorentz-Lie derivative. At first, we find an expression for the ADT conserved current in context of CSLTG which is based on the concept of Killing vector fields. Then, we generalize it such that the generalized ADT current 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 are based on the concept of quasi-local conserved charge which is off-shell and we can calculate them 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 we find a formula to calculate the ce...
It is shown how the E8 Yang-Mills theory is a small sector of a Cl(16) algebra gauge theory and why the 11D Chern-Simons (super) gravity theory can be embedded into a Cl(11) algebra gauge theory. These results may shed some light into the origins behind the hidden E8 symmetry of 11D supergravity. To finalize, we explain how the Clifford algebra gauge theory (that contains the Chern-Simons gravity action in D=11, for example) can itself be embedded into a more fundamental polyvector-valued gauge theory in Clifford spaces involving tensorial coordinates xμ1μ2,xμ1μ2μ3,...,xμ1μ2...μD in addition to antisymmetric tensor gauge fields Aμ1μ2,Aμ1μ2μ3,...,Aμ1μ2...μD. The polyvector-valued supersymmetric extension of this polyvector valued bosonic gauge theory in Clifford spaces may reveal more important features of a Clifford-algebraic structure underlying M, F theory.
Casimir force between Chern-Simons surfaces
Bordag, M.; Vassilevich, D.V.(CMCC-Universidade Federal do ABC, Santo André, SP, Brazil)
1999-01-01
We calculate the Casimir force between two parallel plates if the boundary conditions for the photons are modified due to presence of the Chern-Simons term. We show that this effect should be measurable within the present experimental technique.
Holographic Chern-Simons defects
Fujita, Mitsutoshi; Melby-Thompson, Charles M.; Meyer, René; Sugimoto, Shigeki
2016-06-01
We study SU( N ) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7 branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for 2-dimensional QCD.
Holographic Chern-Simons Defects
Fujita, Mitsutoshi; Meyer, Rene; Sugimoto, Shigeki
2016-01-01
We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.
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. ...
Meusburger, C
2006-01-01
We relate the geometrical and the Chern-Simons description of (2+1)-dimensional gravity for spacetimes of topology $R\\times S_g$, where $S_g$ is an oriented two-surface of genus $g>1$, for Lorentzian signature and general cosmological constant and the Euclidean case with negative cosmological constant. We show how the variables parametrising the phase space in the Chern-Simons formalism are obtained from the geometrical description and how the geometrical construction of (2+1)-spacetimes via grafting along closed, simple geodesics gives rise to transformations on the phase space. We demonstrate that these transformations are generated via the Poisson bracket by one of the two canonical Wilson loop observables associated to the geodesic, while the other acts as the Hamiltonian for infinitesimal Dehn twists. For spacetimes with Lorentzian signature, we discuss the role of the cosmological constant as a deformation parameter in the geometrical and the Chern-Simons formulation of the theory. In particular, we sho...
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.
Recently, the Banados-Teitelboim-Zanelli (BTZ) black hole in the presence of the gravitational Chern-Simons term has been studied, and it is found that the usual thermodynamic quantities, like the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such that the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of a vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative corrections of the gravitational Chern-Simons term. This provides a nontrivial check of the AdS/CFT correspondence, in the presence of higher-derivative terms in the gravity action
Chern-Simons Particles with Nonstandard Gravitational Interaction
Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J.
2000-01-01
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\\"{o}dinger equation with a noninteger angular mome...
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 ...
Banerjee, Nabamita; Roychowdhury, Dibakar
2013-01-01
We study the effect of a bulk Chern-Simons (CS) term on 3+1 dimensional type II superconductor in the context of the AdS/CFT correspondence. We holographically compute the super-current and find that it is non-local in nature. It receives non trivial corrections due to presence of the CS term. Considering a large limit of a parameter "lambda" (we call this limit as long wave length limit), which is effectively the high temperature limit of the theory, we find that this non-local super-current boils down to a local quantity. The leading term (without the CS term) of this current matches with the result of Ginzburg-Landau (GL) theory. We compute the effect of the CS term on GL current and find that the effect is highly suppressed at large temperature (~1/T^4). Finally, free energy of the vortex configuration has been calculated. The free energy also receives non trivial correction at the order of 1/lambda^2 in the long wave length approximation.
Black hole entropy and SU(2) Chern-Simons theory
Engle, Jonathan; Perez, Alejandro
2009-01-01
We show that the isolated horizon boundary condition can be treated in a manifestly SU(2) invariant manner. The symplectic structure of gravity with the isolated horizon boundary condition has an SU(2) Chern-Simons symplectic structure contribution at the horizon with level k=a_H/ (4\\pi \\beta \\ell^2_p). Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points (defects). In the large black hole limit quantum horizon degrees of freedom can be modelled by a single intertwiner. The coupling constant of the defects with the Chern Simons theory on the horizon is precisely given by the ratio of the area contribution of the defect to the macroscopic area a_H, namely \\lambda= 16\\pi^2 \\beta \\ell^2_p (j(j+1))^(1/2)/a_H.
Chern-Simons Particles with Nonstandard Gravitational Interaction
Lukierski, J; Zakrzewski, W J
2001-01-01
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\\"{o}dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels.
Chern-Simons particles with nonstandard gravitational interaction
Lukierski, J. [Wroclaw Univ. (Poland). Inst. of Theoretical Physics; Dept. de Fisica Teorica, Universidad de Valencia, Burjasot (Spain); Stichel, P.C.; Zakrzewski, W.J. [Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom); Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2001-05-01
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparameterization invariant way, to a translational Chern-Simons action. The quantum 2-body problem is described by a nonstandard Schroedinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. (orig.)
Chern-Simons particles with nonstandard gravitational interaction
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparameterization invariant way, to a translational Chern-Simons action. The quantum 2-body problem is described by a nonstandard Schroedinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. (orig.)
Maxwell-Chern-Simons Theory With Boundary
Blasi, A; Magnoli, N; Storace, S
2010-01-01
The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The boundary is introduced according to Symanzik's basic principles of locality and separability. A method of investigation is proposed, which, avoiding the straight computation of correlators, is appealing for situations where the computation of propagators, modified by the boundary, becomes quite complex. For MCS theory, the outcome is that a unique solution exists, in the form of chiral conserved currents, satisfying a Kac-Mody algebra, whose central charge does not depend on the Maxwell term.
Localization in abelian Chern-Simons theory
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 u...
Absence of higher order corrections to noncommutative Chern-Simons coupling
We analyze the structure of noncommutative pure Chern-Simons theory systematically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not renormalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. (author)
Two gravitationally Chern-Simons terms are too many
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.
Optical properties of Chern-Simons systems
Huerta, Luis
2016-05-01
Chern-Simons (CS) systems interacting with electromagnetic radiation are described by a term f FɅF added to the Maxwell action. In (3+1)D, this CS term is a boundary term affecting the system behaviour in its borders. We study the consequences of the above in the properties of electromagnetic radiation, in particular, by considering the interplay between magneto-electric properties and topology. Apart from a modified Kerr polarization rotation, compared to that found for the particular case of topological insulators, we also found two Brewster angles, for s and p polarization of reflected radiation, respectively. Energy distribution between reflected and transmitted radiation is also studied in terms of the magneto-electric properties and topological condition of the system.
Exact Chern-Simons / Topological String duality
Krefl, Daniel; Mkrtchyan, Ruben L.
2015-10-01
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. 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 extended to refined Chern-Simons with orthogonal groups.
Translational Chern--Simons Action and New Planar Particle Dynamics
Lukierski, J.; Stichel, P. C.; 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,...
Maxwell-Chern-Simons theory for curved spacetime backgrounds
We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern-Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the geometrical-optics approximation. The corresponding light path is modified, which allows for new effects. In a Schwarzschild background, for example, there now exist stable bounded orbits of light rays and the two polarization modes of light rays in unbounded orbits can have different gravitational redshifts
Higher Spins from Nambu-Chern-Simons Theory
Arvanitakis, Alex S.
2016-07-01
We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is simple; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the N = 8 supersymmetric NCS-matter model (BLG theory), where the NCS action originated: Its fully supersymmetric M2 brane configurations are interpreted as Hopf fibrations, the homotopy type of the (infinite) gauge group is calculated and its instantons are classified.
Higher spins from Nambu-Chern-Simons theory
Arvanitakis, Alex S
2015-01-01
We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is \\emph{simple}; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the $N=8$ supersymmetric NCS-matter model (BLG theory), where the NCS action originated: Its fully supersymmetric M2 brane configurations are interpreted as Hopf fibrations, the homotopy type of the (infinite) gauge group is calculated and its instantons are classified.
Chern-Simons theory coupled to bifundamental scalars
Banerjee, Shamik
2013-01-01
We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the SU(N)_k \\times SU(M)_{-k} gauge group. At small but fixed M \\ll N, this system approaches the theory of a Chern-Simons field coupled to fundamental matter, conjectured to be dual to a parity-violating version of Vasiliev's higher-spin gauge theory in AdS_4. At finite M/N and large 't Hooft coupling this theory (or its SUSY version) is expected to be dual to an Einstein-like gravity. We show at two loops that this theory possesses a line of fixed points at any value of M/N. We also prove that turning on a finite but small M/N gaps out the light states that Chern-Simons theory coupled to fundamental matter develops when placed on a torus. We also comment on the higher genus case.
The matrix Chern-Simons one-form as a Universal Chern-Simons theory
We consider different large N limits of the one-dimensional Chern-Simons action i∫dtTr(-bar 0+A0) where A0 is an NxN anti-Hermitian matrix. The Hilbert space on which A0 acts as a linear transformation is taken as the quantization of a 2k-dimensional phase space M with different gauge field backgrounds. For slowly varying fields, the large N limit of the one-dimensional CS action is equal to the (2k+1)-dimensional CS theory on MxR. Different large N limits are parametrized by the gauge fields and the dimension 2k. The result is related to the bulk action for quantum Hall droplets in higher dimensions. Since the isometries of M are gauged, this has implications for gravity on fuzzy spaces. This is also briefly discussed
Chern-Simons forms and cyclic cohomology
Cyclic cohomology appears as a noncummutative analogue of de Rham cohomology suggested by K-theory and index theory in non-commutative geometry. It is therefore natural to study cyclic cohomology using known methods linking K-theory and differential forms such as the Chern-Weil approach to characteristic classes of vector bundles based on connections and curvature. In the present paper we consider Chern-Simons forms over the bigraded differential algebra of cochains having values in the noncommutative differential forms ΩA. The DG algebra ΩA plays an important role in Connes approach to cyclic cohomology, because cyclic cocycles are equivalent to closed traces on ΩA. The Chern-Simons forms provide the link between Connes' theory and the algebra cochain theory. In the first part we study Chern-Simons forms in a general noncommutative differential graded algebra. The Chern-Simons forms of different degree are linked by certain relations, called S-relations, because they are connected with the S-operation in cyclic cohomology. In part 2 we begin with a fairly down to earth account of the theory of algebra cochains. We then discuss the Chern-Simons forms over the bigraded algebra of cochains with values in ΩA, and the cyclic cocycles arising from them by applying a closed trace on ΩA. We show these cocycles coincide with the iterates of Connes s-operation applied to the cyclic cocycle corresponding to the closed trace. (author)
Frobenius-Chern-Simons gauge theory
Bonezzi, Roberto; Sezgin, Ergin; Sundell, Per
2016-01-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as...
On Quantum Corrections to Chern-Simons Spinor Electrodynamics
Chaichian, Masud; Fainberg, V Ya
1998-01-01
We make a detailed investigation on the quantum corrections to Abelian Chern-Simons spinor electrodynamics. Starting from Chern-Simons spinor quantum electrodynamics with the Maxwell term $-1/(4\\gamma){\\int}d^3x F_{\\mu\
Chern-Simons Theory on Supermanifolds
Grassi, Pietro Antonio
2016-01-01
We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N=1 D=3 super-Chern-Simons theory.
Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction
Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved
Chern-Simons Theory, Matrix Models, and Topological Strings
Walcher, J [Institute for Advanced Study, Princeton, New Jersey 08540 (United States)
2006-10-21
This book is a find. Marino meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge/gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. Here is a brief summary of the book. The journey begins with matrix models and an introduction to various techniques for the computation of integrals including perturbative expansion, large-N approximation, saddle point analysis, and the method of orthogonal polynomials. The second chapter, on Chern-Simons theory, is the longest and probably the most complete one in the book. Starting from the action we meet Wilson loop observables, the associated perturbative 3-manifold invariants, Witten's exact solution via the canonical duality to WZW models, the framing ambiguity, as well as a collection of results on knot invariants that can be derived from Chern-Simons theory and the combinatorics of U ({infinity}) representation theory. The chapter also contains a careful derivation of the large-N expansion of the Chern-Simons partition function, which forms the cornerstone of its interpretation as a closed string theory. Finally, we learn that Chern-Simons theory can sometimes also be represented as a matrix model. The story then turns to the gravity side, with an introduction to topological sigma models (chapter 3) and topological string theory (chapter 4). While this presentation is necessarily rather condensed (and the
Transport in Chern-Simons-Matter Theories
Gur-Ari, Guy; Mahajan, Raghu
2016-01-01
The frequency-dependent longitudinal and Hall conductivities --- $\\sigma_{xx}$ and $\\sigma_{xy}$ --- are dimensionless functions of $\\omega/T$ in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of charged excitations of the theory and are basic experimental observables. We compute these conductivities for large $N$ Chern-Simons theory with fermion matter. The computation is exact in the 't Hooft coupling $\\lambda$ at $N = \\infty$. We describe various physical features of the conductivity, including an explicit relation between the weight of the delta function at $\\omega = 0$ in $\\sigma_{xx}$ and the existence of infinitely many higher spin conserved currents in the theory. We also compute the conductivities perturbatively in Chern-Simons theory with scalar matter and show that the resulting functions of $\\omega/T$ agree with the strong coupling fermionic result. This provides a new test of the conjectured 3d bosonization duality. In matching the Hall conductivities we re...
Self-dual Chern-Simons theories
Dunne, Gerald
1995-01-01
Self-dual Chern-Simons theories form a new class of self-dual gauge theories and provide a field theoretical formulation of anyonic excitations in planar (i.e., two-space-dimensional) systems. Much of the recent attention of these theories is due to the surprising and novel ways in which they differ from the standard Maxwell, or Yang-Mills, gauge theories. These Chern-Simons theories are particular to planar systems and have therefore received added research impetus from recent experimental and theoretical breakthroughs in actual planar condensed-matter systems, such as the quantum Hall effect. This book gives a pedagogical introduction to the basic properties of the "self-dual" Chern-Simons theories, concluding with an overview of more advanced results and an extensive bibliography. Such models possess Bogomol'nyi energy bounds, topological charges, vortex solutions, and supersymmetric extensions, features which are familiar from other well-known self-dual systems such as instantons, monopoles, and vortices....
Combinatorial quantization of the Hamiltonian Chern-Simons theory
Motivated by a recent paper of Fock and Rosly we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which reproduces the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *-operation and a positive inner product. (authors)
Self-Dual Vortices in Chern-Simons Hydrodynamics
Pashaev, O K; Pashaev, Oktay K.; Lee, and Jyh-Hao
2001-01-01
The classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schr\\"odinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 - $\\hbar^2$) deformed strength of quantum potential the model is gauge equivalent to the standard Schr\\"odinger equation with Planck constant $\\hbar$, while for the strength (1 + $\\hbar^2$), to the pair of diffusion-anti-diffusion equations. Specifying the gauge field as Abelian Chern-Simons (CS) one in 2+1 dimensions interacting with the Nonlinear Schr\\"odinger field (the Jackiw-Pi model), we represent the theory as a planar Madelung fluid, where the Chern-Simons Gauss law has simple physical meaning of creation the local vorticity for the fluid flow. For the static flow, when velocity of the center-of-mass motion (the classical velocity) is equal to the quantum one (generated by quantum potential velocity of the internal motion), the fluid admits N-vortex solution. Applying the Auberson-Sabatier ...
Perturbative Chern-Simons theory revisited
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 data....... The general problem of extending this work to arbitrary three-manifolds is presented and some initial observations are made. Mathematically, this article is closely related to the work of Rumin and Seshadri and an index type theorem in the contact geometric setting....
Resurgence in complex Chern-Simons theory
Gukov, Sergei; Putrov, Pavel
2016-01-01
We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of asymptotic expansions posses expected analytic properties. In examples that we study we observe that contribution of irreducible flat connections to the path integral can be recovered from asymptotic expansions around abelian flat connections. We also discuss connection to Floer instanton moduli spaces, disk instantons in 2d sigma models, and length spectra of "complex geodesics" on the A-polynomial curve.
Localization at large N in Chern-Simons-matter theories
Marino, Marcos
2016-01-01
We review some exact results for the matrix models appearing in the localization of Chern-Simons-matter theories, focusing on the structure of non-perturbative effects and onthe M-theory expansion of ABJM theory. We also summarize some of the results obtained for other Chern-Simons-matter theories, as well as recent applications to topological strings.
Abelian Chern-Simons theory and contact torsion
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 ...... 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 in...
Translational Chern-Simons Action and New Planar Particle Dynamics
Lukierski, J; Zakrzewski, W J
2000-01-01
We consider a nonstandard $D=2+1$ gravity described by a translational Chern--Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. The phase space Hamiltonian $H$ describing two-body interactions satisfies a nonlinear equation $H={\\cal H}(\\vec{x},\\vec{p};H)$ what implies, after quantization, a nonstandard form of the Schr\\"{o}dinger equation with energy-dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles $r\\leq r_0$) and the scattering states with continuous energy correspond to classical motion for $r>r_0$.
Torsion as a Gauge Field in a Lorentz-Chern-Simons Theory
del Pino, Simón
2016-01-01
We explore a model of gravity that arises from the consideration of the Chern-Simons form in 2+1 dimensions for a spin connection with a contorsion described by a scalar and a vector field. The effective Lagrangian presents a local Weyl symmetry allowing us to gauge the scalar field to a constant value. From a gauge field theory perspective, it is shown that the vector part of the torsion (related to its trace) is a gauge field for the Weyl group, which allows the interpretation of the torsion as an electromagnetic field. In the gauge of constant scalar field we obtain Chiral Gravity coupled to a Chern-Simons-Proca theory for the vector field, that at the level of equations of motion is equivalent to Topologically Massive Electrodynamics minimally coupled to Chiral Gravity. Electrodynamics and gravity appear here unified as geometrical features of a Riemann-Cartan manifold.
Chern Simons bosonization along RG flows
Minwalla, Shiraz; Yokoyama, Shuichi
2016-02-01
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 to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the 't Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.
Chern Simons Bosonization along RG Flows
Minwalla, Shiraz
2015-01-01
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 to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the t' Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.
The Chern-Simons Number as a Dynamical Variable
Tye, S -H Henry
2016-01-01
In the standard electroweak theory that describes nature, the Chern-Simons number associated with the vacua as well as the unstable sphaleron solutions play a crucial role in the baryon number violating processes. We recall why the Chern-Simons number should be generalized from a set of discrete values to a dynamical (quantum) variable. Via the construction of an appropriate Hopf invariant and the winding number, we discuss how the geometric information in the gauge fields is also captured in the Higgs field. We then discuss the choice of the Hopf variable in relation to the Chern-Simons variable.
Chern-Simons superconductivity at finite temperature
A simple gauge theory discussed recently in the literature as a model of high temperature superconductors is examined. The model contains a Maxwell field and a Chern-Simons field coupled to fermions in 2+1-dimensional spacetime. This model has been shown to exhibit a kind of Meissner effect at zero temperature which originates in the 1-loop mixing between the two gauge fields. We use a Euclidean effective action formulation to show that the effect persists at all finite temperatures. Although a long range magnetic type interaction arises at non-zero temperatures, in competition with the finite range forces which dominate the zero temperature interaction, the effect varies smoothly with temperature. In our perturbation treatment, we find no indication of a critical transition at which the Meissner effect is extinguished. (author). 9 refs, 3 figs
Diamagnetic Vortices in Chern Simons Theory
Anber, Mohamed M; Sabancilar, Eray; Shaposhnikov, Mikhail
2015-01-01
We find a new type of topological vortex solution in the $U(1)_Z \\times U(1)_A$ Chern Simons gauge theory in the presence of a $U(1)_A$ magnetic field background. In this theory $U(1)_Z$ is broken spontaneously by the $U(1)_A$ magnetic field. These vortices exhibit long range interactions as they are charged under the unbroken $U(1)_A$. They deplete the $U(1)_A$ magnetic field near their core and also break both $C$ and $P$ symmetries. Understanding the nature of these vortices sheds light on the ground state structure of the superconductivity studied in [1]. We also study the Berezinsky-Kosterlitz-Thouless phase transition in this class of theories and point out that superconductivity can be achieved at high temperatures by increasing the $U(1)_A$ magnetic field.
Level/rank Duality and Chern-Simons-Matter Theories
Hsin, Po-Shen
2016-01-01
We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin$_c$ connections and the metric). The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields. In order for the duality to be valid we must add finite counterterms depending on these background fields. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.
Left-right asymmetric holographic RG flow with gravitational Chern-Simons term
We consider the holographic renormalization group (RG) flow in three-dimensional gravity with the gravitational Chern-Simons term coupled to some scalar fields. We apply the canonical approach to this higher derivative case and employ the Hamilton-Jacobi formalism to analyze the flow equations of two-dimensional field theory. Especially we obtain flow equations of Weyl and gravitational anomalies, and derive c-functions for left and right moving modes. Both of them are monotonically non-increasing along the flow, and the difference between them is determined by the coefficient of the gravitational Chern-Simons term. This is completely consistent with the Zamolodchikov's c-theorem for parity-violating two-dimensional quantum field theories.
Chern-Simons theory in SIM(1) superspace
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.)
Lorentz and U(1) Chern-Simons terms in new minimal supergravity
We couple a linear multiplet to new minimal supergravity, modified by the addition of both the U(1) and Lorentz superfield Chern-Simons terms. We write the lagrangian in component form and find that it contains pieces quadratic in the curvature tensor and has only a finite number of terms. We also find that the auxiliary fields am and G tildem become propagating and massive. Very interestingly, however, for a particular ratio of the U(1) and Lorentz Chern-Simons terms, G tildem can be eliminated. This leads to a lagrangian with only a finite number of terms containing a propagating, massive vector field am and terms quadratic in the curvature tensor. (orig.)
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
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.)
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
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.)
New phase transitions in Chern-Simons matter theory
Zahabi, Ali
2016-02-01
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 S2 ×S1 at finite temperature T. This theory admits a discrete matrix integral representation, i.e. a unitary discrete matrix model of two-dimensional Yang-Mills theory. In this study, the effective partition function and phase structure of the Chern-Simons matter theory, in a special case with an effective potential namely the Gross-Witten-Wadia potential, are investigated. We obtain an exact expression for the partition function of the Chern-Simons matter theory as a function of k, N, T, for finite values and in the asymptotic regime. In the Gross-Witten-Wadia case, we show that ratio of the Chern-Simons matter partition function and the continuous two-dimensional Yang-Mills partition function, in the asymptotic regime, is the Tracy-Widom distribution. Consequently, using the explicit results for free energy of the theory, new second-order and third-order phase transitions are observed. Depending on the phase, in the asymptotic regime, Chern-Simons matter theory is represented either by a continuous or discrete two-dimensional Yang-Mills theory, separated by a third-order domain wall.
Anyonic states in Chern-Simons theory
We discuss the canonical quantization of Chern-Simons theory in 2+1 dimensions, minimally coupled to a Dirac spinor field, first in the temporal gauge and then in the Coulomb gauge. In our temporal gauge formulation, Gauss's law and the gauge condition A0=0 are implemented by embedding the formulation in an appropriate physical subspace. We construct a Fock space of charged particle states that satisfy Gauss's law, and show that they obey fermion, not fractional statistics. The gauge-invariant spinor field that creates these charged states from the vacuum obeys the anticommutation rules that generally apply to spinor fields. The Hamiltonian, when described in the representation in which the charged fermions are the propagating particle excitations that obey Gauss's law, contains an interaction between charge and transverse current densities. We observe that the implementation of Gauss's law and the gauge condition does not require us to use fields with graded commutator algebras or particle excitations with fractional statistics. In our Coulomb gauge formulation, we implement Gauss's law and the gauge condition ∂lAl=0 by the Dirac-Bergmann procedure. In this formulation, the constrained gauge fields become functionals of the spinor fields, and are not independent degrees of freedom. The formulation in the Coulomb gauge confirms the results we obtained in the temporal gauge: The ''Dirac-Bergmann'' anticommutation rule for the charged spinor fiels ψ and ψdegree that have both been constrained to obey Gauss's law is precisely identical to the canonical spinor anticommutation rule that generates standard fermion statistics. And we also show that the Hamiltonians for charged particle states in our temporal and Coulomb gauge formulations are identical, once Gauss's law has been implemented in both cases
Perturbative Chern-Simons Theory on Noncommutative R3
A U(N) Chern-Simons theory on noncommutative /mathbb{R}{3} is constructed as a q-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and /q{/m/n}-independent at the one loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological q-deformed Chern-Simons theory is an example of a model which is non-singular in the limit q → 0. (author)
A Dilogarithmic Formula for the Cheeger-Chern-Simons Class
Dupont, Johan Louis; Zickert, C.K.
2005-01-01
We present a simplification of Neumann's formula in [8] for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex.......We present a simplification of Neumann's formula in [8] for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex....
Lecture notes on Chern-Simons-Witten theory
Hu, Sen
2001-01-01
This invaluable monograph has arisen in part from E Witten's lectures on topological quantum field theory in the spring of 1989 at Princeton University. At that time Witten unified several important mathematical works in terms of quantum field theory, most notably the Donaldson polynomial, the Gromov-Floer homology and the Jones polynomials. In his lectures, among other things, Witten explained his intrinsic three-dimensional construction of Jones polynomials via Chern-Simons gauge theory. He provided both a rigorous proof of the geometric quantization of the Chern-Simons action and a very ill
Chern-Simons from Dirichlet 2-brane instantons
O'Loughlin, M H
1996-01-01
In the vicinity of points in Calabi-Yau moduli space where there are degenerating three-cycles the low energy effective action of type IIA string theory will contain significant contributions arising from membrane instantons that wrap around these three-cycles. We show that the world-volume description of these instantons is Chern-Simons theory.
Parity anomaly in D=3 Chern-Simons gauge theory
Ultraviolet divergences are calcelled in the effective action of the D=3 Chern-Simons gauge theory but regularization is needed. It is impossible to introduce gauge invariant regularization and conserve the parity of the classical action. As a result, in the limit when regularization is moved the finite contribution to the effective action induced by parity violating regulators remains. 18 refs
Non-Abelian Chern-Simons Quantum Mechanics
Lee, Taejin; Oh, Phillial
1993-01-01
We propose a classical model for the non-Abelian Chern-Simons theory coupled to $N$ point-like sources and quantize the system using the BRST technique. The resulting quantum mechanics provides a unified framework for fractional spin, braid statistics and Knizhnik-Zamolodchikov equation.
Perturbative and nonperturbative aspects of complex Chern-Simons Theory
Dimofte, Tudor
2016-01-01
We present an elementary review of some aspects of Chern-Simons theory with complex gauge group SL(N,C). We discuss some of the challenges in defining the theory as a full-fledged TQFT, as well as some successes inspired by the 3d-3d correspondence. The 3d-3d correspondence relates partition functions (and other aspects) of complex Chern-Simons theory on a 3-manifold M to supersymmetric partition functions (and other observables) in an associated 3d theory T[M]. Many of these observables may be computed by supersymmetric localization. We present several prominent applications to 3-manifold topology and number theory in light of the 3d-3d correspondence.
Topological entanglement negativity in Chern-Simons theories
Wen, Xueda; Ryu, Shinsei
2016-01-01
We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work (X. Wen, S. Matsuura and S. Ryu, arXiv:1603.08534).
A Lie based 4-dimensional higher Chern-Simons theory
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.
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Angular Momentum Generation from Holographic Gravitational Chern-Simons Model
Wu, Chaolun
2014-01-01
We study parity-violating effects, particularly the generation of angular momentum density and its relation to the parity-odd and dissipationless transport coefficient Hall viscosity, in strongly-coupled quantum fluid systems in 2+1 dimensions using holographic method. We employ a (3+1)-dimensional holographic model of Einstein-Maxwell system with a gravitational Chern-Simons term coupled to a dynamical scalar field. The scalar can condensate and this breaks the parity spontaneously. We find that when the scalar condensates, a non-vanishing angular momentum density and an associated edge current are generated by the gravitational Chern-Simons term, together with the emergence of Hall viscosity. Both angular momentum density and Hall viscosity acquire membrane paradigm forms and are only determined by the geometry and condensate near the horizon. We present both general analytic results and numeric results which take back-reactions into account. The ratio between Hall viscosity and angular momentum density is ...
Chern-Simons-Schwinger model of confinement in $QCD$
Aurilia, Antonio; Spallucci, Euro
2015-01-01
It has been shown that the mechanism of formation of glue-bags in the strong coupling limit of Yang-Mills theory can be understood in terms of the dynamics of a higher-rank abelian gauge field, namely, the 3-form dual to the Chern-Simons topological current. Building on this result, we show that the field theoretical interpretation of the Chern-Simons term, as opposed to its topological interpretation, also leads to the analytic form of the confinement potential that arises in the large distance limit of $QCD$. In fact, for a $(3+1)$-dimensional generalization of the Schwinger model, we explicitly compute the interaction energy. This generalization is due to the presence of the topological gauge field $A_{\\mu\
Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets
Claus, P; 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 quadratically in the Chern-Simons term, which implies nonlinear terms in the supersymmetry transformations and equations of motion. In the second version, which requires a background of at least two abelian vector supermultiplets, the supersymmetry transformations remain at most linear in the vector-tensor components. This version is of the type known to arise from reduction of tensor supermultiplets in six dimensions. Our work applies to any number of vector-tensor multiplets.
Enhancement of hidden symmetries and Chern-Simons couplings
Henneaux, Marc; Lekeu, Victor
2015-01-01
We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories. It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific value. This is heralded by an enhanced isotropy group of the metric on the scalar manifold. Examples of this phenomenon are discussed as well as the relation to supersymmetry. Our results are also connected with rigidity theorems of Borel-like algebras.
Noncommutative Chern-Simons terms and the noncommutative vacuum
It is pointed out that the space noncommutativity parameters θμ ν in noncommutative gauge theory can be considered as a set of superselection parameters, in analogy with the theta-angle in ordinary gauge theories. As such, they do not need to enter explicitly into the action. A simple generic formula is then suggested to reproduce the Chern-Simons action in noncommutative gauge theory, which reduces to the standard action in the commutative limit but in general implies a cascade of lower-dimensional Chern-Simons terms. The presence of these terms in general alters the vacuum structure of the theory and nonstandard gauge theories can emerge around the new vacua. (author)
Chern-Simons: Fano and Calabi-Yau
Hanany, Amihay
2009-01-01
We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane-tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counter-parts: the del Pezzo surfaces.
On supersymmetric Chern-Simons-type theories in five dimensions
Kuzenko, Sergei M.; Novak, Joseph [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia)
2014-02-24
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 supermultiplet is described in superspace for the first time.
A Higher-Spin Chern-Simons Theory of Anyons
Boulanger, Nicolas; Valenzuela, Mauricio
2013-01-01
We propose Chern-Simons models of fractional-spin fields interacting with ordinary tensorial higher-spin fields and internal color gauge fields. For integer and half-integer values of the fractional spins, the model reduces to finite sets of fields modulo infinite-dimensional ideals. We present the model on-shell using Fock-space representations of the underlying deformed-oscillator algebra.
Chern-Simons diffusion rate across different phase transitions
Rougemont, Romulo; Finazzo, Stefano Ivo
2016-05-01
We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate ΓCS 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 nonconformal 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, ΓCS/s T 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, ΓCS/s T behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. In all the cases, ΓCS/s T increases with decreasing T . The behavior of the Chern-Simons diffusion rate across different phase transitions is expected to play a relevant role for the chiral magnetic effect around the QCD critical end point, which is a second order phase transition point connecting a crossover band to a line of first order phase transition. Our findings in the present work add to the literature the first predictions for the Chern-Simons diffusion rate across second order and crossover transitions in strongly coupled nonconformal, non-Abelian gauge theories.
Combinatorial quantization of the Hamiltonian Chern-Simons theory, 2
Alekseev, A Yu; Schomerus, V; Grosse, H; Schomerus, V
1994-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \\cite{AGS}. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathe- matically rigorous definition of the algebra of observables \\A_{CS} of the Chern Simons model. It is a *-algebra of ``functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional \\omega (``integration''). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly \\cite{FoRo}, the algebra \\A_{CS} provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verl...
Combinatorial quantization of the Hamiltonian Chern-Simons theory II
Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.
Fractional angular momentum in noncommutative generalized Chern-Simons quantum mechanics
Zhang, Xi-Lun; Sun, Yong-Li; Wang, Qing; Long, Zheng-Wen; Jing, Jian
2016-07-01
The noncommutative generalized Chern-Simons quantum mechanics, i.e., the Chern-Simons quantum mechanics on the noncommutative plane in the presence of Aharonov-Bohm magnetic vector potentials, is studied in this paper. We focus our attention on the canonical orbital angular momentum and show that there are two different approaches to produce the fractional angular momentum in the noncommutative generalized Chern-Simons quantum mechanics.
Giambelli Identity in Super Chern-Simons Matrix Model
Matsuno, Satsuki
2016-01-01
A classical identity due to Giambelli in representation theory states that the character in any representation is expressed as a determinant whose components are characters in the hook representation constructed from all the combinations of the arm and leg lengths of the original representation. Previously it was shown that the identity persists in taking, for each character, the matrix integration in the super Chern-Simons matrix model in the grand canonical ensemble. We prove here that this Giambelli compatibility still holds in the deformation of the fractional-brane background.
SIM(1)-VSR Maxwell-Chern-Simons electrodynamics
Bufalo, R.
2016-06-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM (1)-VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and healthy departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges is derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
Light-front quantization of Chern-Simons systems
Light-front quantization of the Chern-Simons theory coupled to complex scalars is performed in the local light-cone gauge following the Dirac procedure. The light-front Hamiltonian turns out to be simple one and the framework may be useful to construct renormalized field theory of anions. The theory is shown to be relativistic in spite of the unconventional transformations of the matter and the gauge field, in the non-covariant gauge adopted, under space rotations. (author). 20 refs
Black hole entropy and SU(2) Chern-Simons theory
Engle, Jonathan; Noui, Karim; Perez, Alejandro
2009-01-01
Black holes in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points. Moreover, the counting can be mapped to counting the number of SU(2) intertwiners compatible with the...
Self-Dual Chern-Simons Vortices in Higgs Field
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.
Bosonization of $QED_3$ with an induced Chern - Simons term
Kovner, A
1994-01-01
We extend the bosonization of $2+1$ - dimensional QED with one fermionic flavor performed previously to the case of QED with an induced Chern - Simons term. The coefficient of this term is quantized: $e^2n/8\\pi$, $n\\in {\\bf Z}$. The fermion operators are constructed in terms of the bosonic fields $A_i$ and $E_i$. The construction is similar to that in the $n=0$ case. The resulting bosonic theory is Lorentz invariant in the continuum limit and has Maxwell's equations as its equations of motion. The algebra of bilinears exhibits nontrivial operatorial mixing with lower dimensional operators, which is absent for $n=0$.
Classical optics in generalized Maxwell Chern-Simons theory
The authors consider the propagation of electromagnetic waves in a two-dimensional polarizable medium endowed with Chern-Simons terms. The dispersion relation (refractive index) of the waves is computed and the existence of linear birefringence and anomalous dispersion is shown. When absorption is taken into account, the classic signature of a Voigt effect is found. In the case where linearly-polarized, three-dimensional waves pass through a two-dimensional plane, it is shown that there is optical activity, and the analogue of Verdet's constant is computed. 19 refs., 2 figs
SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics
Bufalo, R
2016-01-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
Dual Superconformal Symmetry of N=6 Chern-Simons Theory
Huang, Yu-tin
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 the 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 implications of dual conformal symmetry for loop-level amplitudes.
Vortex solutions of PCT-invariant Maxwell-Dirac-Chern-Simons gauge theory
Shin, J
1997-01-01
We construct PCT-invariant Maxwell-Chern-Simons gauge theory coupled to fermions with adding the parity partner to the matter and the gauge field= s, which can give nontopological vortex solutions depending on the sign of t= he Chern-Simons coupling constant.
Arbitrariness in the gravitational Chern-Simons-like term induced radiatively
Felipe, J C C; Cherchiglia, A L; Scarpelli, A P Baêta; Sampaio, Marcos
2014-01-01
Lorentz violation through a radiatively induced Chern-Simons-like term in a fermionic theory embedded in linearized quantum gravity with a Lorentz- and CPT-violating axial-vector term in the fermionic sector proportional to a constant field $b_\\mu$ has been recently studied. In a similar fashion as for the extended-QED model of Carroll-Field-Jackiw, we explicitly show that neither gauge invariance nor the more stringent momentum routing invariance condition on underlying Feynman diagrams fix the arbitrariness inherent to such induced term at one loop order. We present the calculation in a nonperturbative expansion in $b_\\mu$ and within a framework which besides operating in the physical dimension (and thus avoiding $\\gamma_5$ matrix Clifford algebra ambiguities), judiciously parametrizes regularization dependent arbitrary parameters usually fixed by symmetries.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Bardeen, William A. [Fermilab
2015-09-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 0t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
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.
How to resum perturbative series in 3d N=2 Chern-Simons matter theories
Honda, Masazumi
2016-01-01
Continuing the work arXiv:1603.06207, we study perturbative series in general 3d $\\mathcal{N}=2$ supersymmetric Chern-Simons matter theory with $U(1)_R$ symmetry, which is given by a power series expansion of inverse Chern-Simons levels. We find that perturbative series are usually non-Borel summable along positive real axis for various observables. Alternatively we prove that the perturbative series are Borel summable along negative (positive) imaginary axis for positive (negative) Chern-Simons levels. It turns out that the Borel resummations along this direction are the same as exact results.
Framing and localization in Chern-Simons theories with matter
Bianchi, Marco S; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-01-01
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.
Framing and localization in Chern-Simons theories with matter
Bianchi, Marco S.; Griguolo, Luca; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-06-01
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.
Resolution of Chern--Simons--Higgs Vortex Equations
Han, Xiaosen; Yang, Yisong
2015-01-01
It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.
Quantum modularity and complex Chern-Simons theory
Dimofte, Tudor
2015-01-01
The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of the knot complement and a geometric solution to the gluing equations) and a complex root of unity $\\zeta$. We prove that the coefficients of our series lie in the trace field of the knot, adjoined a complex root of unity. We conjecture that our series are those that appear in the Quantum Modularity Conjecture and confirm that they match the numerical asymptotics of the Kashaev invariant (at various roots of unity) computed by Zagier and the first author. Our construction is motivated by the analysis of singular limits in Chern-Simons theory with gauge group $SL(2,C)$ at fixed level $k$, where $\\zeta^k=1$.
Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes
We show that for general spherically symmetric configurations, contributions of broad class of gravitational and mixed gauge-gravitational Chern-Simons (CS) terms to the equations of motion vanish identically in D > 3 dimensions. This implies that such terms in the action do not affect Birkhoff's theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in the D > 3 static spherically symmetric case, CS terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields be unrestricted, the results extend almost completely, with only one possible exception-CS Lagrangian terms in which the gravitational part is just the n = 2 irreducible gravitational CS term.
Black hole entropy and SU(2) Chern-Simons theory.
Engle, Jonathan; Noui, Karim; Perez, Alejandro
2010-07-16
Black holes (BH's) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area a(H), the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to a(H) with logarithmic corrections ΔS=-3/2 loga(H). Our treatment from first principles settles previous controversies concerning the counting of states. PMID:20867755
Resolution of Chern-Simons-Higgs Vortex Equations
Han, Xiaosen; Lin, Chang-Shou; Yang, Yisong
2016-04-01
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 that settles a long-standing open problem in the field regarding the general solvability of the equations.
Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge
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].
Dimension of Conformal Blocks in Five Dimensional Kaehler-Chern-Simons Theory
Liu, Haitao
2009-01-01
We briefly review the Kaehler-Chern-Simon theory on 5-manifolds which are trivial circle bundles over 4-dimensional Kaehler manifolds and present a detailed calculation of the path integral, using the method of Blau and Thompson.
The Chern-Simons term induced at high temperature and the quantization of its coefficient
By perturbative calculations of the high-temperature ground-state axial vector current of fermion fields coupled to gauge fields, an anomalous Chern-Simons topological mass term is induced in the three-dimensional effective action. The anomaly in three dimensions appears just in the ground-state current rather than in the divergence of ground-state current. In the Abelian case, the contribution comes only from the vacuum polarization graph, whereas in the non-Abelian case, contributions come from the vacuum polarization graph and the two triangle graphs. The relation between the quantization of the Chern-Simons coefficient and the Dirac quantization condition of magnetic charge is also obtained. It implies that in a (2+1)-dimensional QED with the Chern-Simons topological mass term and a magnetic monopole with magnetic charge g present, the Chern-Simons coefficient must be also quantized, just as in the non-Abelian case. (orig.)
Non-flat pilgrim dark energy FRW models in modified gravity
Rani, Shamaila; Jawad, Abdul; Salako, Ines G.; Azhar, Nadeem
2016-09-01
We study the cosmic acceleration in dynamical Chern-Simons modified gravity in the frame-work of non-flat FRW universe. The pilgrim dark energy (with future event and apparent horizons) interacted with cold dark matter is being considered in this work. We investigate the cosmological parameters (equation of state, deceleration) and planes (state-finders, ω_{θ}-ω_{θ}^' }) in the present scenario. It is interesting to mention here that the obtained results of various cosmological parameters are consistent with various observational schemes. The validity of generalized second law of thermodynamics for present dark energy models is also being analyzed.
Critical behavior of 2+1 dimensional CPN-1 model with a Chern-Simons term
I investigate the critical behaviour of 2+1 dimensional CPN-1 model with a Chern-Simons term. I derive the 1/N expansion in this model and show that the theory is renormalizable in this framework. The critical exponents η and υ are calculated to the O(1/N). They exhibit θ (coefficient of the Chern-Simons term) dependence. (author). 14 refs, 6 figs
Higher derivative Chern-Simons extension in the noncommutative QED$_{3}$
Bufalo, R
2014-01-01
The noncommutative (NC) massive quantum electrodynamics in $2+1$ dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are also obtained. The gauge invariance of the outcome action is also carefully discussed.
Higher derivative Chern-Simons extension in the noncommutative QED$_{3}$
Ghasemkhani, M.; Bufalo, R.
2014-01-01
The noncommutative (NC) massive quantum electrodynamics in $2+1$ dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action is carefully discussed. We then con...
A magnetic model with a possible Chern-Simons phase
Freedman, M H
2003-01-01
A rather elementary family of local Hamiltonians $H_{\\circ, \\ell}, \\ell = 1,2,3, ...$, is described for a 2-dimensional quantum mechanical system of spin ={1/2} particles. On the torus, the ground state space $G_{\\circ, \\ell}$ is essentially infinite dimensional but may collapse under $\\l$perturbation" to an anyonic system with a complete mathematical description: the quantum double of the SO(3)-Chern-Simons modular functor at $q= e^{2 \\pi i/\\ell +2}$ which we call $D E \\ell$. The Hamiltonian $H_\\circ, \\ell}$ defines a \\underline{quantum} \\underline{loop} \\underline{gas}. We argue that for $\\ell = 1$ and 2, $G_\\circ, \\ell}$ is unstable and the collapse to $G_{\\epsilon, \\ell} \\cong D E \\ell$ can occur truly by perturbation. For $\\ell \\geq 3 G_{\\circ, \\ell}$ is stable and in this case finding $G_{\\epsilon, \\ell} \\cong D E \\ell$ must require either $\\epsilon> \\epsilon_\\ell> 0$, help from finite system size, surface roughening (see section 3), or some other trick, hence the initial use of quotes $\\l\\quad$". A hyp...
Chern-Simons diffusion rate across different phase transitions
Rougemont, Romulo
2016-01-01
We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate $\\Gamma_{\\textrm{CS}}$ divided by the product of the entropy density $s$ and temperature $T$ behaves across different kinds of phase transitions in the class of bottom-up non-conformal Einstein-dilaton holographic models originally proposed by Gubser and Nellore. By tuning the dilaton potential, one is able to holographically mimic a first order, a second order, or a crossover transition. In a first order phase transition, $\\Gamma_{\\textrm{CS}}/sT$ jumps at the critical temperature (as previously found in the holographic literature), while in a second order phase transition it develops an infinite slope. On the other hand, in a crossover, $\\Gamma_{\\textrm{CS}}/sT$ behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. Furthermore, we also find that $\\Gamma_{\\textrm{CS}}/sT$ increases by orders of magnitude below the critical temperature in a second order phase transition and in a crossov...
Superconformal Chern-Simons-matter theories in N =4 superspace
Kuzenko, Sergei M.; Samsonov, Igor B.
2015-11-01
In three dimensions, every known N =4 supermultiplet has an off-shell completion. However, there is no off-shell N =4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N =4 superfield realizations for the equations of motion which correspond to various N =4 and N =6 superconformal CS theories, including the Gaiotto-Witten theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. These superfield realizations demonstrate that the superconformal CS theories with N ≥4 (except for the Gaiotto-Witten theory) require a reducible long N =4 vector multiplet, from which the standard left and right N =4 vector multiplets are obtained by constraining the field strength to be either self-dual or antiself-dual. Such a long multiplet naturally originates upon reduction of any off-shell N >4 vector multiplet to N =4 superspace. For the long N =4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N =4 supergravity-matter systems in arXiv:1101.4013. We also couple N =4 superconformal CS theories to N =4 conformal supergravity.
Embedded graph invariants in Chern-Simons theory
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
Refined Chern-Simons Theory in Genus Two
Arthamonov, Semeon
2015-01-01
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a Macdonald q,t-deformation -- refinement -- of these operators that preserves the defining relations of the mapping class groups beyond genus 1. For this we explicitly construct the refined TQFT representation of the genus 2 mapping class group in the case of rank one TQFT. This is a direct generalization of the original genus 1 construction of arXiv:1105.5117, opening a question if it extends to any genus. Our construction is built upon a q,t-deformation of the square of q-6j symbol of U_q(sl_2), which we define using the Macdonald version of Fourier duality. This allows to compute the refined Jones polynomial for arbitrary knots in genus 2. In contrast with genus 1, the refined Jones polynomial in genus 2 does not appear to agree with the Poincare polynomial of the triply ...
Jain, Sachin; Minwalla, Shiraz; Takimi, Tomohisa; Wadia, Spenta R; Yokoyama, Shuichi
2014-01-01
We present explicit computations and conjectures for $2 \\to 2$ scattering matrices in large $N$ {\\it $U(N)$} Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.
Entropy for gravitational Chern-Simons terms by squashed cone method
Guo, Wu-zhong
2015-01-01
In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D we find no anomaly of entropy appears. But the squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation $d\\bm{\\Omega_{4n-1}}=tr(\\bm{R}^{2n})$. We notice that the entropy of $tr(\\bm{R}^{2n})$ is a total derivative locally, i.e. $S=d s_{CS}$. We propose to identify $s_{CS}$ with the entropy of gravitational Chern-Simons terms $\\Omega_{4n-1}$. In the first method ...
Consistent interactions of the 2+1 dimensional noncommutative Chern-Simons field
We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this happens only in a particular gauge
A note on large N thermal free energy in supersymmetric Chern-Simons vector models
Yokoyama, Shuichi [Department of Theoretical Physics, Tata Institute of Fundamental Research,Homi Bhabha Road, Mumbai 400005 (India)
2014-01-27
We compute the exact effective action for N=3U(N){sub k} and N=4,6U(N){sub k}×U(N′){sub −k} Chern-Simons theories with minimal matter content in the ’t Hooft vector model limit under which N and k go to infinity holding N/k,N′ fixed. We also extend this calculation to N=4,6 mass deformed case. We show that those large N effective actions except mass-deformed N=6 case precisely reduce to that of N=2U(N){sub k} Chern-Simons theory with one fundamental chiral field up to overall multiple factor. By using this result we argue the thermal free energy and self-duality of the N=3,4,6 Chern-Simons theories including the N=4 mass term reduce to those of the N=2 case under the limit.
A note on large N thermal free energy in supersymmetric Chern-Simons vector models
We compute the exact effective action for N=3U(N)k and N=4,6U(N)k×U(N′)−k Chern-Simons theories with minimal matter content in the ’t Hooft vector model limit under which N and k go to infinity holding N/k,N′ fixed. We also extend this calculation to N=4,6 mass deformed case. We show that those large N effective actions except mass-deformed N=6 case precisely reduce to that of N=2U(N)k Chern-Simons theory with one fundamental chiral field up to overall multiple factor. By using this result we argue the thermal free energy and self-duality of the N=3,4,6 Chern-Simons theories including the N=4 mass term reduce to those of the N=2 case under the limit
Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories
Bonora, Loriano; Goncalves, Antonio E
2016-01-01
We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.
The Topological Inner Structure of Chern-Simons Tensor Current and the World-Sheet of Strings
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.
Martín-Ruiz, A.; Cambiaso, M.; Urrutia, L. F.
2015-12-01
Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics are analyzed exploiting the Green's function (GF) method. We consider the electromagnetic field coupled to a θ term in a way that has been proposed to provide the correct low-energy effective action for topological insulators (TI). We take the θ term to be piecewise constant in different regions of space separated by a common interface Σ , which will be called the θ boundary. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in CS extended electrodynamics, and solutions for some experimental setups have been found, each with its specific configuration of sources. In this work we illustrate a method to construct the GF that allows us to solve the CS modified field equations for a given θ boundary with otherwise arbitrary configuration of sources. The method is illustrated by solving the case of a planar θ boundary but can also be applied for cylindrical and spherical geometries for which the θ boundary can be characterized by a surface where a given coordinate remains constant. The static fields of a pointlike charge interacting with a planar TI, as described by a planar discontinuity in θ , are calculated and successfully compared with previously reported results. We also compute the force between the charge and the θ boundary by two different methods, using the energy-momentum tensor approach and the interaction energy calculated via the GF. The infinitely straight current-carrying wire is also analyzed.
Dyon of a non-Abelian Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
Navarro-Lerida, Francisco
2013-01-01
Dyons of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions are presented. These solitons carry both magnetic and electric global charges. The SO(3)xSO(2) solutions are constructed numerically. These are Chern-Simons dyons, differing radically from Julia-Zee dyons. The Chern-Simons densities employed are defined in 3+1 dimensions, and they are the first two of the 'new' Chern-Simons densities introduced recently. They are defined in terms of both Yang-Mills fields and a 5-component isomultiplet Higgs. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
Henn, Johannes M.; Plefka, Jan; Wiegandt, Konstantin
2010-01-01
We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order. For both theories we demonstrate that the one-loop contribution to these correlators cancels. For pure Chern-Simons, we find that specific UV divergences arise from diagrams involving two cusps, implying the loss of finiteness and topological invariance at two-loop order. Studying those UV divergences we derive anomalous conformal Ward identities for n-cusped Wilson loops which rest...
Anyons and Chern-Simons theory on compact spaces of finite genus
We study the coupling of an Abelian Chern-Simons field to fermions in space-times of the form RxM2, where M2 is a compact Riemannian manifold. Upon integrating out the non-zero modes of the Chern-Simons field, an effective N-particle Hamiltonian is constructed, which involves a term representing the effects of the zero modes. We also study the transformation to the fractional statistics (anyon) basis. It is shown that unlike the case of the flat Euclidean M2 the anyon wave equation involves some residual metric dependent interactions, and the wave function is multivalued. (author). 7 refs
Self-Dual Chern-Simons Solitons and Generalized Heisenberg Ferromagnet Models
Oh, P; Oh, Phillial
1996-01-01
We consider the (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with the Chern-Simons gauge fields. Self-dual Chern-Simons solitons, the static zero energy solution saturating Bogomol'nyi bounds, are shown to exist when the generalized spin variable is valued in the Hermitian symmetric spaces G/H. By gauging the maximal torus subgroup of H, we obtain self-dual solitons which satisfy vortex-type nonlinear equations thereby extending the two dimensional instantons in a nontrivial way. An explicit example for the CP(N) case is given.
Vortex solutions of a Maxwell-Chern-Simons field coupled to four-fermion theory
We find the static vortex solutions of the model of a Maxwell-Chern-Simons gauge field coupled to a (2+1)-dimensional four-fermion theory. Especially, we introduce two matter currents coupled to the gauge field minimally: the electromagnetic current and a topological current associated with the electromagnetic current. Unlike other Chern-Simons solitons the N-soliton solution of this theory has binding energy and the stability of the solutions is maintained by the charge conservation laws. copyright 1997 The American Physical Society
Vortices and domain walls in a Chern-Simons theory with magnetic moment interactions
We study the structure and properties of vortices in a recently proposed Abelian Maxwell-Chern-Simons model in 2+1 dimensions. The model which is described by a gauge field interacting with a complex scalar field includes two parity- and time-violating terms: the Chern-Simons and the anomalous magnetic terms. Self-dual relativistic vortices are discussed in detail. We also find one-dimensional soliton solutions of the domain wall type. The vortices are correctly described by the domain wall solutions in the large flux limit. copyright 1997 The American Physical Society
Three-dimensional Noncommutative Gravity
Banados, M.; Chandia, O.; Grandi, N.; Schaposnik, F. A.; G. A. Silva
2001-01-01
We formulate noncommutative three-dimensional (3d) gravity by making use of its connection with 3d Chern-Simons theory. In the Euclidean sector, we consider the particular example of topology $T^2 \\times R$ and show that the 3d black hole solves the noncommutative equations. We then consider the black hole on a constant U(1) background and show that the black hole charges (mass and angular momentum) are modified by the presence of this background.
String field theory, non-commutative Chern-Simons theory and Lie algebra cohomology
Motivated by noncommutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We demonstrate the existence of non-trivial classical solutions. We find Wilson loop-like observables in these examples. (author)
Lorentz and PCT Violating Chern-Simons Term in the Derivative Expansion of QED
Chung, J M; Oh, Phillial
1999-01-01
We calculate by the method of dimensional regularization and derivative expansion the one-loop effective action for a Dirac fermion with a Lorentz-violating and PCT-odd kinetic term in the background of a gauge field. We show that this term induces a Chern-Simons modification to Maxwell theory. Some related issues are also discussed.
Probing Wilson loops in N = 4 Chern-Simons-matter theories at weak coupling
Griguolo, Luca; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-02-01
For three-dimensional N = 4 super-Chern-Simons-matter theories associated to necklace quivers U (N0) × U (N1) × ⋯ U (N 2 r - 1), we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced http://arxiv.org/abs/1507
SL(2,C) Chern-Simons Theory, Flat Connections, and Four-dimensional Quantum Geometry
Haggard, Hal M; Kaminski, Wojciech; Riello, Aldo
2015-01-01
The present paper analyze SL(2,$\\mathbb{C}$) Chern-Simons theory on a class of graph complement 3-manifolds, and its relation with classical and quantum geometries on 4-dimensional manifolds. In classical theory, we explain the correspondence between a class of SL(2,$\\mathbb{C}$) flat connections on 3-manifold and the Lorentzian simplicial geometries in 4 dimensions. The class of flat connections on the graph complement 3-manifold is specified by a certain boundary condition. The corresponding simplicial 4-dimensional geometries are made by constant curvature 4-simplices. The quantization of 4d simplicial geometry can be carried out via the quantization of flat connection on 3-manifold in Chern-Simons theory. In quantum SL(2,$\\mathbb{C}$) Chern-Simons theory, a basis of physical wave functions is the class of (holomorphic) 3d block, defined by analytically continued Chern-Simons path integral over Lefschetz thimbles. Here we propose that the (holomorphic) 3d block with the proper boundary condition imposed gi...
Path-integral measure for Chern-Simons theory within the stochastic quantization approach
We discuss how the dependence of the path-integral measure on the metric affects the generating functional for the d=3 Chern-Simons theory. Using the stochastic quantization, we show that the choice of an invariant measure preserves the topological character of the theory. (author). 18 refs
New Chern-Simons densities in both odd and even dimensions
Radu, Eugen; Tchrakian, Tigran
2011-01-01
After reviewing briefly the dimensional reduction of Chern--Pontryagin densities, we define new Chern--Simons densities expressed in terms of Yang-Mills and Higgs fields. These are defined in all dimensions, including in even dimensional spacetimes. They are constructed by subjecting the dimensionally reduced Chern--Pontryagin densites to further descent by two steps.
Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model
Paschoal, Ricardo C.; Helayël-Neto, José A.
2003-01-01
The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effectively described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field non-minimally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1)D Dirac equation is derived.
A first-class approach of higher derivative Maxwell-Chern-Simons-Proca model
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.)
Physical Variables of d=3 Maxwell-Chern-Simons Theory by Symplectic Projector Method
Helayel-Neto, J. A.; Santos, M. A.; Vancea, I. V.
2006-12-01
The Symplectic Projector Method is applied to derive the local physical degrees of freedom and the physical Hamiltonian of the Maxwell-Chern-Simons theory in $d=1+2$. The results agree with the ones obtained in the literature through different approaches.
Physical Variables of $d=3$ Maxwell-Chern-Simons Theory by Symplectic Projector Method
Helayel-Neto, J A; Vancea, I V
2004-01-01
The Symplectic Projector Method is applied to derive the local physical degrees of freedom and the physical Hamiltonian of the Maxwell-Chern-Simons theory in $d=1+2$. The results agree with the ones obtained in the literature through different approaches.
Eigenvalue distributions in matrix models for Chern-Simons-matter theories
The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the planar resolvent in the large 't Hooft coupling limit. Various known exact results on eigenvalue distributions and the expectation value of Wilson loops are reproduced.
Asymptotic completeness and the three-dimensional gauge theory having the Chern-Simon term
The three-dimensional Abelian gauge theory having the Chern-Simon term is studied. When matter current is absent, the gauge field in covariant gauge is explicitly expressed in terms of asymptotic fields. It is shown that the mechanism of mass generation can be understood as a kind of the Higgs mechanism
The Secret Chern-Simons Action for the Hot Gluon Plasma
Efraty, R.; Nair, V. P.
1992-01-01
We show that the generating functional for hard thermal loops with external gluons in QCD is essentially given by the eikonal for a Chern-Simons gauge theory. This action, determined essentially by gauge invariance arguments, also gives an efficient way of obtaining the hard thermal loop contributions without the more involved calculation of Feynman diagrams.
Induced Chern-Simons term in lattice QCD at finite temperature
The general conditions when the Chern-Simons action could arise (in continuum limit) as non universal contribution of fermionic determinant of finite-temperature lattice QCD are formulated. The dependence of this action coefficient on non universal parameters (a chemical potential, vacuum features, etc.) is investigated in detail. Special attention is paid to the role of possible 0>-condensate existence. 42 refs. (author)
Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models
Cantcheff, M B; Minces, Pablo
2003-01-01
By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the noncommutative Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual model.
Energy-momentum conservation laws in higher-dimensional Chern-Simons models
Sardanashvily, G.
2003-01-01
Though a Chern-Simons (2k-1)-form is not gauge-invariant and it depends on a background connection, this form seen as a Lagrangian of gauge theory on a (2k-1)-dimensional manifold leads to the energy-momentum conservation law.
Quaternion based generalization of Chern-Simons theories in arbitrary dimensions
D'Adda, Alessandro; Shimode, Naoki; Tsukioka, Takuya
2016-01-01
A generalization of Chern-Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree. The quaternion algebra structure of this formulation is shown to be equivalent to a three Z(2)-gradings structure, thus clarifying the quaternion role in a previous formulation.
Canonical quantization of the WZW model with defects and Chern-Simons theory
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...
Non-Abelian T-duality, G 2-structure rotation and holographic duals of = 1 Chern-Simons theories
Macpherson, Niall T.
2013-11-01
A new dynamic SU(3)-structure solution in type-IIA is found by T-dualising a deformation of the Maldacena-Nastase solution along an SU(2) isometry. It is argued that this is dual to a quiver gauge theory with multiple Chern-Simons levels. A clear way of defining Chern-Simons levels in terms of Page charges is presented, which is also used to define a Chern-Simons term for the G 2-structure analogue of Klebanov-Strassler, providing evidence of a cascade in both the ranks and levels of the dual quiver.
Electron-electron attractive interaction in Maxwell-Chern-Simons QED{sub 3} at zero temperature
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)
F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
Morita, Takeshi
2011-01-01
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partition functions computed via localization. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
Yokoyama, Shuichi
2016-01-01
We present exact large N calculus of four point function in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine two body scattering amplitudes in these theories combined with 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, usual crossing relation and admits 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 Chern-Simons theory with free fermions.
Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models
DeBellis, Joshua
2013-01-01
We study the BPS spectrum and vacuum moduli spaces in dimensional reductions of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our main example is a matrix model version of the ABJM theory which we relate explicitly to certain reduced 3-algebra models. We find the explicit maps from Chern-Simons quiver matrix models to dual IKKT matrix models. We address the problem of topologically twisting the ABJM matrix model, and along the way construct a new twist of the IKKT model. We construct a cohomological matrix model whose partition function localizes onto a moduli space specified by 3-algebra relations which live in the double of the conifold quiver. It computes an equivariant index enumerating framed BPS states with specified R-charges which can be expressed as a combinatorial sum over certain filtered pyramid partitions.
Physical states of Bianchi type IX quantum cosmologies described by the Chern-Simons functional
Graham, R; Graham, Robert; Paternoga, Robert
1996-01-01
A class of exact solutions of the Wheeler-DeWitt equation for diagonal Bianchi type IX cosmologies with cosmological constant is derived in the metric representation. This class consists of all the ``topological solutions'' which are associated with the Bianchi type IX reduction of the Chern-Simons functional in Ashtekar variables. The different solutions within the class arise from the topologically inequivalent choices of the integration contours in the transformation from the Ashtekarrepresentation to the metric representation. We show how the saddle-points of the reduced Chern-Simons functional generate a complete basis of such integration contours and the associated solutions. Among the solutions we identify two, which, semi-classically, satisfy the boundary conditions proposed by Vilenkin and by Hartle and Hawking, respectively. In the limit of vanishing cosmological constant our solutions reduce to a class found earlier in special fermion sectors ofsupersymmetric Bianchi type IX models.
Dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model
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, νμ. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of νμ . 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)
Chern-Simons dilaton black holes in 2+1 dimensions
Moussa, Karim Ait; Guennoune, Hakim
2015-01-01
We construct rotating magnetic solutions to the three-dimensional Einstein-Maxwell-Chern-Simons-dilaton theory with a Liouville potential. These include a class of black hole solutions which generalize the warped AdS black holes. The regular black holes belong to two disjoint sectors. The first sector includes black holes which have a positive mass and are co-rotating, while the black holes of the second sector have a negative mass and are counter-rotating. We also show that a particular, non-black hole, subfamily of our three-dimensional solutions may be uplifted to new regular non-asymptotically flat solutions of five-dimensional Einstein-Maxwell-Chern-Simons theory.
Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories
Mikhaylov, Victor
2015-01-01
We consider topological field theories that compute the Reidemeister-Milnor-Turaev torsion in three dimensions. These are the psl(1|1) and the U(1|1) Chern-Simons theories, coupled to a background complex flat gauge field. We use the 3d mirror symmetry to derive the Meng-Taubes theorem, which relates the torsion and the Seiberg-Witten invariants, for a three-manifold with arbitrary first Betti number. We also present the Hamiltonian quantization of our theories, find the modular transformations of states, and various properties of loop operators. Our results for the U(1|1) theory are in general consistent with the results, found for the GL(1|1) WZW model. We also make some comments on more general supergroup Chern-Simons theories.
Notes on Planar Resolvents of Chern-Simons-matter Matrix Models
Suyama, Takao
2016-01-01
We revisit planar resolvents of matrix models corresponding to ${\\cal N}\\ge3$ Chern-Simons-matter theories with the gauge groups of the form ${\\rm U}(N_1)\\times{\\rm U}(N_2)$ coupled to any number of bi-fundamental hypermultiplets. We find that the derivative of a suitably defined planar resolvent can be written explicitly. From this resolvent, we derive the explicit formula for (a linear combination of) the vevs of BPS Wilson loops.
Chern-Simons Theory with Complex Gauge Group on Seifert Fibred 3-Manifolds
Blau, Matthias
2016-01-01
We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use the method of Abelianisation. In certain cases the path integral can be seen to factorize neatly into holomorphic and anti-holomorphic parts. We obtain closed formulae of this factorization for the expectation values of torus knots.
BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
Fujita, Mitsutoshi
2009-01-01
We consider the small deformation of the pointlike Wilson loop in the 3-dimensional N=6 superconformal Chern-Simons theory. By Taylor expansion of the pointlike Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.
Monopole operators in N=4 Chern-Simons theories and wrapped M2-branes
Imamura, Yosuke
2009-01-01
Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of untwisted and twisted hypermultiplets, respectively. For monopole operators corresponding to the roots, we propose a correspondence between the monopole operators and states of a wrapped M2-brane in the dual geometry.
Extensions of the Duflo map and Chern-Simons expectation values
Sahlmann, Hanno
2015-01-01
The Duflo map is a valuable tool for operator ordering in contexts in which Kirillov-Kostant brackets and their quantizations play a role. A priori, the Duflo map is only defined on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. Here we discuss extensions to the whole symmetric algebra, as well as their application to the calculation of Chern-Simons theory expectation values.
N=2-Maxwell-Chern-Simons model with anomalous magnetic moment coupling via dimensional reduction
An N=1-supersymmetric version of the Cremmer-Scherk-Kalb-Ramond model with non-minimal coupling to matter is built up both in terms of superfields and in a component field formalism. By adopting a dimensional reduction procedure, the N=2-D=3 counterpart of the model comes out, with two main features: a genuine (diagonal) Chern-Simons term and an anomalous magnetic moment coupling between matter and the gauge potential. (author)
Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model
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)
Split Chern-Simons theory in the BV-BFV formalism
Cattaneo, Alberto; Wernli, Konstantin
2015-01-01
The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to perform perturbative quantisation of Lagrangian field theories on manifolds with boundary, and present a special case of Chern-Simons theory as a new example.
Chern-Simons Couplings for Dielectric F-Strings in Matrix String Theory
Brecher, Dominic; Janssen, Bert; Lozano, Yolanda
2002-01-01
We compute the non-abelian couplings in the Chern-Simons action for a set of coinciding fundamental strings in both the type IIA and type IIB Matrix string theories. Starting from Matrix theory in a weakly curved background, we construct the linear couplings of closed string fields to type IIA Matrix strings. Further dualities give a type IIB Matrix string theory and a type IIA theory of Matrix strings with winding.
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.
Brihaye, Yves; Radu, Eugen; Tchrakian, D H
2011-02-18
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. PMID:21405506
Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
Polychronakos, Alexios P.
2001-01-01
We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the quantization of the inverse filling fraction and of the quasiparticle number, are reproduced by the quantum mechanics of the matrix model. We also point out that this system is holographically described in terms of the one-dimensional Sutherland integrable...
Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
Ghasemkhani, M.; Bufalo, R.
2015-01-01
In this paper, we study the three-dimensional noncommutative Maxwell-Chern-Simons theory. In the present analysis, a complete account for the gauge field two-point function renormalizability is presented and physical significant quantities are carefully established. The respective form factor expressions from the gauge field self-energy are computed at one-loop order. More importantly, an analysis of the gauge field dispersion relation, in search of possible noncommutative anomalies and infra...
Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
Ghasemkhani, M
2015-01-01
In this paper we study the three-dimensional noncommutative Maxwell-Chern-Simons theory. In the present analysis, a complete account for the gauge field two-point function renormalizability is presented and physical significant quantities are carefully established. We compute the respective form factor expressions from the gauge field self-energy at one-loop order. Moreover, a detailed discussion on the gauge field dispersion relation is presented for three particular cases, with particular interest in the highly noncommutative limit.
Some quantum aspects of complex vector fields with Chern-Simons term
Del Cima, O M
1993-01-01
Complex vector fields with Maxwell, Chern-Simons and Proca terms are minimally coupled to an Abelian gauge field. The consistency of the spectrum is analysed and 1-loop quantum corrections to the self-energy are explicitly computed and discussed. The incorporation of 2-loop contributions and the behaviour of tree-level scattering amplitudes in the limit of high center-of-mass energies are also commented.
Perturbative expansion of Chern-Simons theory with non-compact gauge group
Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)
Symmetry algebras in Chern-Simons theories with boundary: canonical approach
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
Chern-Simons Path Integrals in S2 × S1
Adrian P. C. Lim
2015-08-01
Full Text Available Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \\(S_{CS}^\\kappa\\, \\(\\kappa\\ is some parameter. Instead of making sense of the path integral over the space of \\(\\mathfrak{g}\\-valued smooth 1-forms on \\(S^2 \\times S^1\\, we use the Segal Bargmann transform to define the path integral over \\(B_i\\, the space of \\(\\mathfrak{g}\\-valued holomorphic functions over \\(\\mathbb{C}^2 \\times \\mathbb{C}^{i-1}\\. This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \\(C(B_1^{\\times^4} \\times B_2^{\\times^2}, \\mathbb{C}\\ and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \\(\\mathbb{R}^3\\. We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \\(\\kappa\\. The second half of the article concentrates on taking \\(\\kappa\\ goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \\(SU(N\\ and \\(SO(N\\. In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \\(SU(N\\ and a Conway type skein relation in the case of \\(SO(N\\. By imposing quantization condition on the charge of the link \\(L\\, we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of
Phase transition in D=3 Yang-Mills Chern-Simons gauge theory
SU(N) Yang-Mills theory in three dimensions, with a Chern-Simons term of level k (an integer) added, has two-dimensionful coupling constants g2k and g2N; its possible phases depend on the size of k relative to N. For k>N, this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has shown; it can be treated semiclassically. For k=0, the theory is badly infrared singular in perturbation theory, a nonperturbative mass and subsequent quantum solitons are generated, and Wilson loops show an area law. We argue that there is a phase transition between these two behaviors at a critical value of k, called kc, with kc/N≅2±0.7. Three lines of evidence are given. First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if k≤29N/12. The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the k=0 case. Second, we study in a rough approximation the free energy and show that for k≤kc there is a nontrivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass M, while both the condensate and M vanish for k≥kc. Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass m and a (gauge-invariant) dynamical mass M. We show that if M approx-gt 0.5m, there are finite-action quantum sphalerons, while none survive in the classical limit M=0, as shown earlier by D'Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as M→0. copyright 1996 The American Physical Society
Jackiw-Pi's model of the self-gravitating gas of nonrelativistic bosons coupled to the Chern-Simons gauge field is known to exhibit asymptotically vanishing, lump-like soliton solutions. We show that in order to extend this model to include the case of repulsive gases where the matter field approaches nonzero values at infinities, one has to add, for instance, the background electric charge. Reformulating the model arising in this way as a constrained Hamiltonian system allows to find the self-duality limit in the pure Chern-Simons and in the mixed Chern-Simons-Maxwell cases. We prove that the linear momentum of the topologically nontrivial configuration can only be defined as a translationally noninvariant quantity and the algebra is spontaneously broken {Px, Py}=2πρ0n. 22 refs., 2 figs
BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
Fujita, Mitsutoshi
2009-01-01
We consider the small deformation of the point-like Wilson loop in the 3-dimensional $\\mathcal{N}=6$ superconformal Chern-Simons theory. By Taylor expansion of the point-like Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.
On the role of the Chern-Simons action for the description of the QHE
The role of the Chern-Simons action in the description of the quantum Hall effects is stressed. The 2D-electromagnetic picture of Widom and Srivastava is shown to be valid in a superlattice of 2D-electron gases. A Meissner-like effect appears in such systems. In them, the difference between the external and the integer filling factor fields is exponentially screened by the surface (edge) currents. Also, effective Maxwell equations for one sheet or a superlattice are obtained. (author). 21 refs
Gauge invariant variables and the Yang-Mills-Chern-Simons theory
A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level k Chern-Simons term is carried out using a gauge invariant matrix parametrization of the potentials. The gauge boson states are constructed and the contribution of the dynamical mass gap to the gauge boson mass is obtained. Long distance properties of vacuum expectation values are related to a Euclidean two-dimensional YM theory coupled to k flavors of Dirac fermions in the fundamental representation. We also discuss the expectation value of the Wilson loop operator and give a comparison with previous results
Effect of VSR invariant Chern-Simons Lagrangian on photon polarization
We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term
An alternative S-matrix for N = 6 Chern-Simons theory?
We have recently proposed an S-matrix for the planar limit of the N = 6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena which leads to the all-loop Bethe ansatz equations conjectured by Gromov and Vieira. An unusual feature of this proposal is that the scattering of A and B particles is reflectionless. We consider here an alternative S-matrix, for which A-B scattering is not reflectionless. We argue that this S-matrix does not lead to the Bethe ansatz equations which are consistent with perturbative computations.