Topological Chern-Simons Term Research Articles

Deconfined Criticality and Bosonization Duality in Easy-Plane Chern-Simons Two-Dimensional Antiferromagnets

Two-dimensional quantum systems with competing orders can feature a deconfined quantum critical point, yielding a continuous phase transition that is incompatible with the Landau-Ginzburg-Wilson scenario, predicting instead a first-order phase transition. This is caused by the LGW order parameter breaking up into new elementary excitations at the critical point. Canonical candidates for deconfined quantum criticality are quantum antiferromagnets with competing magnetic orders, captured by the easy-plane CP^{1} model. A delicate issue however is that numerics indicates the easy-plane CP^{1} antiferromagnet to exhibit a first-order transition. Here we show that an additional topological Chern-Simons term in the action changes this picture completely in several ways. We find that the topological easy-plane antiferromagnet undergoes a second-order transition with quantized critical exponents. Further, a particle-vortex duality naturally maps the partition function of the Chern-Simons easy-plane antiferromagnet into one of massless Dirac fermions.

Holographic Projection of Electromagnetic Maxwell Theory

The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Kaç-Moody algebra formed by a subset of the bulk fields is obtained with central charge proportional to the inverse of the Maxwell coupling constant, and the degrees of freedom of the boundary theory are identified as two vector fields, also suggesting that the 3D theory should be a gauge theory. Finally the holographic contact between bulk and boundary theory is reached in two inequivalent ways, both leading to a unique 3D action describing a new gauge theory of two coupled vector fields with a topological Chern-Simons term with massive coefficient. In order to check that the 3D projection of 4D Maxwell theory is well defined, we computed the energy-momentum tensor and the propagators. The role of discrete symmetries is briefly discussed.

Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions

The electromagnetic response of topological insulators and superconductors is governed by a modified set of Maxwell equations that derive from a topological Chern-Simons (CS) term in the effective Lagrangian with coupling constant $\kappa$. Here we consider a topological superconductor or, equivalently, an Abelian Higgs model in $2+1$ dimensions with a global $O(2N)$ symmetry in the presence of a CS term, but without a Maxwell term. At large $\kappa$, the gauge field decouples from the complex scalar field, leading to a quantum critical behavior in the $O(2N)$ universality class. When the Higgs field is massive, the universality class is still governed by the $O(2N)$ fixed point. However, we show that the massless theory belongs to a completely different universality class, exhibiting an exotic critical behavior beyond the Landau-Ginzburg-Wilson paradigm. For finite $\kappa$ above a certain critical value $\kappa_c$, a quantum critical behavior with continuously varying critical exponents arises. However, as a function $\kappa$ a transition takes place for $|\kappa| < \kappa_c$ where conformality is lost. Strongly modified scaling relations ensue. For instance, in the case where $\kappa^2>\kappa_c^2$, leading to the existence of a conformal fixed point, critical exponents are a function of $\kappa$.

Planar phenomena in CPT -even chiral QED with Lorentz violation

Quantum gravity models as string theory, loop quantum gravity, and noncommutative field theories allow for the violation of Lorentz symmetry in the Planck scale. In order to examine the implications of such violation in planar models, we present here a $CPT$-even effective model, in the Standard Model extension framework, for Maxwell-Chern-Simons quantum electrodynamics $({\mathrm{QED}}_{3})$, with a Lorentz violation tensor parameter coupled to the photon field. The magnetoelectric effect induced by the space-time anisotropy in the model is discussed. We then derive the exact classical photon propagator. The electrostatic interaction is investigated and the long-range classical potential, corrected to second order in the Lorentz-violating tensor parameter, is obtained as well as its radiative correction in the isotropic violation scenario, derived at one-loop approximation from the vacuum polarization tensor. Also, the contribution of the space-time anisotropy to the magnetic moment of the fermion trough the vertex diagram is evaluated on shell and in the forward scattering approximation, in the absence of the topological Chern-Simons term.

Unimodular gravity theory with external sources in a Lorentz-symmetry breaking scenario

This paper is dedicated to the study of interactions between stationary field sources for the linearized unimodular gravity or WTDIFF theory in a model which exhibits Lorentz symmetry breaking due to the presence of the linearized topological Chern-Simons term in $3 + 1$ dimensions, where the Lorentz symmetry breaking is caused by a single background vector $v^{\mu}$. Since the background vector is very tiny, we treat it perturbatively up to second order and we focus on physical phenomena which have no counterpart in standard WTDIFF theory. We consider effects related to field sources describing point-like particles and cosmic strings. We show that in a Lorentz violating scenario the interaction between external sources lead to numerically different results for linerarized Eintein-Hilbert (LEH) and WTDIFF theories, however both results are qualitatively similar and can be equalized after a rescaling of the Lorentz breaking source term which makes an experimental distinction impossible at leading order in pertubation theory as far as point particles and cosmic strings are concerned.

Semimetal-insulator transition on the surface of a topological insulator with in-plane magnetization

A thin film of ferromagnetically ordered material proximate to the surface of a three-dimensional topological insulator explicitly breaks the time-reversal symmetry of the surface states. For an out-of-plane ferromagnetic order parameter on the surface, the parity is also broken since the Dirac fermions become massive. This leads, in turn, to the generation of a topological Chern-Simons term by quantum fluctuations. On the other hand, for an in-plane magnetization the surface states remain gapless for the noninteracting Dirac fermions. In this work we study the possibility of spontaneous breaking of parity due to a dynamical gap generation on the surface in the presence of a local, Hubbard-like interaction of strength $g$ between the Dirac fermions. A gap and a Chern-Simons term are generated for $g$ larger than some critical value ${g}_{c}$, provided the number of Dirac fermions $N$ is odd. For an even number of Dirac fermions the masses are generated in pairs having opposite signs, and no Chern-Simons term is generated. We discuss our results in the context of recent experiments in EuS/Bi${}_{2}$Se${}_{3}$ heterostructures.

HIGH SPIN TOPOLOGICALLY MASSIVE GRAVITY

We study the high spin fields coupled to topologically massive gravity in AdS3, paying special attention to the nature of the theory at the critical point. We propose an action incorporating the high spin AdS3 gravity and the topological Chern-Simons term for high spin fields. We discuss the fluctuation spectrum around the AdS3 vacuum and find that besides the usual massless modes there are local massive modes.

Chern-Simons gravity with(curvature)2and(torsion)2terms and a basis of degree-of-freedom projection operators

We investigate the effects of (Curvature)$^{2}$- and (Torsion)$^{2}$- terms in the Einstein-Hilbert-Chern-Simons Lagrangian. The purposes are two-fold: (i) to show the efficacy of an orthogonal basis of degree-of-freedom projection operators recently proposed and to ascertain its adequacy for obtaining propagators of general parity-breaking gravity models in three dimensions; (ii) to analyze the role of the topological Chern-Simons term for the unitarity and the particle spectrum of the model squared-curvature terms in connection with dynamical torsion. Our conclusion is that the Chern-Simons term does not influence the unitarity conditions imposed on the parameters of the Lagrangian, but significantly modifies the particle spectrum.

Dynamical breaking of gauge symmetry in supersymmetric quantum electrodynamics in three-dimensional spacetime

The dynamical breaking of gauge symmetry in the supersymmetric quantum electrodynamics in three-dimensional spacetime is studied at two-loop approximation. At this level, the effective superpotential is evaluated in a supersymmetric phase. At one-loop order, we observe a generation of the Chern-Simons term due to a parity violating term present in the classical action. At two-loop order, the scalar background superfield acquires a nonvanishing vacuum expectation value, generating a mass term A{sup {alpha}}A{sub {alpha}} through the Coleman-Weinberg mechanism. It is observed that the mass of gauge superfield is predominantly an effect of the topological Chern-Simons term.

Boson-boson effective nonrelativistic potential for higher-derivative electromagnetic theories inDdimensions

The problem of computing the effective nonrelativistic potential $U_{D}$ for the interaction of charged scalar bosons within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that $U_3$ cannot bind a pair of identical charged scalar bosons; nevertheless, numerical calculations indicate that boson-boson bound states do exist in the framework of three-dimensional higher-derivative electromagnetism augmented by a topological Chern-Simons term.

Can one cure the nonunitarity of three-dimensional quadratic gravity using a topological Chern-Simons term?

Abstract Quadratic gravity in (2+1)D is nonunitarity at the tree level. When a topological Chern-Simons term is added to this theory, the harmless massive scalar mode of the former 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. Therefore, unlike what it is claimed in the literature, quadratic Chern-Simons gravity in (2+1)D is nonunitary at the tree level.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

It is astonishing that a locally trivial and globally nontrivial Einstein-type gravitational theory can be built only by lowering the dimension of our space-time—which is supposed to be four dimensional—by one unit. In fact, threedimensional general relativity is dynamically trivial: outside sources, spacetime is flat—all effects of the localized sources are on the global geometry, which is fixed by the singularities of the worldlines of the particles @1#. The quantum mechanical analogue of this triviality emerges when the HilbertEinstein action related to this theory is quantized. It is easy to establish that the theory does not possess any propagating degrees of freedom. In other words, there are no gravitons. The preceding considerations lead us to raise the following important question: Is it possible to build a nontrivial generally covariant three-dimensional gravity theory having propagating degrees of freedom? The answer is affirmative. Actually, this can be done at least in two different ways: ~i! Adding a topological nontrivial term to general relativity in ~211!D @2#. Ordinary Einstein gravity which is trivial acquires now a propagating, massive, spin-2 mode. This theory is ghost-free and causal, although of the thirdderivative order. ~ii! Including the four-derivatives terms *R 2 Agd 3 x and

On anomalies in orbifold theories

We study the issue of gauge invariance in five-dimensional theories compactified on an orbifold S1/(Z2×Z′2) in the presence of an external U(1) gauge field. From the four-dimensional point of view the theory contains a tower of Kaluza–Klein Dirac fermions with chiral couplings and it looks anomalous at the quantum level. We show that this “anomaly” is cancelled by a topological Chern–Simons term which is generated in the effective action when the gauge theory is regularized introducing a Pauli–Villars fermion with an odd mass term. In the presence of a classical background gauge field, the fermionic current acquires a vacuum expectation value, thus generating the suitable Chern–Simons term and a gauge invariant theory.

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.

Chern-Simons as a geometrical setup for three-dimensional gauge theories

Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field

A simple remark on three dimensional gauge theories

Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is provided.

Finite Temperature Chern-Simons Coefficient

We compute the exact finite temperature effective action in a 0+1-dimensional field theory containing a topological Chern-Simons term, which has many features in common with 2+1-dimensional Chern-Simons theories. This exact result explains the origin and meaning of puzzling temperature dependent coefficients found in various naive perturbative computations in the higher dimensional models.

Spinning charged BTZ black holes and self-dual particle-like solutions

We generate from the static charged BTZ black hole a family of spinning charged solutions to the Einstein-Maxwell equations in 2+1 dimensions. These solutions go over, in a suitable limit, to self-dual spinning charged solutions, which are horizonless and regular, with logarithmically divergent mass and spin. To cure this divergence, we add a topological Chern-Simons term to the gauge field action. The resulting self-dual solution is horizonless, regular, and asymptotic to the extreme BTZ black hole.

Geometric quantization of topological gauge theories

We study the symplectic quantization of Abelian gauge theories in $2+1$ space-time dimensions with the introduction of a topological Chern-Simons term.

Induced Topological Terms, Hidden Local Symmetry, and Anyon Superconductivity

We show how the topological Chern-Simons term in three dimensions and the θ-term, [Formula: see text] in four dimensions can be dynamically generated due to quantum fluctuations in Nambu-Jona-Lasinio models. These results give a vivid demonstration of hidden local symmetry at work. The fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity. Possible phenomenological implications of this approach in particle physics are also discussed.