Chern-Simons Mass Research Articles

On the photon mass generation in Rarita–Schwinger QED

This work examines the dynamical mass generation for the photon in Rarita–Schwinger QED. We focus our attention on the cases of ω=2,3 dimensional spacetime. In these frameworks, it is well known that in the usual QED, the photon field (dynamically) acquires a gauge invariant mass (the Schwinger and Chern–Simons mass, respectively). We wish to scrutinize this phenomenon in terms of the Rarita–Schwinger fields. The presence of higher-derivative terms is shown as the leading contributions to the 1PI function ⟨AA⟩ at one-loop order. We study the pole structure of the photon’s complete propagator to unveil the main effects of the Rarita–Schwinger fields on the photon’s mass. In addition, we present some remarks about the renormalizability of this model (in different dimensions) due to the presence of higher-derivative corrections at one-loop.

How planar superconductors cure their infrared divergences

Planar superconductors, emerging in thin films with thickness comparable to the superconducting coherence length, differ crucially from their bulk counterparts. Coulomb interactions between charges are logarithmic up to distances comparable to typical sample sizes and the Anderson-Higgs mechanism is ineffective to screen the infrared divergences of the resulting (2+1)-dimensional QED because the Pearl length screening the vortex interactions is also typically larger than the sample size. As a result, the system decomposes into superconducting droplets with the typical size of order of superconducting coherence length. We show that two possible phases of the film match the two known mechanisms for curing the (2+1)-dimensional QED infrared divergences, either by generating a mixed topological Chern-Simons mass or by magnetic monopole instantons. The former mechanism works in superconductors, the latter one governs mirror-dual superinsulators. Planar superconductors are thus described by a topological Chern-Simons gauge (TCSG) theory that replaces the Ginzburg-Landau model in two dimensions. In the TCSG model, the Higgs field is absent. Accordingly, in planar superconductors Abrikosov vortices do not form, and only Josephson vortices without normal core do exist.

Implications of the topological Chern-Simons mass in the gap equation

In this paper, we solve the gap equation of the Yang-Mills-Gribov-Zwanziger-Chern-Simon theory by considering the first order in the Chern-Simon topological mass term, $M$. As a result, we find three possible solutions to the gap equation, i.e. three different Gribov parameters. In addition, we analyze the regime of the theory for each of these Gribov parameters and we obtain a different result from the literature.

On the ultraviolet finiteness of parity-preserving [formula omitted] massive QED[formula omitted

The parity-preserving UA(1)×Ua(1) massive QED3 is ultraviolet finiteness – exhibits vanishing β-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern–Simons mass parameter, and all the anomalous dimensions of the fields – as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi–Rouet–Stora (BRS) algebraic renormalization method in the framework of Bogoliubov–Parasiuk–Hepp–Zimmermann (BPHZ) subtraction scheme.

The BTZ black hole violates strong cosmic censorship

We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker \\rough" version of the conjecture is respected. We calculate the renormalized energymomentum tensor of a scalar field in the Hartle-Hawking state in the BTZ geometry. We show that the result is finite at the inner horizon of a near-extremal black hole. Hence the backreaction of vacuum polarization does not enforce strong cosmic censorship.

Dynamical signatures of black holes in massive Chern-Simons gravity: Quasibound modes and time evolution

Dynamical Chern-Simons (dCS) gravity is a promising extension of general relativity (GR), arising naturally from the low-energy limit of some string motivated theories. Even though dCS possesses an additional scalar degree of freedom, interestingly, the Schwarzschild black hole is an exact solution of it. Concerning dynamical phenomena, however, gravitational and scalar perturbations couple with each other, generating possible scenarios to understand the differences between dCS and GR. We study dynamical signatures of dCS considering that the scalar field potential has a mass term. We analyze the influence of the theory's parameter into the quasibound states and in the time evolution of purely gravitational initial profiles. We find that the coupling can make the dipolar modes \textit{less stable} and that at late times initial gravitational perturbations become contaminated with the scalar sector, presenting an oscillation that depends on the quasibound state frequencies. These results may be interesting in the light of superradiant instabilities in rotating systems and to find signatures of alternative theories in gravitational wave detections.

Medium generated gap in gravity and a 3D gauge theory

It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in $d = D+1$ spacetime dimensions, and for a solid in $D = 2$ spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of $D = 2$ spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory and motivated by this we recast the massive theory of gravity in AdS$_3$ as a massive Chern-Simons gauge theory with an unusual mass term. We find that in the flat space limit the Chern-Simons theory has a novel gauge invariance that mixes the kinetic and mass terms, and enables the massive theory with a non-compact internal group to be free of ghosts and tachyons.

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

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

Yang-Mills as Massive Chern-Simons Theory: A Third Way to Three-Dimensional Gauge Theories

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with an inverse mass parameter, in addition to a possible topological mass term. The novelty is that the modified YM equation is not the Euler-Lagrange equation of any gauge-invariant local action for the YM gauge potential alone. Instead, consistency is achieved in the "third way" exploited by 3D minimal massive gravity. We relate our results to the "novel Higgs mechanism" for Chern-Simons gauge theories.

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

Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada, Phys. Rev. Lett. 109, 231101 (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity. We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter $m_{CS}$. Therefore, the international space station site as well as a ground-based experiment is also discussed.

Thermal screening at finite chemical potential on a topological surface and its interplay with proximity-induced ferromagnetism

Motivated by recent experiments on EuS/Bi$_2$Se$_3$ heterostructures, we study the temperature dependent screening effects on the surface of a three-dimensional topological insulator proximate to a ferromagnetically ordered system. In general, we find that besides the chemical potential and temperature, the screening energy scale also depends on the proximity-induced electronic gap in an essential way. In particular, at zero temperature the screening energy vanishes if the chemical potential is smaller than the proximity-induced electronic gap. We show that at finite temperature, $T$, and/or chemical potential, $\mu$, the Chern-Simons (topological) mass, which is generated by quantum fluctuations arising from the proximity-effect, can be calculated analytically in the insulating regime. In this case the topological mass yields the Hall conductivity associated to edge states. We show that when the chemical potential is inside the gap the topological mass remains nearly quantized at finite temperature.

Vacuum instability in Chern-Simons gravity

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.

MONOPOLE-INSTANTON SOLUTIONS FOR THE MASSIVE SU(2) YANG–MILLS–HIGGS THEORY

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.

Repulsive Maxwell–Chern–Simons Casimir effect

Abstract In the present Letter we discuss the role of different boundary conditions on the Casimir effect between parallel lines in a planar ( 2 + 1 ) system, specifically in the context of a Maxwell theory with a Chern–Simons mass term. We consider parallel lines of a different nature, namely a perfectly conducting line and an infinitely permeable one. We also discuss the case of two infinitely permeable lines. We compare our results with those found in the literature for the case of two perfectly conducting lines.

Yang–Mills–Chern–Simons supergravity

N = (1, 0) supergravity in six dimensions admits AdS3 × S3 as a vacuum solution. We extend our recent results presented in Lü et al (2002 Preprint hep-th/0212323), by obtaining the complete N = 4 Yang–Mills–Chern–Simons supergravity in D = 3, up to quartic fermion terms, by S3 group manifold reduction of the six-dimensional theory. The SU(2) gauge fields have Yang–Mills kinetic terms as well as topological Chern–Simons mass terms. There is in addition a triplet of matter vectors. After diagonalization, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3, R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can be obtained by a consistent reduction of string theory or M-theory and that admits AdS3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N = (1, 0) supergravity in D = 6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited.

Gauge theories of Yang–Mills vector fields coupled to antisymmetric tensor fields

A non-Abelian class of massless/massive nonlinear gauge theories of Yang–Mills vector potentials coupled to Freedman–Townsend antisymmetric tensor potentials is constructed in four space–time dimensions. These theories involve an extended Freedman–Townsend-type coupling between the vector and tensor fields, and a Chern–Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang–Mills theory and Freedman–Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern–Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here.

Non-Abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with a Chern-Simons term

An exact time-dependent solution of field equations for the 3-d gauge field model with a Chern-Simons (CS) topological mass is found. Limiting cases of constant solution and solution with vanishing topological mass are considered. After Lorentz boost, the found solution describes a massive nonlinear non-abelian plane wave. For the more complicate case of gauge fields with CS mass interacting with a Higgs field, the stochastic character of motion is demonstrated.

Two-loop corrections to the topological mass term in thermal QED 3

We study the radiative corrections to the Chern–Simons mass term at two loops in (2+1)-dimensional quantum electrodynamics at finite temperature. We show that, in contrast to the behavior at zero temperature, thermal effects lead to a non-vanishing contribution at this order. Using this result, as well as the large gauge Ward identity for the leading parity violating terms in the static limit, we determine the leading order parity violating effective action in this limit at two loops, which generalizes the one-loop effective action proposed earlier.

Supersymmetric anyon model coupled to the electromagnetic field

We construct a supersymmetric gauge model describing the electromagnetic interaction of anyons. This is done by means of the supersymmetric generalization of theU(1) ×U(1) gauge theory. The model contains the statisticalU(1) gauge field endowed with a Chern-Simons mass term and the electromagnetic field, both with the corresponding superpartners, coupled to matter fields. This constrained system is analyzed from the Hamiltonian point of view and the canonical quantization is found. The path-integral method is used to develop the perturbative formalism. We define suitable propagators and vertices and give the diagrammatics and the Feynman rules.

Phase transition in D=3 Yang-Mills Chern-Simons gauge theory.

$\mathrm{SU}(N)$ Yang-Mills theory in three dimensions, with a Chern-Simons term of level $k$ (an integer) added, has two-dimensionful coupling constants ${g}^{2}k$ and ${g}^{2}N$; its possible phases depend on the size of $k$ relative to $N$. For $k\ensuremath{\gg}N$, 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 ${k}_{c}$, with $\frac{{k}_{c}}{N}\ensuremath{\approx}2\ifmmode\pm\else\textpm\fi{}0.7$. Three lines of evidence are given. First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if $k<~\frac{29N}{12}$. 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 $k<~{k}_{c}$ 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 $k>~{k}_{c}$. 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 $M\ensuremath{\gtrsim}0.5m$, 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 $M\ensuremath{\rightarrow}0$.