Chern-Simons Coupling Research Articles

The 4d superconformal index near roots of unity and 3d Chern-Simons theory

We consider the S3×S1 superconformal index ℐ(τ) of 4d mathcal{N} = 1 gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential τ coupled to a combination of angular momenta on S3 and the U(1) R-charge. We develop the all-order asymptotic expansion of the index as q = e2πiτ approaches a root of unity, i.e. as overset{sim }{tau } ≡ mτ+n → 0, with m, n relatively prime integers. The asymptotic expansion of log ℐ(τ) has terms of the form overset{sim }{tau } k, k = −2, −1, 0, 1. We determine the coefficients of the k = −2, −1, 1 terms from the gauge theory data, and provide evidence that the k = 0 term is determined by the Chern-Simons partition function on S3/ℤm. We explain these findings from the point of view of the 3d theory obtained by reducing the 4d gauge theory on the S1. The supersymmetric functional integral of the 3d theory takes the form of a matrix integral over the dynamical 3d fields, with an effective action given by supersymmetrized Chern-Simons couplings of background and dynamical gauge fields. The singular terms in the overset{sim }{tau } → 0 expansion (dictating the growth of the 4d index) are governed by the background Chern-Simons couplings. The constant term has a background piece as well as a piece given by the localized functional integral over the dynamical 3d gauge multiplet. The linear term arises from the supersymmetric Casimir energy factor needed to go between the functional integral and the Hamiltonian index.

Magnetoelectric boundary simulated by a Chern\u2013Simons-like model

In this work we study some physical phenomena that emerge in the vicinity of a magnetoelectric boundary. For simplicity, we restrict to the case of a planar boundary described by a coupling between the gauge field with a planar external Chern–Simons-like potential. The results are obtained exactly. We compute the correction undergone by the photon propagator due to the presence of the Chern–Simons coupling and we investigate the interaction between a stationary point-like charge and the magnetoelectric boundary. In the limit of a perfect mirror, where the coupling constant between the field and the potential diverges, we recover the image method. For a non perfect mirror, we show that we have an attenuated image charge and, in addition, an image magnetic monopole whose field strength does not exhibit the presence of the undesirable and artificial divergences introduced by Dirac strings. We also study the interaction between the plate and a quantum particle with spin. In this case we have a kind of charge-magnetic dipole interaction due to the magnetoelectric properties of the plate.

Analytic study of dark photon and gravitational wave production from axion

Axion-like fields heavier than about 10−27 eV are expected to oscillate in the radiation dominated epoch when the Hubble parameter drops below their mass. Considering the Chern-Simons coupling with a dark gauge boson, large amount of dark photons are produced during a short time interval through tachyonic resonance instability. The produced dark photons then source gravitational tensor modes leading to chiral gravitational waves. Through this process, one can indirectly probe a large parameter space of coupled axion-dark photon models. In this work we first find an analytic expression for the number density of the dark photons produced during the tachyonic resonance regime. Second, by using the saddle point approximation we find an analytic expression for the gravitational wave spectrum in terms of the mass, coupling and misalignment angle. Our analytic results can be used for the observational analysis of these types of scenarios.

Bootstrapping BPS spectra of 5d/6d field theories

We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup hat{mathrm{mathbb{C}}} 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d mathcal{N} = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

Particle dynamics and geometric optics in Chern–Simons black holes

In this paper we study the effects of the coupling constant of the Chern–Simons modified gravity on some physical properties of black holes. The Hawking mass is one of the proposed definitions of quasilocal mass. We find that, for slowly rotating Chern–Simons black holes, the Hawking mass is independent of the coupling constant. Next, we show the dependence on the centre of mass energy, for two neutral colliding particles, of coupling constant and the rotation parameter. We also investigate energy extraction through Penrose process and find that the energy gain and efficiency of the Penrose process are independent of this coupling constant. Rotation of the polarization vector is also studied for dependence on the Chern–Simons coupling constant.

On symmetries and dynamics of exotic supermultiplets

Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an mathcal{N} = (4, 0) multiplet has a four index exotic graviton and it was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M theory compactified on T6. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional field theory, finding in particular that the six-dimensional momenta do not correspond to a conventional space-time section. When compactified on a circle, the six-dimensional multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies (computed using the product multiplets construction) and the generation of Chern-Simons couplings, we find reason to doubt that their dynamics will agree with the five-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular fixed-volume T3-fibered space-times play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity.

Quantum chaos in topologically massive gravity

We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.

New chiral gravity

The phase space of three-dimensional gravity with Compere-Song-Strominger (CSS) boundary conditions is endowed with asymptotic symmetries consisting in the semi-direct product of a Virasoro and a $\hat{u}(1)$ Ka\v{c}-Moody algebra, and contains BTZ black holes whose entropy can be accounted for by the degeneracy of states of a Warped CFT. By embedding these boundary conditions in Topologically Massive Gravity, we observe the existence of two special points in the space of couplings parameterized by the AdS$_3$ radius $\ell$ and the Chern-Simons coupling $\mu$. When $\mu = \pm {1\over \ell}$, the asymptotic symmetries reduce to either a chiral Virasoro algebra or a pure $\hat{u}(1)$ Ka\v{c}-Moody current algebra. At those points, black holes have positive energy while that of linearized excitations are non-negative.

Constraining the gravitational coupling of axion dark matter at LIGO

The axion-gravity Chern-Simons coupling is well motivated but is relatively weakly constrained, partly due to difficult measurements of gravity. We study the sensitivity of LIGO measurements of chirping gravitational waves (GWs) on such coupling. When the frequency of the propagating GW matches with that of the coherent oscillation of axion dark matter field, the decay of axions into gravitons can be stimulated, resonantly enhancing the GW. Such a resonance peak can be detected at LIGO as a deviation from the chirping waveform. Since all observed GWs will undergo similar resonant enhancement from the Milky-Way (MW) axion halo, LIGO O1+O2 observations can potentially provide the strongest constraint on the coupling, at least for the axion mass $m_a = 5 \times 10^{-13} - 5 \times 10^{-12}$ eV. Along the course, we also emphasize the relevance of the finite coherence of axion fields and the ansatz separating forward and backward propagations of GWs. As a result, the parity violation of the Chern-Simons coupling is not observable from chirping GWs.

Big Bounce Baryogenesis

We explore the possibility of an Ekpyrotic contraction phase harbouring a mechanism for Baryogenesis. A Chern-Simons coupling between the fast-rolling Ekpyrotic scalar and the Standard Model Hypercharge gauge field enables the generation of a non-zero helicity during the contraction phase. The baryon number subsequently produced at the Electroweak Phase Transition is consistent with observation for a range of couplings and bounce scales. Simultaneously, the gauge field production during the contraction provides the seeds for galactic magnetic fields and sources gravitational waves, which may provide additional avenues for observational confirmation.

Gravitational Waves in Axion Dark Matter

Axion dark matter is interesting as it allows a natural coupling to the gravitational Chern–Simons term. In the presence of an axion background, the gravitational Chern–Simons term produces parity violating effects in the gravitational sector, in particular on the propagation of gravitational waves. Previously, it has been shown that the coherent oscillation of the axion field leads to a parametric amplification of gravitational waves with a specific frequency. In this paper, we focus on the parity violating effects of the Chern–Simons coupling and show the occurrence of gravitational birefringence. We also find deviation from the speed of light of the velocity of the gravitational waves. We give constraints on the axion-Chern–Simons coupling constant and the abundance of axion dark matter from the observation of GW170817 and GRB170817A.

Effects of gravitational Chern-Simons during Axion-SU(2) inflation

In this paper we examine the viability of inflation models with a spectator axion field coupled to both gravitational and SU(2) gauge fields via Chern-Simons couplings. Requiring phenomenological success of the axion-SU(2) sector constrains the coupling strength of the gravitational Chern-Simons term. We find that the impact of this term on the production and propagation of gravitational waves can be as large as fifty percent enhancement for the helicity that is not sourced by the gauge field, if the cut-off scale is as low as Λ = 20H. The effect becomes smaller for a larger value of Λ, while the impact on the helicity sourced by the gauge field is negligible regardless of Λ.

O-plane couplings at order \u03b1\u20322: one R-R field strength

It is known that the anomalous Chern-Simons (CS) coupling of Op-plane is not consistent with the T-duality transformations. Compatibility of this coupling with the T-duality requires the inclusion of couplings involving one R-R field strength. In this paper we find such couplings at order α′2. By requiring the R-R and NS-NS gauge invariances, we first find all independent couplings at order α′2. There are 1, 6, 28, 20, 19, 2 couplings corresponding to the R-R field strengths F(p−4), F(p−2), F(p), F(p+2), F(p+4) and F(p+6), respectively. We then impose the T-duality constraint on these couplings and on the CS coupling C(p−3) ∧ R ∧ R at order α′2 to fix their corresponding coefficients. The T-duality constraint fixes all coefficients in terms of the CS coefficient. They are fully consistent with the partial couplings that have been already found in the literature by the S-matrix method.

Extended BRST–anti-BRST transformations in non-Abelian self-dual Chern–Simons coupling theory

We establish the extended BRST and anti-BRST transformations for non-Abelian relativistic self-dual Chern–Simons theory coupled to scalar fields within the Batalin–Vilkovisky framework. Based on these constructions, we describe the total effective extended BRST-invariant Lagrangian density of the coupling theory by means of superfields with one Grassmann coordinates. Moreover, we need two fermionic variables to reexpress the extended BRST–anti-BRST-invariant Lagrangian in the superspace.

Atacama Cosmology Telescope: Constraints on cosmic birefringence

We present new constraints on anisotropic birefringence of the cosmic microwave background polarization using two seasons of data from the Atacama Cosmology Telescope covering 456 square degrees of sky. The birefringence power spectrum, measured using a curved-sky quadratic estimator, is consistent with zero. Our results provide the tightest current constraint on birefringence over a range of angular scales between 5 arc minutes and 9°. We improve previous upper limits on the amplitude of a scale-invariant birefringence power spectrum by a factor of between 2 and 3. Assuming a nearly massless axion field during inflation, our result is equivalent to a 2σ upper limit on the Chern-Simons coupling constant between axions and photons of gαγ<4.0×10−2/HI, where HI is the inflationary Hubble scale.Received 1 February 2020Accepted 2 April 2020DOI:https://doi.org/10.1103/PhysRevD.101.083527© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic microwave backgroundCosmologyPhysical SystemsAxionsGravitation, Cosmology & Astrophysics

Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly

It is well-known that chiral anomaly can be macroscopically detected through the energy and charge transport, due to the chiral magnetic effect. On the other hand, in a holographic many body system, the chaotic modes might be only associated with the energy conservation. This suggests that, perhaps, one can detect microscopic anomalies through the diagnosis of quantum chaos in such systems. To investigate this idea, we consider a magnetized brane in AdS space time with a Chern-Simons coupling in the bulk. By studying the shock wave geometry in this background, we first compute the corresponding butterfly velocities, in the presence of an external magnetic field B, in μ « T and B « T2 limit. We find that the butterfly propagation in the direction of B has a different velocity than in the opposite direction; the difference is ∆vB = (log(4)−1)∆vsound with ∆vsound being the difference between the velocity of two sound modes propagating in the system. The splitting of butterfly velocities confirms the idea that chiral anomaly can be macroscopically manifested via quantum chaos. We then show that the pole-skipping points of energy density Green’s function of the boundary theory coincide precisely with the chaos points. This might be regarded as the hydrodynamic origin of quantum chaos in an anomalous system. Additionally, by studying the near horizon dynamics of a scalar field on the above background, we find the spectrum of pole-skipping points associated with the two-point function of dual boundary operator. We find that the sum of wavenumbers corresponding to pole-skipping points at a specific Matsubara frequency is a universal quantity, which is independent of the scaling dimension of the dual boundary operator. We then show that this quantity follows from a closed formula and can be regarded as another macroscopic manifestation of the chiral anomaly.

Chiral anomaly, Schwinger effect, Euler-Heisenberg Lagrangian and application to axion inflation

Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of parallel electric and magnetic fields. We review the Schwinger particle production rate, clarify the emergence of the chiral anomaly equation and compute the induced current of charged fermions. We distinguish the contributions from non-perturbative particle production, from the running of the gauge coupling constant and from non-linearities in the effective QED Lagrangian, and clarify how these contributions arise within a single framework. We apply these results to axion inflation. A Chern-Simons coupling between the pseudoscalar particle driving cosmic inflaton and an abelian gauge group induces a dual production of gauge fields and charged fermions. We show that the resulting scalar and gravitational wave power spectra strongly depend on the fermion mass.

Resonant magnetogenesis from axions

We investigate the generation of seed magnetic field through the Chern-Simons coupling between the U(1) gauge field and an axion field that commences to oscillate at various epoch, depending on the mass scale. We address axions which begin oscillation during inflation, reheating, and also the radiation dominated era after the thermalization of the Universe. We study the resonant generation mechanisms and highlight that a small oscillation time scale with respect to that of the cosmic expansion can lead to an efficient generation of (hyper) magnetic field via resonant generation, even for \U0001d4aa(1) coupling. In addition, we demonstrate that the generated field can be helical due to the tachyonic amplification phase prior to the onset of oscillation. Furthermore, it is shown that the parametric resonance during reheating can generate a circularly polarized (hyper) magnetic field in a void region with the present amplitude B0 =3× 10−15Gauss and the coherent length λ0 = 0.3pc without being plagued by the backreaction issue.

Propagation of gravitational waves in Chern-Simons axion Einstein gravity

In this paper we shall investigate the propagation of gravitational waves in a flat Friedman-Robertson-Walker background, in the context of a string motivated corrected Einstein gravity. Particularly, we shall consider a misalignment axion Einstein gravity in the presence of a string originating Chern-Simons coupling of the axion field to the Chern-Pontryagin density in four dimensions. We shall focus our study on the propagation of the gravitational waves, and we shall investigate whether there exists any difference in the propagation of the polarization states of the gravitational waves. As we demonstrate, the dispersion relations are different in the Right-handed mode and the Left-handed mode. Finally, we compare the propagation of the axion Chern-Simons Einstein theory with that of standard $F(R)$ gravity.

The analysis of solutions for Maxwell–Chern–Simons O(3) sigma model

In this paper, we prove the uniqueness of topological solutions for the self-dual Maxwell–Chern–Simons O(3) sigma model under the conditions on Chern–Simons coupling parameter and the charge of electron. Besides, we also provide the quantitative analysis of radial solutions of all types for single vortex-point case.