Chern-Simons Term Research Articles

Revisit the entanglement entropy with gravitational anomaly

In this paper we study the entanglement entropy in the CFT2, whose gravity dual is AdS3 spacetime with a Chern-Simons term. Using the generalized Rindler method, we obtain the Rindler transformation in the two-dimensional planar CFT and compute the entanglement entropy of the CFT with gravitational anomalies. The conditions under which the entanglement entropy may have anomalous contributions is also discussed. In addition, we present a relatively general form of the Rindler AdS metric and compute its thermal entropy, which agrees with the entanglement entropy in the field theory. Moreover, we utilize the conformal transformation, which maps a cylinder to a plane, to compute the entanglement entropy of the CFT residing on a cylinder, as well as the entanglement entropy of the CFT at finite temperature on a plane. The corresponding contribution of the Chern-Simons term in gravity to the black hole thermal entropy is also obtained from this approach. These results are important for further understandings of the two-dimensional CFT with gravitational anomalies.

Anomalous hydrodynamics effective actions from holography

We derive an effective action for charged plasmas with an anomalous (abelian) global current charge current using holography. The holographic description is captured by the dynamics of an Einstein-Maxwell-Chern-Simons theory in an asymptotically AdS spacetime. The ’t Hooft anomaly contribution, which is encoded in the Chern-Simons term, contributes at the Gaussian order in the effective action only in the momentum diffusion sector, where it leads to chiral shear waves. However, as we demonstrate, beyond the Gaussian order, there is non-trivial imprint of the parity-violating anomaly term in sound and charge diffusion dynamics as well.

The role of the Callan–Witten anomaly density as a Chern–Simons term in Skyrme model *

We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy M electric charge Qe and angular momentum J can be both positive and negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.

Kinetic Axion f(R) Gravity Phase Space

In this work, we studied the phase space of f(R) gravity in the presence of a misalignment axion, including parity violating Chern–Simons terms. We construct the autonomous dynamical system by using appropriate dimensionless variables and find the cosmological attractors of the phase space, which are basically the fixed points of the autonomous dynamical system. We focus on the R2 model and the misalignment axion potential near the minimum. We demonstrate that the Chern–Simons terms have no effect on the phase space. We found four distinct, possibly unstable fixed points with physical significance. Specifically, we found two identical de Sitter fixed points, one radiation domination fixed point, and one dark matter dominated fixed point. Thus, in the presence of a kinetic misalignment axion, the vacuum f(R) gravity contains all of the cosmological fixed points that can characterize all of the known evolution eras of our universe.

Is cosmic birefringence model-dependent?

Exciting clues to isotropic cosmic birefringence have recently been detected in the EB cross-power spectra of the polarization data of the cosmic microwave background (CMB). Early Dark Energy (EDE) models with a pseudoscalar field coupled to photons via a Chern-Simons term can be used to explain this phenomenon, and can also potentially be used to simultaneously resolve the H 0 tension. In this work we incorporate an early dark energy scalar field, including a Chern-Simons coupling, into an existing Boltzmann solver and numerically recover the EB cross-power spectrum for two models in the literature; the α-attractor, and the Rock `n' Roll field. We find that both the models fit the EB spectra, and the EB spectra alone do not possess sufficient constraining power to distinguish the two models based on current data.

Quantum double structure in cold atom superfluids

The theory of topological quantum computation is underpinned by two important classes of models. One is based on non-abelian Chern–Simons theory, which yields the so-called SU(2)k anyon models that often appear in the context of electrically charged quantum fluids. The physics of the other is captured by symmetry broken Yang–Mills theory in the absence of a Chern–Simons term and results in the so-called quantum double models. Extensive resources have been invested into the search for SU(2)k anyon quasi-particles, in particular, the so-called Ising anyons (k = 2) of which Majorana zero modes are believed to be an incarnation. In contrast to the SU(2)k models, quantum doubles have attracted little attention in experiments despite their pivotal role in the theory of error correction. Beyond topological error correcting codes, the appearance of quantum doubles has been limited to contexts primarily within mathematical physics, and as such, they are of seemingly little relevance for the study of experimentally tangible systems. However, recent works suggest that quantum double anyons may be found in spinor Bose–Einstein condensates. In light of this, the core purpose of this article is to provide a self-contained exposition of the quantum double structure, framed in the context of spinor condensates, by constructing explicitly the quantum doubles for various ground state symmetry groups and discuss their experimental realisability. We also derive analytically an equation for the quantum double Clebsch–Gordan coefficients from which the relevant braid matrices can be worked out. Finally, the existence of a particle-vortex duality is exposed and illuminated upon in this context.

Spin 12 from gluons

The theta vacuum in QCD is obtained from the standard vacuum, after twisting by the exponential of the Chern–Simons term. However, a question remains–what is the quantum operator [Formula: see text] for winding number 1? We construct this operator [Formula: see text] in this note. The Poincaré rotation generators commute with it only if they are augmented by the spin [Formula: see text] representation of the Lorentz group, coming from large gauge transformations. This result is analogous to the well-known “spin-isopin” mixing result due to Jackiw and Rebbi [Phys. Rev. Lett. 36, 1116 (1976)], and Hasenfratz and ’t Hooft [Phys. Rev. Lett. 36, 1119 (1976)]. There is a similar result in fuzzy physics literature of Balachandran, Kurkcuoglu and Vaidya [Lectures on Fuzzy and Fuzzy Susy Physics (World Scientific Publishing Company, 2007)]. This shows that states can drastically affect representations of observables. This fact is further shown by charged states dressed by infrared clouds. Following Mund, Rehren and Schroer [arXiv:hep-th/2109.10342], we find that Lorentz invariance is spontaneously broken in these sectors. This result has been extended earlier to QCD (Balachandran, Nair, Pinzul, Reyes-Lega and Vaidya [arXiv:2112.08631 [hep-th]], reference given in the Final Remarks) where even the global QCD group is shown to be broken. It is argued that the escort fields of Mund, Rehren and Schroer [arXiv:hep-th/2109.10342] are the Higgs fields for Lorentz and color breaking. They are string-localized fields where the strings live in a union of de Sitter spaces. Their oscillations and those of the infrared cloud can generate the associated Goldstone modes.

Scalar induced gravitational waves from Chern-Simons gravity during inflation era

We investigate the scalar induced gravitational waves (SIGWs) in the Chern-Simons (CS) gravity with a dynamical scalar field during slow roll inflation. Due to the parity violation in the CS term, the SIGWs are generally polarized, which are effectively characterized by the degree of circular polarization. We derive the semianalytic expression to evaluate the power spectra and the degree of circular polarization of the SIGWs, which receive contributions from the general relativity and the parity-violating term, respectively. We find that the correction from the parity-violating CS term is negligible on large scales, which means that the degree of circular polarization of SIGWs is very small.

Anomalous conductivities in the holographic Stückelberg model

We have studied a massive U(1) gauge holographic model with pure gauge and mixed gauge-gravitational Chern-Simons terms. The full backreaction of the gauge field on the metric tensor has been considered in order to explore the vortical and energy transport sector. The background solution has been computed numerically. On this background, we have considered the fluctuation of the fields and evaluated the different correlators. We have found that all the correlators depend on the mass of the gauge field. Correlators such as the current-current one, 〈JxJx〉, which were completely absent in the massless case, in the presence of a finite gauge boson mass start picking up some finite value even at zero chemical potential. Similarly, the energy-current correlator, 〈T0xJx〉, which was also absent in the massless theory, has now a non-vanishing value but for finite values of the chemical potential. Our findings for the chiral vortical conductivity, σV, and the chiral magnetic/vortical conductivity of energy current, {sigma}_B^{varepsilon }={sigma}_V^{varepsilon } , are completely new results. In addition to this, we have found that these anomalous transport coefficients depend linearly both on the pure Chern-Simon coupling, κ, and on the mixed gauge-gravity Chern-Simon coupling, λ. One of the results that we would like to highlight is that it’s not just κ that contributes to the σB but there is an additional contribution from λ as well unlike the previous studies.

Boundary terms and conserved charges in higher-derivative gauged supergravity

We address some issues in higher-derivative gauged supergravity with Chern-Simons terms, focusing on the five-dimensional case. We discuss the variational problem with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald’s formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and U(1) gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between Noether charges and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS5 from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the entropy as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory.

Anomalies, the Dark Universe and Matter-Antimatter asymmetry

I review a (3+1)-dimensional, string-inspired cosmological model with gravitational anomalies (of Chern-Simons (CS) type) at early epochs, and a totally-antisymmetric torsion, dual to a massless axion-like field (“gravitational axion”), which couples to the CS term. Under appropriate conditions, primordial gravitational waves can condense, leading to a condensate of the CS anomaly term. As a consequence, one obtains inflation in this theory, of running-vacuum-model (RVM) type, without the need for external inflatons. At the end of the inflationary era, chiral fermionic matter is generated, whose gravitational anomalies cancel the primordial ones. On the other hand, chiral anomalies of gauge type, which are also generated by the chiral matter, remain present during the post-inflationary epochs and become responsible for the generation of a non-perturbative mass for the torsion-related gravitational axion, which, in this way, might play the rôle of a Dark Matter component of geometrical origin. Moreover, in this model, stringy non-perturbative effects during the RVM inflationary phase generate periodic structures for the potential of axion-like particles that arise due to compactification, and co-exist with the gravitational axions. Such periodic potential modulations may lead to an enhanced production of primordial black holes during inflation, which in turn affects the profile of the generated gravitational waves during the radiation era, with potentially observable consequences. This model also entails an unconventional mechanism for Leptogenesis, due to Lorentz-violating backgrounds of the gravitational axions that are generated during inflation, as a consequence of the anomaly condensates, and remain undiluted in the radiation era.

Systematics of boundary actions in gauge theory and gravity

We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the corresponding boundary action. Such actions capture all the dynamics of the system that are implied by its asymptotic symmetry group, such as correlation functions of the corresponding conserved currents. Working in the covariant phase space formalism, we develop a collection of approaches for isolating the boundary modes and their dynamics, and illustrate with various examples, notably AdS3 gravity (with and without a gravitational Chern-Simons terms) subject to assorted boundary conditions.

Non-invertible defects in 5d, boundaries and holography

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible codimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become codimension one non-invertible defects of a boundary theory with an ABJ anomaly.

Spontaneous scalarization of dyonic black hole in Einstein–Maxwell-scalar theory

In this paper, we study the scalarization of the static and spherically symmetric dyonic Reissner–Nordstrom (RN) black holes in the Einstein–Maxwell-scalar theory where the scalar field is coupled to an electromagnetic Chern–Simons term. When both electric and magnetic charges are present, there exists an unstable region of parametric space for the dyonic RN black holes where the scalarization of black holes should occur. That is to say, mixing electric and magnetic charges can reduce the scalarization in this theory. Firstly, we calculate the perturbation field equations under the dyonic RN black hole background and obtain the corresponding asymptotic-flat perturbation solutions, which are the bifurcation points at the dyonic RN branch. The results show that the perturbation scalarization demands a lower bound of the coupling constant. Then, we calculate the scalarized black hole solutions bifurcating from the dyonic RN solutions. We find that there exist a lot of discrete branches of the scalarized solutions. Contract to the dyonic RN solutions, these scalarized solutions can be overcharged and their mass could even approach zero. After illustrating the behavior of the entropy for the scalarized black holes, we demonstrate that the scalarized configurations might be thermodynamically more stable than GR configurations. Moreover, we also show that for each scalarized branch, the black hole cannot reach the extremal limit with vanishing temperature.

S-Dual of Maxwell–Chern-Simons Theory

We discuss the dynamics of three-dimensional Maxwell theory coupled to a level-k Chern-Simons term. Motivated by S-duality in string theory, we argue that the theory admits an S-dual description. The S-dual theory contains a nongauge one-form field, previously proposed by Deser and Jackiw [Phys. Lett. 139B, 371 (1984).PYLBAJ0370-269310.1088/1126-6708/1999/10/036] and a level-k U(1) Chern-Simons term, Z_{MCS}=Z_{DJ}Z_{CS}. The couplings to external electric and magnetic currents and their string theory realizations are also discussed.

Slow-rotating charged black hole solution in dynamical Chern-Simons modified gravity

Chern-Simons (CS) gravity is a modified theory of Einstein's general relativity. The CS theory arises from the low energy limit of string theory which involves anomaly correction to the Einstein-Hilbert action. The CS term is given by the product of the Pontryagin density with a scalar field. In this study, we derive a charged slowly rotating black hole (BH) solution. The main incentives of this BH solution are axisymmetric and stationary and form distortion of the Kerr-Newman BH solution with a dipole scalar field. Additionally, we investigate the asymptotic correction of the metric with the inverse seventh power of the radial distance to the BH solution, This indicates that it will escape any meaningful constraints from weak field experiments. To find this kind of BH by observations, we investigate the propagation of the photon near the BH and we show that the difference between the left-rotated polarization and the right-handed one could be observed as stronger than the case of the Kerr-Newman BH. Finally, we derived the stability condition using the geodesic deviations.

Generating enhanced parity-violating gravitational waves during inflation with violation of the null energy condition

A violation of the null energy condition (NEC) during inflation in a single-field inflation model will naturally enhance the amplitude of the parity violation effect (defined by $\Delta\chi$) of inflationary primordial gravitational waves (GWs), provided the inflaton is non-minimally coupled to a gravitational Chern-Simons term. After going through the NEC-violating phase, the Universe enters subsequent slow-roll inflation with a higher energy scale (i.e., a greater Hubble parameter $H$), which results in an enhanced nearly scale-invariant power spectrum (i.e., $P_{\rm T}$) of inflationary primordial GWs in the high-frequency band, while $P_{\rm T}$ remains consistent with observations in the frequency band of the cosmic microwave background. Therefore, the violation of NEC during inflation will amplify the observability (i.e., $P_{\rm T}\cdot\Delta\chi$) of the parity violation effect on small scales. Intriguingly, our model has particular oscillatory features on $\Delta\chi$ that may not be mimicked by others.

Symmetry TFTs for 3d QFTs from M-theory

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their ’t Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold Y7, which either is the link of a conical Calabi-Yau four-fold or part of an AdS4× Y7 holographic solution. In the holographic setting we first consider the 3d mathcal{N} = 6 ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d mathcal{N} = 2 quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type Y7 = Yp,k( mathbbm{CP} 2). The SymTFT encodes 0- and 1-form symmetries, as well as potential ’t Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for U(1) Chern-Simons terms in the dual field theory.

Isotropic cosmic birefringence from early dark energy

A tantalizing hint of isotropic cosmic birefringence has been found in the $E B$ cross-power spectrum of the cosmic microwave background (CMB) polarization data with a statistical significance of $3\sigma$. A pseudoscalar field coupled to the CMB photons via the Chern-Simons term can explain this observation. The same field may also be responsible for early dark energy (EDE), which alleviates the so-called Hubble tension. Since the EDE field evolves significantly during the recombination epoch, the conventional formula that relates $E B$ to the difference between the $E$- and $B$-mode auto-power spectra is no longer valid. Solving the Boltzmann equation for polarized photons and the dynamics of the EDE field consistently, we find that currently favored parameter space of the EDE model yields a variety of shapes of the $EB$ spectrum, which can be tested by CMB experiments.

Landau damping for gravitational waves in parity-violating theories

We discuss how tensor polarizations of gravitational waves can suffer Landau damping in the presence of velocity birefringence, when parity symmetry is explicitly broken. In particular, we analyze the role of the Nieh-Yan and Chern-Simons terms in modified theories of gravity, showing how the gravitational perturbation in collisionless media can be characterized by a subluminal phase velocity, circumventing the well-known results of General Relativity and allowing for the appearance of the kinematic damping. We investigate in detail the connection between the thermodynamic properties of the medium, such as temperature and mass of the particles interacting with the gravitational wave, and the parameters ruling the parity violating terms of the models. In this respect, we outline how the dispersion relations can give rise in each model to different regions of the wavenumber space, where the phase velocity is subluminal, superluminal or does not exist. Quantitative estimates on the considered models indicate that the phenomenon of Landau damping is not detectable given the sensitivity of present-day instruments.