Gravitational Chern-Simons Research Articles

Chern-Simons action and the Carrollian Cotton tensors

In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated.

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.

Singular supertranslations and Chern-Simons theory on the black hole horizon

We construct the standard and dual supertranslation charges on the future horizon of the Schwarzschild black hole, using the first-order formulation of gravity with the Holst action. The Dirac bracket algebra of standard and dual supertranslation charges is shown to exhibit a central term in the presence of singularities in the two-sphere function associated with supertranslation. We show that one can cancel this anomalous term and restore the asymptotic symmetry algebra by introducing a gravitational Chern-Simons theory on the horizon. This demonstrates that consistency of the asymptotic symmetry algebra requires a new structure on the horizon.

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.

Generation of gravitational waves in dynamical Chern-Simons gravity

We investigate gravitational waves (GWs) generated in a two-field inflationary model with a noncanonical kinetic term, in which the gravitational Chern-Simons term is coupled to a heavy dynamical field. In such a model, primordial GWs experience a period of resonant amplification for some modes. In addition, isocurvature perturbations suffer from a temporary tachyonic instability due to an effective negative mass, which source curvature perturbations, resulting in large induced GWs. These two stochastic gravitational wave backgrounds correspond to different frequency bands, which are expected to be detected by future GW detectors such as SKA, LISA, and Taiji.

Holography from Singular Supertranslations on a Black Hole Horizon.

We investigate the standard and dual Bondi-Metzner-Sachs (BMS) supertranslation generators on a black hole horizon and draw some conclusions about black hole physics. Recently, it has been shown that in addition to conventional BMS supertranslation symmetries, there exists an additional infinite set of magnetic asymptotic symmetries, dual BMS supertranslations, again parametrized by a function on the two-sphere. We show that the Dirac bracket between these generators exhibits an anomalous central term when one parameter function exhibits a singularity in the complex stereographical coordinates on the sphere. In order to preserve general coordinate invariance, we demonstrate that this central term can be removed by postulating a holographic gravitational Chern-Simons theory on the horizon. This indicates that for an anomaly-free theory of quantum gravity in the presence of a black hole, one should include a boundary theory on the horizon.

Constraining gravitational wave amplitude birefringence and Chern-Simons gravity with GWTC-2

We perform a new test of general relativity (GR) with signals from GWTC-2, the LIGO and Virgo catalog of gravitational wave detections. We search for the presence of amplitude birefringence, in which left versus right circularly polarized modes of gravitational waves are exponentially enhanced and suppressed during propagation. Such an effect is present in various beyond-GR theories but is absent in GR. We constrain the amount of amplitude birefringence consistent with the data through an opacity parameter $\kappa$, which we bound to be $\kappa \lesssim 0.74 \textrm{ Gpc}^{-1}$. We then use these theory-agnostic results to constrain Chern-Simons gravity, a beyond-GR theory with motivations in quantum gravity. We bound the canonical Chern-Simons lengthscale to be $\ell_0 \lesssim 1.0 \times 10^3$ km, improving on previous long-distance measurement results by a factor of two.

Erratum: Entanglement negativity, reflected entropy, and anomalous gravitation [Phys. Rev. D 105 , 086013 (2022)

We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS$_3$ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.

Axion gravitodynamics, Lense-Thirring effect, and gravitational waves

We investigate physical implications of a gravitational analog of axion electrodynamics with a parity-violating gravitoelectromagnetic theta term. This is related to the Nieh-Yan topological invariant in gravity with torsion, in contrast to the well-studied gravitational Chern-Simons term quadratic in curvature, coupled via a dynamical axionlike scalar field. Axion gravitodynamics is the corresponding linearized theory. We find that potentially observable effects are over 80 orders of magnitude stronger than for its Chern-Simons counterpart and could be in reach for detection by experiments in the near future. For a near-Earth scenario, we derive corrections to the Lense-Thirring effect and compare them to data from satellite-based experiments (Gravity Probe B). For gravitational waves, we find modified dispersion relations, derive the corresponding polarization-dependent modified group and phase velocities, and compare them to data from neutron star mergers (GW170817) to derive even stronger bounds.

Entanglement negativity, reflected entropy, and anomalous gravitation

We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in ${\mathrm{AdS}}_{3}$ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.

Fast gravitational wave bursts from axion clumps

The axion objects such as axion miniclusters and axion clouds around spinning black holes induce parametric resonances of electromagnetic waves through the axion-photon interaction. In particular, it has been known that the resonances from the axion with the mass around ${10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{eV}$ may explain the observed fast radio bursts (FRBs). Here we argue that similar bursts of high frequency gravitational waves, which we call fast gravitational wave bursts (FGBs), are generated from axion clumps with the presence of gravitational Chern-Simons (CS) coupling. The typical frequency is half of the axion mass, which in general can range from kHz to GHz. We also discuss the secondary gravitational wave production associated with FRB, as well as the possible host objects of the axion clouds, such as primordial black holes with typical masses around ${10}^{\ensuremath{-}5}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. Future detections of FGBs together with the observed FRBs are expected to provide more evidence for the axion.

Inflationary physics and trans-Planckian conjecture in the stringy running vacuum model: from the phantom vacuum to the true vacuum

In previous works we have embedded the Running Vacuum Model (RVM) of Cosmology in the framework of string theory. Specifically, we considered a string-inspired Cosmology with primordial gravitational waves (GW) and gravitational anomalies, which were argued to lead, via appropriate condensation during the very-early-universe era, to dynamical inflation, of RVM type, without the need for extra inflaton fields. A crucial role for the associated slow-roll nature of the inflationary era was played by the fundamental axion field that exists in the gravitational multiplet of strings, viz. the Kalb-Ramond (KR) axion. In this paper, we study further this model and demonstrate several novel facts, completing our previous studies. We clarify the different roles played by the background KR axions, which constitute a form of stiff matter that dominates a pre-RVM-inflationary epoch of the Universe. We show that the KR axion when combined with the gravitational Chern-Simons contribution obey together a peculiar equation of state $p=-\rho$, with negative energy density $\rho < 0$, which we call `phantom vacuum'. Eventually, this state transmutes into the standard vacuum state thanks to the contribution from the gravitational Chern-Simons condensate, which makes the total $\rho_{\rm total} =-p_{\rm total} >0$. At this point the RVM vacuum picture emerges naturally, with an overall equation of state of true vacuum type. We find that our scenario is consistent with the trans-Planckian censorship hypothesis, given that the rate of change of the KR axion takes only sub-Planckian values. We also discuss some explicit scenarios on the creation of GWs within the context of supergravity models that could be embedded in our string theory framework. {Finally, we argue how the RVM in our context can help to alleviate the current tensions of the $\Lambda$CDM.}

Chern-Simons caps for rotating black holes

We study the dynamical Chern-Simons gravity as an effective quantum field theory, and discuss a broad range of its parameter space where the theory is valid. Within that validity range, we show that slowly rotating black holes acquire novel geometric structures due to the gravitational dynamical Chern-Simons term. In particular, the rotating black-hole solutions get endowed with two caplike domains, emanating from the north and south poles in the standard Boyer-Lindquist coordinates. The domains extend out to a distance that is approximately a few percent of the black hole's size. The caplike domains have an unusual equation of state, pointing to nonstandard dynamics within the caps. In particular, the focusing condition for geodesics is violated in those domains. This in turn implies that the Hawking-Penrose singularity theorem cannot be straightforwardly applied to hypothetical probe matter placed within the Chern-Simons caps.

Extended Nappi-Witten geometry for the fractional quantum Hall effect

Motivated by the recent progresses in the formulation of geometric theories for the fractional quantum Hall states, we propose a novel non-relativistic geometric model for the Laughlin states based on an extension of the Nappi-Witten geometry. We show that the U(1) gauge sector responsible for the fractional Hall conductance, the gravitational Chern-Simons action and Wen-Zee term associated to the Hall viscosity can be derived from a single Chern-Simons theory with a gauge connection that takes values in the extended Nappi-Witten algebra. We then provide a new derivation of the chiral boson associated to the gapless edge states from the Wess-Zumino-Witten model that is induced by the Chern-Simons theory on the boundary.

Gravitational Leptogenesis in Bounce Cosmology

We investigate whether successful Gravitational Leptogenesis can take place during an Ekpyrotic contraction phase. Two possible paths by which this can occur are coupling the Ekpyrotic scalar to a gravitational Chern-Simons term, or to a U(1) gauge field Chern-Simons term. These couplings lead to the production of chiral gravitational waves, which generate a lepton number asymmetry through the gravitational-lepton number anomaly. This lepton asymmetry is subsequently reprocessed by equilibrium sphaleron processes to produce a baryon asymmetry. We find successful Gravitational Leptogenesis to be possible in Ekpyrotic bounce cosmologies through both of these mechanisms.

Chiral massive news: null boundary symmetries in topologically massive gravity

We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtain Heisenberg ⊕ Virasoro algebra with a central charge proportional to the gravitational Chern-Simons term of TMG. We also discuss that the flux of the chiral massive gravitons appears as the (Bondi) news through the null surface.

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.

Renormalization in gravitational leptogenesis with pseudo-scalar-tensor coupling

We consider the renormalization in the pseudo-scalar inflation models with the gravitational Chern-Simons term. In this model, lepton asymmetry is generated from the chiral gravitational waves produced due to the Chern-Simons term through the gravitational chiral anomaly. However, it is known that the naive estimate of the expectation value of the gravitational Chern-Pontryagin density as well as the resultant lepton number density depend on the UV-cutoff scale, which raises a question on their validity. In this paper, we propose a way to renormalize the expectation value of the Chern-Pontryagin density to remove the UV-cutoff dependence. We also discuss the renormalized lepton number density when we adopt the minimal subtraction scheme and the viability of the gravitational leptogenesis scenario.

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.

Five-dimensional supergravity in N = 1/2 superspace

We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincaré symmetries manifestly. The remaining four supersymmetries and the rest of the Poincaré symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we discuss the construction of the 5D gravitational Chern-Simons invariant ∫ A ∧ R ∧ R in this superspace.