arXiv subjects

Jyotirmoy Bhattacharya

Publications and source records attributed to Jyotirmoy Bhattacharya.

At least 19 recordsLinked to original sources

arXiv2026

Chern-Simons propagators in AdS$_3$

We introduce parity-odd spin-1 harmonic functions in AdS$_3$ and study their properties. We demonstrate that such parity-odd harmonics are related to their parity-even counterparts through the action of a `Chern-Simons operator', which we present as a novelty in this paper. This relation leads to the construction of simultaneous eigen-functions of the Laplacian and the Chern-Simons operators. Subsequently, these harmonic functions are employed to construct propagators in pure abelian Chern-Simons theory as well as Maxwell-Chern-Simons theory in a covariant gauge. We demonstrate the consistency of the Chern-Simons propagator with the expected two-point function of the boundary currents. Our results are built upon the embedding formalism, which we modify suitably to incorporate parity-odd structures. This formalism also readily helps us write down parity odd structures for the propagators of higher-spin fields. Finally, we construct a split representation for the parity-odd harmonic functions, which may be useful to compute Witten diagrams with loops. Our results are expected to be useful in perturbative studies of parity violating QFTs on AdS$_3$.

hep-th↗

arXiv2025

Thermal Product Formula for Shear Modes

We investigate the validity of the thermal product formula proposed in [arXiv:2304.12339], for the shear channel fluctuations of R-charged black branes in five-dimensional AdS where the shear mode is coupled with charge diffusion mode at non-zero momentum. When these modes are suitably decoupled, we are able to obtain an exact formula for the two point functions of the boundary current and energy-momentum tensor in terms of the quasinormal modes of this channel. This exact formula is a simple modification of the previous version of the product formula. We also obtain a similar formula for the case involving a boundary global R-symmetry anomaly, when we have a bulk Chern-Simons term which introduces additional couplings in the shear channel. Also based on insights from the quasinormal mode spectrum, we report on an instability as well as the presence of high momentum long-lived modes associated with large values of the anomaly coefficient.

hep-th↗

arXiv2023

Holographic entanglement entropy for relativistic hydrodynamic flows

We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d=2,3,4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence, at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of a sound mode, considering first order in derivative expansion. As a simplified setup, we first work with non-dissipative dynamics in $d=2$, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d= 4, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to `area law divergence'. No such divergence is observed for dissipative sound mode in d=3.

hep-th↗

arXiv2023

Machine learning of Ising criticality with spin-shuffling

We investigate the performance of neural networks in identifying critical behaviour in the 2D Ising model with next-to-nearest neighbour interactions. We train DNN and CNN based classifiers on the Ising model configurations with nearest neighbour interactions and test the ability of our models to identify the critical (cross-over) region, as well as the phases in the presence of next-to-nearest neighbour interactions. Our main objective is to investigate whether our models can learn the notion of criticality and universality, in contrast to merely identifying the phases by simply learning the value of the order parameter, magnetization in this case. We design a simple adversarial training process which forces our models to ignore learning about the order parameter while training. We find that such models are able to identify critical region with reasonable success, implying that it has learned to identify the structure of spin-spin correlations near criticality.

cond-mat.stat-mech↗

arXiv2022

Numerical Bootstrap in Quantum Mechanics

We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative aspects. Using this technique we then investigate quantum mechanical potentials related by supersymmetry and recover the expected spectra. Finally, we also study the singlet sector of O(N) vector model quantum mechanics, where we find that the bootstrap method yields results which in the large N agree with saddle point analysis.

hep-th↗

arXiv2021

Indian urban workers' labour market transitions

This paper studies gross labour market flows and determinants of labour market transitions for urban Indian workers using a panel dataset constructed from Indian Periodic Labour Force Survey (PLFS) data for the period 2017--18 to 2019--20. Longitudinal studies based on the PLFS have been hampered by data problems that prevent a straightforward merging of the 2017--18 and 2018--19 data releases. In this paper, we propose and validate a matching procedure based on individual and household characteristics that can successfully link almost all records across these two years. We use the constructed data set to document a number of stylised facts about gross worker flows and to estimate the effects of different individual characteristics and work histories on probabilities of job gain and loss.

econ.GN↗

arXiv2020

An entropy current for dynamical black holes in four-derivative theories of gravity

We propose an entropy current for dynamical black holes in a theory with arbitrary four derivative corrections to Einstein's gravity, linearized around a stationary black hole. The Einstein-Gauss-Bonnet theory is a special case of the class of theories that we consider. Within our approximation, our construction allows us to write down a completely local version of the second law of black hole thermodynamics, in the presence of the higher derivative corrections considered here. This ultra-local, stronger form of the second law is a generalization of a weaker form, applicable to the total entropy, integrated over a compact `time-slice' of the horizon, a proof of which has been recently presented in arXiv:1504.08040. We also provide a general algorithm to construct the entropy current for the four derivative theories, which may be straightforwardly generalized to arbitrary higher derivative corrections to Einstein's gravity. This algorithm highlights the possible ambiguities in defining the entropy current.

hep-th↗

arXiv2019

A holographic superconductor forced through interactions

We propose a novel mechanism to achieve superconductivity at zero chemical potential, within the holographic framework. Extending previous construction of the holographic superconductors, we consider an Einstein-Maxwell system coupled with two interacting scalars in Anti-de Sitter space. One of the scalar fields is charged and therefore, interacts non-trivially with the gauge field, while the other is uncharged. We find that, if we turn on a boundary source for the uncharged scalar field, it forces the condensation of the charged scalar, leading to a superconducting phase in the dual boundary theory. The condensation occurs at a certain critical value of the source, depending on the value of the chemical potential, which can even be zero. We work out the complete phase diagram of this scenario. We further corroborate the existence of superconductivity at zero chemical potential, through a fluctuation analysis on our solution. Notably, the conductivity of the system, as a function of probing frequency, exhibits characteristics of usual holographic superconductors. We also investigate how these properties of the system changes, as we vary the interaction strength between the scalar fields. Our results indicate a controlled mechanism to manipulate the phase transition temperature of superconductors with strongly coupled microscopics.

hep-th↗

arXiv2017

On the surface of superfluids

Developing on a recent work on localized bubbles of ordinary relativistic fluids, we study the comparatively richer leading order surface physics of relativistic superfluids, coupled to an arbitrary stationary background metric and gauge field in $3+1$ and $2+1$ dimensions. The analysis is performed with the help of a Euclidean effective action in one lower dimension, written in terms of the superfluid Goldstone mode, the shape-field (characterizing the surface of the superfluid bubble) and the background fields. We find new terms in the ideal order constitutive relations of the superfluid surface, in both the parity-even and parity-odd sectors, with the corresponding transport coefficients entirely fixed in terms of the first order bulk transport coefficients. Some bulk transport coefficients even enter and modify the surface thermodynamics. In the process, we also evaluate the stationary first order parity-odd bulk currents in $2+1$ dimensions, which follows from four independent terms in the superfluid effective action in that sector. In the second part of the paper, we extend our analysis to stationary surfaces in $3+1$ dimensional Galilean superfluids via the null reduction of null superfluids in $4+1$ dimensions. The ideal order constitutive relations in the Galilean case also exhibit some new terms similar to their relativistic counterparts. Finally, in the relativistic context, we turn on slow but arbitrary time dependence and answer some of the key questions regarding the time-dependent dynamics of the shape-field using the second law of thermodynamics. A linearized fluctuation analysis in $2+1$ dimensions about a toy equilibrium configuration reveals some new surface modes, including parity-odd ones. Our framework can be easily applied to model more general interfaces between distinct fluid-phases.

hep-th↗

arXiv2016

6d Dual Conformal Symmetry and Minimal Volumes in AdS

The S-matrix of a theory often exhibits symmetries which are not manifest from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering amplitudes are imposed by the dual conformal symmetry of planar 4d $\mathcal{N}=4$ super Yang-Mills theory and the ABJM theory. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions, which may provide useful insight into the worldvolume theory of M5-branes (if it enjoys such a symmetry). We find that 6d dual conformal symmetry uniquely fixes the integrand of the one-loop 4-point amplitude, and its structure suggests a Lagrangian with more than two derivatives. On integrating out the loop momentum in $6-2 ε$ dimensions, the result is very similar to the corresponding amplitude of $\mathcal{N}=4$ super Yang-Mills theory. We confirm this result holographically by generalizing the Alday-Maldacena solution for a minimal area string in Anti-de Sitter space to a minimal volume M2-brane ending on pillow-shaped Wilson surface in the boundary whose seams correspond to a null-polygonal Wilson loop. This involves careful treatment of a prefactor which diverges as $1/ε$, and we comment on its possible interpretation. We also study 2-loop 4-point integrands with 6d dual conformal symmetry and speculate on the existence of an all-loop formula for the 4-point amplitude.

hep-th↗

arXiv2016

Surface transport in plasma-balls

We study the surface transport properties of stationary localized configurations of relativistic fluids to the first two non-trivial orders in a derivative expansion. By demanding that these finite lumps of relativistic fluid are described by a thermal partition function with arbitrary stationary background metric and gauge fields, we are able to find several constraints among surface transport coefficients. At leading order, besides recovering the surface thermodynamics, we obtain a generalization of the Young-Laplace equation for relativistic fluid surfaces, by considering a temperature dependence in the surface tension, which is further generalized in the context of superfluids. At the next order, for uncharged fluids in 3+1 dimensions, we show that besides the 3 independent bulk transport coefficients previously known, a generic localized configuration is characterized by 3 additional surface transport coefficients, one of which may be identified with the surface modulus of rigidity. Finally, as an application, we study the effect of temperature dependence of surface tension on some explicit examples of localized fluid configurations, which are dual to certain non-trivial black hole solutions via the AdS/CFT correspondence.

hep-th↗

arXiv2015

Entanglement density and gravitational thermodynamics

In an attempt to find a quasi-local measure of quantum entanglement, we introduce the concept of entanglement density in relativistic quantum theories. This density is defined in terms of infinitesimal variations of the region whose entanglement we monitor, and in certain cases can be mapped to the variations of the generating points of the associated domain of dependence. We argue that strong sub-additivity constrains the entanglement density to be positive semi-definite. Examining this density in the holographic context, we map its positivity to a statement of integrated null energy condition in the gravity dual. We further speculate that this may be mapped to a statement analogous to the second law of black hole thermodynamics, for the extremal surface.

hep-th↗

arXiv2015

Intermediate scalings in holographic RG flows and conductivities

We construct numerically finite density domain-wall solutions which interpolate between two $AdS_4$ fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared $AdS_4$ fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with $AdS_2 \times \mathbb{R}^2$. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies.

hep-th↗

arXiv2014

A theory of first order dissipative superfluid dynamics

We determine the most general form of the equations of relativistic superfluid hydrodynamics consistent with Lorentz invariance, time-reversal invariance, the Onsager principle and the second law of thermodynamics at first order in the derivative expansion. Once parity is violated, either because the $U(1)$ symmetry is anomalous or as a consequence of a different parity-breaking mechanism, our results deviate from the standard textbook analysis of superfluids. Our general equations require the specification of twenty parameters (such as the viscosity and conductivity). In the limit of small relative superfluid velocities we find a seven parameter set of equations. In the same limit, we have used the AdS/CFT correspondence to compute the parity odd contributions to the superfluid equations of motion for a generic holographic model and have verified that our results are consistent.

hep-th↗

arXiv2014

Non-dissipative hydrodynamics: Effective actions versus entropy current

While conventional hydrodynamics incorporating dissipative effects is hard to derive from an action principle, it is nevertheless possible to construct classical actions when the dissipative terms are switched off. In this note we undertake a systematic exploration of such constructions from an effective field theory approach and argue for the existence of non-trivial second order non-dissipative hydrodynamics involving pure energy-momentum transport. We find these fluids to be characterized by five second-order transport coefficients based on the effective action (a three parameter family is Weyl invariant). On the other hand since all flows of such fluids are non-dissipative, they entail zero entropy production; one can therefore understand them using the entropy current formalism which has provided much insight into hydrodynamic transport. An analysis of the most general stress tensor with zero entropy production however turns out to give a seven parameter family of non-dissipative hydrodynamics (a four parameter sub-family being Weyl invariant). The non-dissipative fluids derived from the effective action approach are a special case of the fluid dynamics constrained by conservation of the entropy current. We speculate on the reasons for the mismatch and potential limitations of the effective action approach.

hep-th↗

arXiv2013

Entropic Counterpart of Perturbative Einstein Equation

Entanglement entropy in a field theory, with a holographic dual, may be viewed as a quantity which encodes the diffeomorphism invariant bulk gravity dynamics. This, in particular, indicates that the bulk Einstein equations would imply some constraints for the boundary entanglement entropy. In this paper we focus on the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and analyze the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state. Specifically, we consider linear fluctuations about BTZ black hole in 3 dimension, pure AdS and AdS Schwarzschild black holes in 4 dimensions and obtain a diffeomorphism invariant reformulation of linearized Einstein equation in terms of holographic entanglement entropy. We will also show that entanglement entropy for boosted subsystems provides the information about all the components of the metric with a time index.

hep-th↗

arXiv2013

On the IR completion of geometries with hyperscaling violation

We study solutions to Einstein-Maxwell-dilaton gravity with a constant magnetic flux which describe, in the holographic AdS/CFT framework, field theories characterized by a dynamical critical exponent and a hyperscaling violation exponent. Such solutions are known to be IR-incomplete due to the presence of a running dilaton, which drives the theory towards strong coupling in the IR, where quantum corrections become important. After introducing generic corrections, in this note we examine the conditions for the emergence of an AdS_2 x R^2 region close to the horizon, which provides an IR-completion for the hyperscaling violating solutions. In the presence of these corrections, we construct explicit numerical solutions where the geometry flows from AdS_4 in the UV to AdS_2 x R^2 in the deep IR, with an intermediate region which exhbits both hyperscaling violation and Lifshitz scaling.We also provide constraints on the structure of Einstein-Maxwell-dilaton theories that admit such solutions, as well as an emergent AdS_2 x R^2 region in the infrared.

hep-th↗

arXiv2012

Thermodynamical Property of Entanglement Entropy for Excited States

We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.

hep-th↗