arXiv subjects

Nilay Kundu

Publications and source records attributed to Nilay Kundu.

At least 19 recordsLinked to original sources

arXiv2026

A comparison of two constructions for dynamical corrections to Wald entropy

In this work, we analyze the differences and similarities between two recent constructions, which are distinct in their methodologies for extending the Wald entropy of stationary black holes to non-stationary situations in general higher-derivative gravity. One of them, denoted by $S_\text{Wall}$, is constructed by exploiting the boost symmetry of the near-horizon geometry, whereas the other, denoted by $S_\text{dyn}$, is obtained from a covariant phase-space analysis based on the Wald-Iyer Noether charge formalism. While $S_\text{dyn}$ is, by construction, defined only for linearized fluctuations around a stationary black hole solution, $S_\text{Wall}$ does not require such a linearization for its construction. Although the linearization is necessary to interpret $S_\text{Wall}$ as a well-defined notion of entropy, the construction itself naturally contains terms that are higher order in the dynamical fluctuations. By comparing the technical structures underlying the two constructions, we clarify the fundamental differences between the methods on which they are based. We demonstrate that while the construction of $S_\text{dyn}$ given the $S_\text{Wall}$ is straightforward, the converse is more subtle. We develop an algorithm to obtain a local expression for $S_\text{Wall}$ from a known expression for $S_\text{dyn}$ in a generic diffeomorphism-invariant theory of gravity, provided certain technical conditions are satisfied. We justify our analytical findings with explicit demonstrations in a particular case: the Riemann-squared example of the higher-derivative theory of gravity.

hep-th↗

arXiv2026

Homothetic Killing horizons in generic Vaidya spacetimes

We study the conformal Killing equation for generic Vaidya-like spacetimes, including those with rotation. We show that these spacetimes admit a unique class of conformal Killing vectors that are homothetic for mass, charge, or rotation parameters being linear functions of the advanced null-time. For the Kerr-Vaidya metric, the solution to the conformal Killing equation exists iff both mass and rotation parameters become dynamic. The presence of a homothetic Killing vector (HKV) for such a spacetime enables one to conformally map the original dynamical spacetime to a stationary spacetime, enabling access to the standard methods pertaining to a Killing horizon. The surface where an HKV becomes null is termed the homothetic Killing horizon. We discuss the thermodynamic properties of such homothetic Killing horizons and formulate a version of the first law (or flux balance law) for spherically symmetric Vaidya spacetimes. We further study the maximal analytic extension of a charged Vaidya metric and indicate its implications for studying particle creation in such backgrounds.

gr-qc↗

arXiv2026

Reconstructing cosmological correlators via dispersion: from cutting to dressing rules

In this work, we investigate how cosmological correlators can be reconstructed by applying the momentum-space dispersion formula to their discontinuities, treating them as functions of momentum variables associated with the corresponding de Sitter Witten diagrams. We focus on conformally coupled and massless polynomial scalar interactions (both IR-divergent and IR-convergent), and consider tree-level de Sitter Witten diagrams. We explicitly utilize the single-cut discontinuity relations, or cutting rules, involving the cosmological correlators recently constructed in arXiv:2512.20720. For diagrams with multiple interaction vertices, we apply the dispersion formula by cutting all internal lines in the diagram one by one, successively, thereby allowing us to reconstruct the full correlator using only lower-point contact-level objects and their discontinuity data, up to contact diagram ambiguities. We also rediscover how the cosmological correlators on the late-time slice of de Sitter space can be obtained from flat-space Feynman diagrams via a set of dressing rules. Our starting point, being the cutting rules for the cosmological correlators, also emphasizes how basic principles, such as unitarity for in-in correlators, can lead us to the dressing rules, which were previously derived in literature following a different method.

hep-th↗

arXiv2025

A single-cut discontinuity for cosmological correlators from unitarity and analyticity

We derive discontinuity relations, also known as cutting rules, and explore the analytic properties of cosmological correlators, fundamental observables of the primordial universe. Our emphasis is on how these relations arise from unitarity and hermitian analyticity in interacting quantum field theories on de Sitter space-time. Instead of analyzing wave-function coefficients, we apply these relations directly to cosmological correlators. By studying conformally coupled and massless scalar fields with $ϕ^n$ self-interactions, we demonstrate that the discontinuity of a cosmological correlator can be expressed as a sum of products of lower-point discontinuities, stemming from a single-cut of one internal line in the corresponding tree-level exchange Witten diagram. Notably, beyond lower-point correlators, the decomposition of the discontinuities of cosmological correlators includes contributions from auxiliary elements that consist of both the real and imaginary parts of the lower-point wave-function coefficients, which have not been reported in the existing literature. Interestingly, depending on whether $n$ is even or odd in a $ϕ^n$ interaction, these different lower-point discontinuities contribute as the leading or sub-leading piece in the late-time limit to the discontinuity relations. Additionally, our single-cut discontinuity relation leads to a decomposition rule for the residue of the cosmological correlators at partial energy singularities, incorporating contributions from these auxiliary objects. Through explicit calculations in several models, we confirm that our discontinuity relations are consistent with results from the in-in formalism. While primarily developed using tree-level exchanges with polynomial interactions, we also demonstrate that our framework can be extended to include loop corrections and cases with derivative interactions.

hep-th↗

arXiv2025

A classical Bousso bound for higher derivative corrections to general relativity

Focussing on theories for which the higher derivative terms are considered as small corrections in the Lagrangian to Einstein's two-derivative theory of general relativity (GR), we prove the classical version of the covariant entropy bound (also known as the Bousso bound) in arbitrary diffeomorphism invariant gravitational theories. Even if the higher derivative corrections are treated perturbatively, we provide instances of specific configurations for which they can potentially violate the Bousso bound. To tackle this obstruction, we propose a modification in the Bousso bound that incorporates the offending contributions from the higher derivative corrections. We argue that the modified Bousso bound that we propose holds to all orders in the higher curvature corrections. Our proposed modifications are equivalent to replacing the Bekenstein-Hawking area term by Wald's definition (with dynamical corrections as suggested by Wall) for the black hole entropy. Hence, the modifications are physically well motivated by results from the laws of black hole mechanics in higher derivative theories.

hep-th↗

arXiv2024

Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries

We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as the $α$-vacuum, in single-field slow-roll inflation. The $α$-vacuum is a one-parameter family of states, including the Bunch-Davies one, that preserves the conformal symmetry of inflationary dynamics in a nearly de-Sitter space-time. Working within the leading slow-roll approximation, we compute the four-point scalar correlator (the trispectrum) in $α$-vacuum using the in-in formalism. We check that the conformal Ward identities are met between the three and four-point scalar $α$-vacua correlators. Surprisingly, this contrasts the previously reported negative result of the Ward identities being violated between the two and the three-point correlators. We have also extended the wave-functional method, previously used for correlators with Bunch-Davies initial condition, to compute the three and four-point scalar correlators in $α$-vacua. The results obtained from the wave-function method match the corresponding in-in results, adding further justification to our check of Ward identities with $α$-vacua correlators.

hep-th↗

arXiv2023

Entropy-current for dynamical black holes in Chern-Simons theories of gravity

We construct an entropy current and establish a local version of the classical second law of thermodynamics for dynamical black holes in Chern-Simons (CS) theories of gravity. We work in a chosen set of Gaussian null coordinates and assume the dynamics to be small perturbations around the Killing horizon. In explicit examples of both purely gravitational and mixed gauge gravity CS theories in $(2+1)$ and $(4+1)$-dimensions, the entropy current is obtained by studying the off-shell structure of the equations of motion evaluated on the horizon. For the CS theory in $(2+1)$ dimensions, we argue that the second law holds to quadratic order in perturbations by considering it as a low energy effective field theory with the leading piece given by Einstein gravity. In all such examples, we show that the construction of entropy current is invariant under the reparameterization of the null horizon coordinates. Finally, extending an existing formalism for diffeomorphism invariant theories, we construct an abstract proof for the linearised second law in arbitrary Chern-Simons theories in any given odd dimensions by studying the off-shell equations of motion. As a check of consistency, we verify that the outcome of this algorithmic proof matches precisely with the results obtained in explicit examples.

hep-th↗

arXiv2022

Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law

This work extends the proof of a local version of the linearized second law involving an entropy current with non-negative divergence by including the arbitrary non-minimal coupling of scalar and $U(1)$ gauge fields with gravity. In recent works, the construction of entropy current to prove the linearized second law rested on an important assumption about the possible matter couplings to gravity: the corresponding matter stress tensor was assumed to satisfy the null energy conditions. However, the null energy condition can be violated, even classically, when the non-minimal coupling of matter fields to gravity is considered. Considering small dynamical perturbations around stationary black holes in diffeomorphism invariant theories of gravity with non-minimal coupling to scalar or gauge fields, we prove that an entropy current with non-negative divergence can still be constructed. The additional non-minimal couplings that we have incorporated contribute to the entropy current, which may even survive in the equilibrium limit. We also obtain a spatial current on the horizon apart from the entropy density in out-of-equilibrium situations. We achieve this by using a boost symmetry of the near horizon geometry, which constraints the off-shell structure of a specific component of the equations of motion with newer terms due to the non-minimal couplings. The final expression for the entropy current is $U(1)$ gauge-invariant for gauge fields coupled to gravity. We explicitly check that the entropy current obtained from our abstract arguments is consistent with the expressions already available in the literature for specific model theories involving non-minimal coupling of matter with higher derivative theories of gravity. Finally, we also argue that the physical process version of the first law holds for these theories with arbitrary non-minimal matter couplings.

hep-th↗

arXiv2022

The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity

We consider diffeomorphism invariant theories of gravity with arbitrary higher derivative terms in the Lagrangian as corrections to the leading two derivative theory of Einstein's general relativity. We construct a proof of the zeroth law of black hole thermodynamics in such theories. We assume that a stationary black hole solution in an arbitrary higher derivative theory can be obtained by starting with the corresponding stationary solution in general relativity and correcting it order by order in a perturbative expansion in the coupling constants of the higher derivative Lagrangian. We prove that surface gravity remains constant on its horizon when computed for such stationary black holes, which is the zeroth law. We argue that the constancy of surface gravity on the horizon is related to specific components of the equations of motion in such theories. We further use a specific boost symmetry of the near horizon space-time of the stationary black hole to constrain the off-shell structure of the equations of motion. Our proof for the zeroth law is valid up to arbitrary order in the expansion in the higher derivative couplings.

hep-th↗

arXiv2022

A CFT interpretation of cosmological correlation functions in $α-$vacua in de-Sitter space

de-Sitter(dS) space allows for a generalized class of vacua, known as $α-$vacua, described by some parameters. The Bunch-Davies (BD) vacua is a point in this parameter space. The cosmological correlation function is mostly discussed in BD vacuum in four dimensions and can be interpreted as $CFT_3$ correlation function of certain operators. However, the correlation function in $α-$vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in $α-$vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the $α-$vacua can be related to three-dimensional CFT correlation functions if we relax the requirement of consistency with OPE limit. Relaxation of consistency with OPE limit can be naturally achieved in momentum space.

hep-th↗

arXiv2021

An entropy current and the second law in higher derivative theories of gravity

We construct a proof of the second law of thermodynamics in an arbitrary diffeomorphism invariant theory of gravity working within the approximation of linearized dynamical fluctuations around stationary black holes. We achieve this by establishing the existence of an entropy current defined on the horizon of the dynamically perturbed black hole in such theories. By construction, this entropy current has non-negative divergence, suggestive of a mechanism for the dynamical black hole to approach a final equilibrium configuration via entropy production as well as the spatial flow of it on the null horizon. This enables us to argue for the second law in its strongest possible form, which has a manifest locality at each space-time point. We explicitly check that the form of the entropy current that we construct in this paper exactly matches with previously reported expressions computed considering specific four derivative theories of higher curvature gravity. Using the same set up we also provide an alternative proof of the physical process version of the first law applicable to arbitrary higher derivative theories of gravity.

hep-th↗

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↗

arXiv2018

Path-Integral Complexity for Perturbed CFTs

In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories. Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings. Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence. Last but not the least, we estimate contributions to complexity from relevant perturbations.

hep-th↗

arXiv2017

Fundamental Flavours, Fields and Fixed Points: A Brief Account

In this article we report on a preliminary study, {\it via} Holography, of infrared fixed points in a putative strongly coupled SU$(N_c)$ gauge theory, with $N_f$ fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently {\it effective} or a {\it bottom up} approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: AdS$_m \times {\mathbb R}^n$--type, and AdS$_m \times$EAdS$_n$--type, where $m$ and $n$ are suitable integers. Both these classes of solutions are {\it non-perturbative} in back-reaction. The AdS$_m \times$EAdS$_n$--type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS$_5$ ultraviolet to both an AdS$_2$ and an AdS$_3$ IR.

hep-th↗

arXiv2017

Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories

We introduce a new optimization procedure for Euclidean path integrals which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalently this is interpreted as a position-dependent UV cutoff. For two-dimensional CFT vacua, we find the optimized metric is given by that of a hyperbolic space and we interpret this as a continuous limit of the conjectured relation between tensor networks and Anti--de Sitter (AdS)/conformal field theory (CFT) correspondence. We confirm our procedure for excited states, the thermofield double state, the Sachdev-Ye-Kitaev model and discuss its extension to higher-dimensional CFTs. We also show that when applied to reduced density matrices, it reproduces entanglement wedges and holographic entanglement entropy. We suggest that our optimization prescription is analogous to the estimation of computational complexity.

hep-th↗

arXiv2017

Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT

We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

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↗

arXiv2017

Towards a second law for Lovelock theories

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

hep-th↗