arXiv subjects

Sudipta Mukherji

Publications and source records attributed to Sudipta Mukherji.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamic criticality of coupled oscillators

Strict thermodynamic scaling relations, such as the Rushbrooke inequality, are fundamentally established for equilibrium critical phenomena in the thermodynamic limit. In finite-size dynamical systems exhibiting synchronization, the direct application of such identities is hindered both by the finiteness of the network and the nonequilibrium nature of the spontaneous synchronization transition. To bypass this difficulty, we rigorously study the dynamical counterparts of the order parameter, susceptibility, and specific heat in finite systems of dynamical oscillators with nonlinear coupling. By measuring these quantities as a function of system size, we extract the associated critical exponents governing the transition. The validity of our thermodynamic mapping is tested by directly confirming the Rushbrooke inequality. Our results establish that standard equilibrium thermodynamic scaling architectures can be systematically applied to the finite-size scaling of nonequilibrium synchronization dynamics.

nlin.AO↗

arXiv2026

Criticality of ISCOs and AdS/CFT

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $γ$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{Δ_H}$ to $γ$ in the dual CFT, and dsicuss the implications of our results.

hep-th↗

arXiv2025

Static spheres and Aschenbach effect for black holes in massive gravity

In this paper, we study the trajectories of massive and massless particles in four dimensional static and spherically symmetric black holes in de Rham-Gabadadze-Tolley (dRGT) massive gravity theory via phase-plane analysis and point out several novel features. In particular, we show the existence of a static sphere, a finite radial distance outside the black holes in these theories, where a massive particle can be at rest, as seen by an asymptotic zero angular momentum observer. Topological arguments show that the stable and unstable static spheres, which come in pairs, have opposite charges. In the presence of angular momentum, we first study the behaviour of massless particles and find the presence of stable and unstable photon spheres in both neutral and charged black holes. Subsequently, we study the motion of massive test particles around these black holes, and find one pair of stable and unstable time-like circular orbits (TCOs), such that the stable and unstable TCO's are disconnected in certain regions. Computing the angular velocity $Ω_{\text{\tiny CO}}$ of the TCOs, measured by a static observer at rest, shows the unusual nature of its monotonic increase with the radius of TCO, near the location of stable photon sphere. This confirms the existence of Aschenbach effect for spherically symmetric black holes in massive gravity, which was only found to exist in rapidly spinning black holes, with the only other exception being the rare example of gravity coupled to quasi-topological electromagnetism.

gr-qc↗

arXiv2024

Topology of critical points in boundary matrix duals

Computation of topological charges of the Schwarzschild and charged black holes in AdS in canonical and grand canonical ensembles allows for a classification of the phase transition points via the Bragg-Williams off-shell free energy. We attempt a topological classification of the critical points and the equilibrium phases of the dual gauge theory via a phenomenological matrix model, which captures the features of the ${\cal{N}}=4$, $SU(N)$ Super Yang-Mills theory on $S^3$ at finite temperature at large $N$. With minimal modification of parameters, critical points of the matrix model at finite chemical potential can be classified as well. The topological charges of locally stable and unstable dynamical phases of the system turn out to be opposite to each other, totalling to zero, and this matches the analysis in the bulk.

hep-th↗

arXiv2023

Cardy-Verlinde formula from boundary matrix model

Cardy-Verlinde (CV) formula relates the entropy of a conformal field theory (CFT) in arbitrary dimensions to its total energy (with an appropriate insertion of additional internal energy for charged systems) and Casimir energy. While several aspects of the CV formula have been tested directly for weakly coupled CFTs, the aim of the present paper is to verify it in the strongly coupled regime, by employing a phenomenological matrix model, which captures the features of the ${\cal{N}}=4$, $SU(N)$ Super Yang-Mills theory on $S^3$ at finite temperature and chemical potential at large $N$.

hep-th↗

arXiv2023

Topology of Hawking-Page transition in Born-Infeld AdS black holes

Black holes in anti de Sitter (AdS) spacetimes undergo phase transitions which typically lead to the existence of critical points, that can be classified using topological techniques. Availing the Bragg-Williams construction which provides an off-shell free energy formalism, we compute the topological charge of the Hawking-Page (HP) transition for Einstein-Born-Infeld black holes in anti de Sitter spacetime and match the result with the confinement-deconfinement transition in the dual gauge theory, which turn out to be in perfect agreement.

gr-qc↗

arXiv2022

Novel logarithmic corrections to black hole entropy

For a thermodynamic system, apart from thermal fluctuations, there are also fluctuations in thermodynamic volume when the system is in contact with a volume reservoir. For the case of black holes in anti-de Sitter spacetimes, the effect of thermal fluctuations on the entropy is well studied. The aim of this work is to compute novel logarithmic corrections to black hole entropy coming from simultaneous fluctuations of energy and thermodynamic volume. We work in the isothermal-isobaric ensemble and first obtain a general form of corrections to entropy which are valid for any thermodynamic system. Applying the formalism to Kerr black holes in AdS reveals that the black hole entropy gets corrected as: $\mathcal{S} = S_0 - k \ln S_0 + \cdots$ where $S_0$ is given by the Bekenstein-Hawking formula and $k = - 1$. The same leading coefficient is also obtained in the canonical ensemble, i.e. by considering energy fluctuations alone. This coefficient is found to be unaltered in the slowly rotating and high temperature limits.

hep-th↗

arXiv2022

Milne Spacetime with Conical Defect: Some Holographic Studies

In this work, we initiate a holographic study of field theory on time dependent background with conical defect. We focus on the Milne space-time to which, in the absence of cosmological constant, at late time any hyperbolic Friedmann-Robertson-Walker metric flows to. When the Milne vacuum is represented by the adiabatic one, we are able to compute the two point correlators of operators which are dual to the massive scalars in the bulk AdS-Milne background with defect. We find, for both twisted and untwisted operators, the correlators can be represented as the sum over images. This sum can be carried out explicitly to write the results in compact forms.

hep-th↗

arXiv2022

Topology of critical points and Hawking-Page transition

Using the Bragg-Williams construction of an off-shell free energy we compute the topological charge of the Hawking-Page transition point for black holes in AdS. A computation following from a related off-shell effective potential in the boundary gauge dual matches the value of topological charge obtained in the bulk. We also compute the topological charges of the equilibrium phases of these systems, which follow from the saddle points of the appropriate free energy. The locally stable and unstable phases turn out to have topological charges opposite to each other, with the total being zero, in agreement with the result obtained from a related construction [arXiv:2208.01932].

hep-th↗

arXiv2022

Logarithmic corrections to the entropy function of black holes in the open ensemble

An `open' or $(μ,P,T)$-ensemble describes equilibrium systems whose control parameters are chemical potential $μ$, pressure $P$ and temperature $T$. Such an unconstrained ensemble is seldom used for applications to standard thermodynamic systems due to the fact that the corresponding free energy identically vanishes as a result of the Euler relation. However, an open ensemble is perfectly regular for the case of black holes, as the entropy is a quasi-homogeneous function of extensive thermodynamic variables with scaling dictated by the Smarr formula. Following a brief discussion on thermodynamics in the open ensemble, we compute the general form of logarithmic corrections to the entropy of a typical system, due to fluctuations in energy, thermodynamic volume and a generic charge $N$. This is then used to obtain the exact analytic form of the logarithmically corrected black hole entropy for charged and rotating black holes in anti-de Sitter spacetimes.

hep-th↗

arXiv2022

Logarithmic corrections to black hole entropy and holography

We compute logarithmic corrections to the black hole entropy $S_{\rm bh}$ in a holographic set up where the cosmological constant $Λ$ and Newton's constant $G_D$ are taken to be thermodynamic parameters, related to variations in bulk pressure $P$ and central charge $c$. In the bulk, the logarithmic corrections are of the form: $\mathcal{S} = S_{\rm bh} - k \ln S_{\rm bh} + \cdots$ arising due to fluctuations in thermodynamic volume, induced by a variable $Λ$, in addition to energy fluctuations. We explicitly compute this coefficient $k$ for the BTZ black hole and show that the result matches with the one coming from the logarithmic corrections to the Cardy's formula. We propose an entropy function in the CFT, which exactly reproduces the logarithmic corrections to black hole entropy in arbitrary dimensions.

hep-th↗

arXiv2019

A note on Quantum Fields in Conformally flat Space-times

We develop a technique relating scalar fields with different masses in different conformally flat space-times. We apply this technique to the case of FRW space-times, with $k=\pm 1,0$, and discuss several examples. We also study various energy conditions and discuss how they constrain the space-times related by this technique. In addition, we use this technique to study correlators for the related space-times in an example.

gr-qc↗

arXiv2017

Non-vacuum AdS cosmology and comments on gauge theory correlator

Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the non-vacuum Kasner-AdS geometry and its solitonic generalization. To characterize these space-times, we provide ways to embed them in higher dimensional flat space-times. General space-like geodesics are then studied and used to compute the two point boundary correlators within the geodesic approximation.

hep-th↗

arXiv2015

A note on AdS cosmology and gauge theory correlator

Using AdS/CFT prescription, we compute two point Yang-Mills correlator on a constant time slice for the Kasner background. Pushing the surface close to the initial singularity, we find, in some cases, the correlator does not develop pole. This is consistent with the observations made in a recent work. We further numerically calculate similar correlator where the bulk is a Kasner AdS soliton. We find that the qualitative behaviour of the correlator remains unchanged.

hep-th↗

arXiv2013

Anisotropic branes

We present a class of anisotropic brane configurations which shows BKL oscillations near their cosmological singularities. Near horizon limits of these solutions represent Kasner space embedded in AdS background. Dynamical probe branes in these geometries inherit anisotropies from the background. Amusingly, for a probe M5 brane, we find that there exists a parameter region where three of its world-volume directions expand while the rest contract.

hep-th↗

arXiv2012

A Comparative Note on Tunneling in AdS and in its Boundary Matrix Dual

For charged black hole, within the grand canonical ensemble, the decay rate from thermal AdS to the black hole at a fixed high temperature increases with the chemical potential. We check that this feature is well captured by a phenomenological matrix model expected to describe its strongly coupled dual. This comparison is made by explicitly constructing the kink and bounce solutions around the de-confinement transition and evaluating the matrix model effective potential on the solutions.

hep-th↗

arXiv2011

Anisotropic Power Law Inflation from Rolling Tachyons

We provide an explicit solution representing an anisotropic power law inflation within the framework of rolling tachyon model. This is generated by allowing a non-minimal coupling between the tachyon and the world-volume gauge field on non-BPS D3 brane. We also show that this solution is perturbatively stable.

hep-th↗

arXiv2011

Black hole phase transitions via Bragg-Williams

We argue that a convenient way to analyze instabilities of black holes in AdS space is via Bragg-Williams construction of a free energy function. Starting with a pedagogical review of this construction in condensed matter systems and also its implementation to Hawking-Page transition, we study instabilities associated with hairy black holes and also with the $R$-charged black holes. For the hairy black holes, an analysis of thermal quench is presented.

hep-th↗