arXiv subjects

Pratik Roy

Publications and source records attributed to Pratik Roy.

At least 19 recordsLinked to original sources

arXiv2026

Quasi-local form for $\alpha$--$z$ R\'enyi QNEC from fixed-ray escorts

The fixed-ray escort integral representation expresses $\alpha$--$z$ R\'enyi divergence as an average over ordinary relative entropy of a family of escort states. Working in the standard UV-regulated density-matrix description of QFT subregions, we use this representation to derive an escort-averaged entanglement first law, an escort-averaged representation of the $\alpha$--$z$ information kernel, and an escort-averaged Bekenstein-type bound for ball-shaped regions in conformal field theories. For the conjectural $\alpha$--$z$ quantum null energy condition (QNEC), we obtain a quasi-local form in which the null energy is evaluated in an escort-averaged state and is corrected by an escort-transport term encoding the failure of escort formation to commute with restriction to a null-deformed region. The $z=\alpha$ specialization gives a similar quasi-local form of the R\'enyi QNEC for sandwiched R\'enyi divergence. We explicitly compute the R\'enyi QNEC, including the explicit escort transport term, for coherent-state excitations in a free scalar field theory. For the same coherent family, we obtain a positive $\alpha$--$z$ null Hessian, verifying the conjectured diagonal $\alpha$--$z$ QNEC for this family.

hep-th↗

arXiv2026

Fixed-ray escort representations of sandwiched and $\alpha$--$z$ R\'enyi divergences on von Neumann algebras

We represent sandwiched and $\alpha$-$z$ R\'enyi divergences as averages of ordinary relative entropy. The $\alpha$-$z$ R\'enyi divergence is shown to be an integral over the relative entropy of a canonical family of fixed-ray escort states along the ray $z=c\alpha$. We prove this representation for normal states on an arbitrary von Neumann algebra, using Haagerup non-commutative $L^p$ spaces and interpolation. The formula holds for every $z>0$: for $0<\alpha<1$ it holds when the support of the first state is contained in that of the reference state, and for $\alpha>1$ it holds whenever the divergence is finite. When the lower-order support condition fails, we identify the exact fixed-ray support-boundary term. The representation yields a monotone escort profile and a convex order potential. We use these to reformulate one-shot testing converses, exact sandwiched strong-converse exponents, and work-extraction reliability as signed-area or level-crossing statements, and discuss a restricted two-parameter pair-conversion rate.

quant-ph↗

arXiv2026

No off-diagonal quantum focusing for R\'enyi divergences

The quantum focusing conjecture is a mathematical expression of the idea that semiclassical gravity remains universally attractive. Its off-diagonal part is a monotonicity condition on the double null shape variation of relative entropy on distinct null generators, and has been argued to follow from strong subadditivity of entanglement entropy. Recent proof of a diagonal R\'enyi quantum null energy condition raises the question: does a full R\'enyi focusing statement also hold? We answer this question negatively for any R\'enyi-type divergence satisfying data processing, tensor additivity, and matched classical--quantum conditioning.

hep-th↗

arXiv2026

A general proof of integer R\'enyi QNEC

The R\'enyi quantum null energy condition conjectures that the second null shape variation of the sandwiched R\'enyi divergence (SRD) of an excited state relative to the vacuum is non-negative in local Poincar\'e-invariant quantum field theory, giving a one-parameter generalization of the quantum null energy condition (QNEC). We prove R\'enyi QNEC for all integer R\'enyi parameters $n\geq 2$ for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum. Concretely, for any $\sigma$-finite von Neumann algebra with such an inclusion, we prove log-convexity, under the associated null-translation semigroup, of the Kosaki $L^n$ norm of any normal positive functional with finite $L^n$ norm.

hep-th↗

arXiv2026

Residue sums for superconformal indices

We study superconformal indices of four-dimensional $SU(N)$ gauge theories with $\mathcal{N}=1,2,4$ supersymmetry. The usual representation of a gauge theory index involves multiple contour integrals and reflects the BPS spectrum at zero Yang-Mills coupling. To find an alternative, closed form expression, it is natural to attempt an evaluation of the integrals through residues. However, the presence of non-isolated essential singularities prevents a straightforward evaluation. We show how this difficulty can be resolved by fixing the residual Weyl symmetry of the integral. This allows us to evaluate the residue sums for superconformal indices of $SU(2)$ gauge theories in terms of basic and elliptic hypergeometric series. For the Macdonald index of the $\mathcal{N}=4$ $SU(2)$ super Yang--Mills theory, we show how known transformation formulas for basic hypergeometric series can be used to simplify the residue sum. We observe that the simplified form encodes features of the BPS spectrum at non-zero coupling and suggests the absence of fortuitous or non-graviton operators in the Macdonald sector. Furthermore, we evaluate the residue sums for the Macdonald and full superconformal indices of a general class of $SU(2)$ gauge theories. In the process, we find various applications to the theory of basic and elliptic hypergeometric integrals, including a convergent residue sum for Spiridonov's elliptic beta integral. Finally, we discuss the generalization of our method to higher rank gauge groups and evaluate the $\mathcal{N}=4$ $SU(3)$ Macdonald index in closed form.

hep-th↗

arXiv2025

Quantum null energy condition in quenched 2d CFTs

The quantum null energy condition (QNEC) is a lower bound on the expectation value of the null-null component of the energy-momentum tensor in terms of null variations of the entanglement entropy. A stronger version of the QNEC (the primary QNEC) is expected to hold in 1+1 dimensional conformal field theories (CFT). QNEC has been shown to impose non-trivial quantum thermodynamic restrictions on irreversible entropy production in quenches in 1+1 dimensional holographic CFTs. It is therefore natural to study if QNEC imposes similar bounds in other quench setups. In this paper we study QNEC in the Calabrese-Cardy global and local joining quenches using standard CFT techniques. In the global quench we show that the primary QNEC must hold at sufficiently early times and find that it imposes bounds on the four point correlators of twist fields in a boundary state. This is a constraint on the set of boundary states that satisfy the primary QNEC. Furthermore, we find that a violation of the primary QNEC implies a violation of the averaged null energy condition (ANEC) in a conformally transformed frame. In the local quench we find similar bounds on four point correlators from both the primary and the usual QNEC.

hep-th↗

arXiv2025

Machine learning automorphic forms for black holes

Modular, Jacobi, and mock-modular forms serve as generating functions for BPS black hole degeneracies. By training feed-forward neural networks on Fourier coefficients of automorphic forms derived from the Dedekind eta function, Eisenstein series, and Jacobi theta functions, we demonstrate that machine learning techniques can accurately predict modular weights from truncated expansions. Our results reveal strong performance for negative weight modular and quasi-modular forms, particularly those arising in exact black hole counting formulae, with lower accuracy for positive weights and more complicated combinations of Jacobi theta functions. This study establishes a proof of concept for using machine learning to identify how data is organized in terms of modular symmetries in gravitational systems and suggests a pathway toward automated detection and verification of symmetries in quantum gravity.

hep-th↗

arXiv2025

Generalized Clausius inequalities and entanglement production in holographic two-dimensional CFTs

Utilizing quantum information theory, it has been shown that irreversible entropy production is bounded from both below and above in physical processes. Both these bounds are positive and generalize the Clausius inequality. Such bounds are, however, obtained from distance measures in the space of states, which are hard to define and compute in quantum field theories. We show that the quantum null energy condition (QNEC) can be utilized to obtain both lower and upper bounds on irreversible entropy production for quenches leading to transitions between thermal states carrying uniform momentum density in two dimensional holographic conformal field theories. We achieve this by refining earlier methods and developing an algebraic procedure for determining HRT surfaces in arbitrary Bañados-Vaidya geometries which are dual to quenches involving transitions between general quantum equilibrium states (e.g. thermal states) where the QNEC is saturated. We also discuss results for the growth and thermalization of entanglement entropy for arbitrary initial and final temperatures and momentum densities. The rate of quadratic growth of entanglement just after the quench depends only on the change in the energy density and is independent of the entangling length. For sufficiently large entangling lengths, the entanglement tsunami phenomenon can be established. Finally, we study recovery of the initial state from the evolving entanglement entropy and argue that the Renyi entropies should give us a refined understanding of scrambling of quantum information.

hep-th↗

arXiv2025

Colored Jones Polynomials and the Volume Conjecture

Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-colored Jones polynomials or adjoint Jones polynomials. Training a subset of the data using a fully connected feedforward neural network, we predict the volume of the knot complement of hyperbolic knots from the adjoint Jones polynomial or its evaluations with 99.34% accuracy. A function of the adjoint Jones polynomial evaluated at the phase $q=e^{ 8 πi / 15 }$ predicts the volume with nearly the same accuracy as the neural network. From an analysis of 2-colored and 3-colored Jones polynomials, we conjecture the best phase for $n$-colored Jones polynomials, and use this hypothesis to motivate an improved statement of the volume conjecture. This is tested for knots for which closed form expressions for the $n$-colored Jones polynomial are known, and we show improved convergence to the volume.

math.GT↗

arXiv2024

Massive fields in AdS from Constructive Holography

Collective field theory offers a constructive framework for exploring the AdS/CFT duality. In this article, we focus on constructing rotations within the light-front quantized collective field theory for the full set of spatial coordinates in the dual bulk AdS spacetime. Two intricate aspects require attention: how rotations involving the emergent holographic coordinate are implemented, and how rotations that involve the spatial coordinates participating in the construction of the light-cone coordinates $X^{\pm}$ are realized. Our construction is in agreement with Metsaev's construction directly in the gravity theory. Additionally, we derive the eigenfunctions of the AdS mass operator, which dictate the GKPW rule for the emergent higher-dimensional theory.

hep-th↗

arXiv2024

Reconstructing the spacetime dual to a free matrix

In this paper we consider the collective field theory description of the singlet sector of a free matrix field in 2+1 dimensions. This necessarily involves the study of $k$-local collective fields, which are functions of $2k+1$ coordinates. We argue that these coordinates have a natural interpretation: the $k$-local collective field is a field defined on an AdS$_4\times$S$^{k-2}\times$S$^{k-1}$ spacetime. The modes of a harmonic expansion on the S$^{k-2}\times$S$^{k-1}$ portion of the spacetime leads to the spinning bulk fields of the dual gravity theory.

hep-th↗

arXiv2024

Bounds on $T\bar {T}$ deformation from entanglement

Motivated by the existence of complex spectrum in $T\bar T$-deformed CFTs, in this paper we revisit the broadly studied topic of (holographic) entanglement entropy in the deformed theory to investigate its complex behaviour. As a concrete example, we show that in case of a 1+1 dimensional holographic CFT at finite temperature $β^{-1}$ and chemical potential $Ω$, the holographic entanglement entropy in the deformed theory remains to be real only within the range $-\frac{β^2}{8π^2}\frac{(1-Ω^2)^2}{Ω^2}< μ< \frac{β^2}{8π^2}(1-Ω^2) $ of the deformation parameter. While the upper bound overlaps with the familiar Hagedorn bound in the deformed theory, the novel lower bound on the negative values of the deformation parameter does not show up in thermodynamic quantities. However, from a holographic perspective we show that this intriguing lower bound is related to a spacelike to null transition of the associated Ryu-Takayanagi surface in the deformed geometry. We also investigate the Quantum Null Energy Condition in the deformed theory, within its regime of validity.

hep-th↗

arXiv2024

Holography of a single free matrix

In this paper we consider the collective field theory description of a single free massless scalar matrix theory in 2+1 dimensions. The collective fields are given by $k$-local operators obtained by tracing a product of $k$-matrices. For $k=2$ and $k=3$ we argue that the collective field packages the fields associated to a single and two Regge trajectories respectively. We also determine the coordinate transformation between the coordinates of the collective field theory and the bulk AdS space time. This is used to verify that the bulk equations of motion holds in the collective field theory description.

hep-th↗

arXiv2023

Proof of Renyi QNEC for free fermions

Quantum null energy condition (QNEC) is usually stated as a bound on the expectation value of null components of the stress energy tensor at a point in terms of second null shape variations of the entanglement entropy at the same point. It can be recast as the statement that the sign of the second null shape variation of the relative entropy of any state with respect to the vacuum is positive. Using instead a Renyi generalization of relative entropy, called sandwiched Renyi divergence (SRD), leads to what is termed the Renyi QNEC: the second null shape variation of SRD of any state with respect to the vacuum is positive. In this work, we prove the Renyi QNEC for free and superrenormalizable fermionic quantum field theories in spacetime dimensions greater than 2 using null quantization, for the case where the Renyi parameter $n>1$. We end with comments on multiple possible generalizations.

hep-th↗

arXiv2022

Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC

The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a sub-region along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, are necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentum which are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the non-saturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length $l$ always thermalizes in time $l/2$ with an exponent $3/2$. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any $l$, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

hep-th↗

arXiv2022

Erasure tolerant quantum memory and the quantum null energy condition in holographic systems

Investigating principles for storage of quantum information at finite temperature with minimal need for active error correction is an active area of research. We bear upon this question in two-dimensional holographic conformal field theories via the quantum null energy condition (QNEC) that we have shown earlier to implement the restrictions imposed by quantum thermodynamics on such many-body systems. We study an explicit encoding of a logical qubit into two similar chirally propagating excitations of finite von-Neumann entropy on a finite temperature background whose erasure can be implemented by an appropriate inhomogeneous and instantaneous energy-momentum inflow from an infinite energy memoryless bath due to which the system transits to a thermal state. Holographically, these fast erasure processes can be depicted by generalized AdS-Vaidya geometries described previously in which no assumption of specific form of bulk matter is needed. We show that the quantum null energy condition gives analytic results for the minimal finite temperature needed for the deletion which is larger than the initial background temperature in consistency with Landauer's principle. In particular, we find a simple expression for the minimum final temperature needed for the erasure of a large number of encoding qubits. We also find that if the encoding qubits are localized over an interval shorter than a specific localization length, then the fast erasure process is impossible, and furthermore this localization length is the largest for an optimal amount of encoding qubits determined by the central charge. We estimate the optimal encoding qubits for realistic protection against fast erasure. We discuss possible generalizations of our study for novel constructions of fault-tolerant quantum gates operating at finite temperature.

hep-th↗

arXiv2018

Geroch Group Description of Bubbling Geometries

The Riemann-Hilbert approach to studying solutions of supergravity theories allows us to associate spacetime independent monodromy matrices (matrices in the Geroch group) with solutions that effectively only depend on two spacetime coordinates. This offers insights into symmetries of supergravity theories, and in the classification of their solutions. In this paper, we initiate a systematic study of monodromy matrices for multi-center solutions of five-dimensional U(1)$^3$ supergravity. We obtain monodromy matrices for a class of collinear Bena-Warner bubbling geometries. We show that for this class of solutions, monodromy matrices in the vector representation of SO(4,4) have only simple poles with residues of rank two and nilpotency degree two. These properties strongly suggest that an inverse scattering construction along the lines of [arXiv:1311.7018 [hep-th]] can be given for this class of solutions, though it is not attempted in this work. Along the way, we clarify a technical point in the existing literature: we show that the so-called "spectral flow transformations" of Bena, Bobev, and Warner are precisely a class of Harrison transformations when restricted to the situation of two commuting Killing symmetries in five-dimensions.

hep-th↗

arXiv2018

Linearized Einstein's Equation around pure BTZ from Entanglement Thermodynamics

It is known that the linearized Einstein's equation around the pure $AdS$ can be obtained from the constraint $ ΔS = Δ\left< H \right> $, known as the first law of entanglement, on the boundary $CFT$. The corresponding dual state in the boundary $CFT$ is the vacuum state around which the linear perturbation is taken. In this paper we revisit this question, in the context of $ {AdS}_3/{CFT}_2 $, with the state of the boundary ${CFT}_2$ as a thermal state. The corresponding dual geometry is a planar BTZ black hole. By considering the linearized perturbation around this black brane we show that Einstein's equation follows from the first law of entanglement. The modular Hamiltonian in a thermal state of the ${CFT}_2$ that we have used has been recently found in arXiv:1608.01283 [cond-mat.stat-mech].

hep-th↗