arXiv subjects

R. Loganayagam

Publications and source records attributed to R. Loganayagam.

At least 19 recordsLinked to original sources

arXiv2026

Loops Outside a Black Hole

We present a general conjecture for evaluating multiple discontinuity integrals arising from bulk loop diagrams in the gravitational Schwinger-Keldysh geometry. This generalises earlier tree-level results in arXiv:2403.10654 to arbitrary bulk loops with no tadpoles (for scalar non-derivative interactions). The conjectured result takes the form of loop integrals performed in a real-time finite-temperature field theory living on the exterior of the black hole. We check our conjecture against all one-loop and many two and three-loop contributions to two, three, and four-point functions. Our diagrammatic rules for the exterior field theory are consistent with microscopic unitarity and thermality at arbitrary loop level. We also remark on a novel approach to real-time finite-temperature holography based on bulk Schwinger-Dyson equations, with the vertices integrated over the black hole exterior.

hep-th↗

arXiv2025

Influence Phase of a dS Observer II: Electromagnetism

We extend our proposal for static patch holography made in part I (arXiv:2309.07290) to the case of electromagnetism. Using the on-shell action on de Sitter Schwinger-Keldysh (dS-SK) geometry, we derive the influence phase of an observer in dS$_{d+1}$ interacting with bulk electromagnetic fields. This influence phase, computed with appropriate boundary conditions and counterterms, encodes the physics of electromagnetic radiation reaction and corresponding dS Hawking radiation. The self-force is rendered finite through holographic renormalisation. In the short-time limit, we reproduce electromagnetic flat space radiation reaction ala Abraham-Lorentz-Dirac, along with cosmological corrections. We give a fully covariantised expression for this radiation reaction in several even spacetime dimensions. In this process, we also extend many existing results to cosmological spacetimes: multipole expansions including smearing effects, non-relativistic expansion for electromagnetism, and classical renormalisation in odd spacetime dimensions. Further, we review and extend many properties of vector spherical harmonics(VSHs) in arbitrary dimensions, explain the relation between spherical and cartesian VSH, and derive an addition theorem for VSHs.

hep-th↗

arXiv2025

An Exterior EFT for Hawking Radiation

We present a general conjecture for evaluating the multiple-discontinuity integrals that appear in real-time holography using gravitational Schwinger-Keldysh (grSK) geometry. Our conjecture is valid for arbitrary non-derivative interactions with any number of bulk tree-level exchanges. It is also consistent with a unitary exterior EFT at finite temperature with correct causal structure. We present a set of Feynman rules underlying this exterior EFT and illustrate it with the computation of four and five-point functions.

hep-th↗

arXiv2024

Influence Phase of a dS Observer I : Scalar Exchange

Inspired by real-time computations in AdS black holes, we propose a method to obtain the influence phase of a cosmological observer by calculating the on-shell action on a doubled spacetime geometry. The influence phase is the effective action for an open system: for a dS static patch observer coupled to a scalar field it incorporates the radiation reaction due to the bulk fields and their dS Hawking radiation. For a general extended source in dS, we describe how to account for finite size effects. In the long-time limit, we get a Markovian open quantum system susceptible to cosmological fluctuations, whereas the short-time limit reproduces the worldline theory of flat-space radiation reaction. We also present a fully covariantised form for the cubic corrections to the radiation reaction in even spacetime dimensions, including Hubble contributions, and find an intriguing recursive structure across dimensions.

hep-th↗

arXiv2023

Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours

We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the ramification points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, the energy density operator does not possess an exponentially growing mode, associated with `pole-skipping' (from one such apparent singularity). Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.

hep-th↗

arXiv2023

Holographic open quantum systems: Toy models and analytic properties of thermal correlators

We present a unified picture of open quantum systems, the theory of a system probing a noisy thermal environment, distilling lessons learnt from previous holographic analyses. Our treatment is applicable both when the system is coupled to short-lived (Markovian), and long-lived (non-Markovian) environmental degrees of freedom. The thermal environment is modeled using an asymptotically AdS black hole, and the systems of interest are simple probe field theories. The effective stochastic dynamics of the system is governed by real-time thermal correlators, which we compute using the gravitational Schwinger-Keldysh (grSK) geometry. We describe the structure of arbitrary tree-level contact and exchange Witten diagrams in the grSK geometry. In particular, we argue, that all such diagrams reduce to integrals supported on a single copy of the exterior of the black hole. The integrand is obtained as a multiple discontinuity of a function comprising ingoing boundary-bulk propagators, monodromy functions which appear as radial Boltzmann weights, and vertex factors. These results allow us to deduce the analytic structure of real-time thermal n-point functions in holographic CFTs. We illustrate the general statements by a two-dimensional toy model, dual to fields in the BTZ background, which we argue captures many of the essential features of generic open holographic QFTs.

hep-th↗

arXiv2023

An effective description of charge diffusion and energy transport in a charged plasma from holography

We discuss the physics of sound propagation and charge diffusion in a plasma with non-vanishing charge density. Our analysis culminates the program initiated in arXiv:2108.03244 to construct an open effective field theory of low-lying modes of the stress tensor and charge current in such plasmas. We model the plasma holographically as a Reissner-Nordstrom-AdS black hole, and study linearized fluctuations of longitudinally polarized scalar gravitons and photons in this background. We demonstrate that the perturbations can be decoupled and repackaged into the dynamics of two designer scalars, whose gravitational coupling is modulated by a non-trivial dilatonic factor. The holographic analysis allows us to isolate the phonon mode from the charge diffusion mode, and identify the combination of currents that corresponds to each of them. We use these results to obtain the real-time Gaussian effective action, which includes both the retarded response and the associated stochastic (Hawking) fluctuations, accurate to quartic order in gradients.

hep-th↗

arXiv2022

An effective description of momentum diffusion in a charged plasma from holography

We discuss the physics of momentum diffusion in a charged plasma. Following the holographic strategy outlined in arXiv:2012.03999 we construct an open effective field theory for the low-lying modes of the conserved currents. The charged plasma is modeled holographically in terms of a Reissner-Nordstrom-AdS black hole. We analyze graviton and photon fluctuations about this background, decoupling in the process the long-lived momentum diffusion mode from the short-lived charged transport mode. Furthermore, as in the aforementioned reference, we argue that the dynamics of these modes are captured by a set of designer scalars in the background geometry. These scalars have their gravitational coupling modulated by an auxiliary dilaton with long-lived modes being weakly coupled near the spacetime asymptopia. Aided by these observations, we obtain the quadratic effective action that governs the fluctuating hydrodynamics of charge current and stress tensor, reproducing in the process transport data computed previously. We also point out an interesting length scale lying between the inner and outer horizon radii of the charged black hole associated with Ohmic conductivity.

hep-th↗

arXiv2022

The timbre of Hawking gravitons: an effective description of energy transport from holography

Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index (3-d) for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.

hep-th↗

arXiv2021

Effective field theory of stochastic diffusion from gravity

Planar black holes in AdS have long-lived quasinormal modes which capture the physics of charge and momentum diffusion in the dual field theory. How should we characterize the effective dynamics of a probe system coupled to the conserved currents of the dual field theory? Specifically, how would such a probe record the long-lived memory of the black hole and its Hawking fluctuations? We address this question by exhibiting a universal gauge invariant framework which captures the physics of stochastic diffusion in holography: a designer scalar with a gravitational coupling governed by a single parameter, the Markovianity index. We argue that the physics of gauge and gravitational perturbations of a planar Schwarzschild-AdS black hole can be efficiently captured by such designer scalars. We demonstrate that this framework allows one to decouple, at the quadratic order, the long-lived quasinormal and Hawking modes from the short-lived ones. It furthermore provides a template for analyzing fluctuating open quantum field theories with memory. In particular, we use this set-up to analyze the diffusive Hawking photons and gravitons about a planar Schwarzschild-AdS black hole and derive the quadratic effective action that governs fluctuating hydrodynamics of the dual CFT. Along the way we also derive results relevant for probes of hyperscaling violating backgrounds at finite temperature.

hep-th↗

arXiv2020

Heisenberg Picture for Open Quantum Systems

In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete Heisenberg picture for an open quantum system involves multiple image Heisenberg operators for each system observable. For a given system observable, the number of such image operators is equal to the dimension of the environment Hilbert space. We derive a perturbative expression, accurate upto arbitrary orders in the system environment coupling, for these image operators in terms of a single one point operator. This expression depends non-linearly on the state of the environment. This perturbative expression can equivalently be thought of as deforming the operator product on the Hilbert space of the open quantum system. In the Markovian limit, the one point operator evolves by an adjoint Lindblad equation. We illustrate these ideas using a simple spin system.

quant-ph↗

arXiv2020

Fermionic Open EFT from Holography

In this work we initiate the study of open effective field theories of fermions interacting with holographic baths. As a first step in this direction, we explain how the recently identified holographic Schwinger-Keldysh saddles naturally reproduce the Fermi-Dirac statistics of boundary correlators. We study Dirac fermions propagating in the background of a doubled $AdS_{d+1}$ Schwarzchild blackbrane. We solve for both ingoing (quasi-normal) as well as outgoing (Hawking) modes of the Dirac field in a boundary gradient expansion and compare our findings against exact results in $d=2$. The holographic Schwinger-Keldysh boundary conditions automatically select a unique combination of these modes consistent with fermionic KMS relations. Evaluating the bulk on-shell action using these solutions, we obtain an explicit expression for the influence phase of the probe fermion in a gradient expansion.

hep-th↗

arXiv2020

Holographic KMS relations at finite density

We extend the holographic Schwinger-Keldysh prescription introduced in arXiv:1812.08785 to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study real-time fluctuations of the dual CFT held at finite temperature and finite chemical potential. We check our prescription using charged Dirac probe fields. We solve the Dirac equation in a boundary derivative expansion extending the results in arXiv:2011.07039. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dirac factors.

hep-th↗

arXiv2020

Open quantum systems and Schwinger-Keldysh holograms

We initiate the study of open quantum field theories using holographic methods. Specifically, we consider a quantum field theory (the system) coupled to a holographic field theory at finite temperature (the environment). We investigate the effects of integrating out the holographic environment with an aim of obtaining an effective dynamics for the resulting open quantum field theory. The influence functionals which enter this open effective action are determined by the real-time (Schwinger-Keldysh) correlation functions of the holographic thermal environment. To evaluate the latter, we exploit recent developments, wherein the semiclassical gravitational Schwinger-Keldysh saddle geometries were identified as complexified black hole spacetimes. We compute real-time correlation functions using holographic methods in these geometries, and argue that they lead to a sensible open effective quantum dynamics for the system in question, a question that hitherto had been left unanswered. In addition to shedding light on open quantum systems coupled to strongly correlated thermal environments, our results also provide a principled computation of Schwinger-Keldysh observables in gravity and holography. In particular, these influence functionals we compute capture both the dissipative physics of black hole quasinormal modes, as well as that of the fluctuations encoded in outgoing Hawking quanta, and interactions between them. We obtain results for these observables at leading order in a low frequency and momentum expansion in general dimensions, in addition to determining explicit results for two dimensional holographic CFT environments.

hep-th↗

arXiv2020

Nonlinear Langevin dynamics via holography

In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black-brane solution. We compute the Feynman-Vernon influence phase for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black-brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime.

hep-th↗

arXiv2019

Out of Time Ordered Quantum Dissipation

We consider a quantum Brownian particle interacting with two harmonic baths, which is then perturbed by a cubic coupling linking the particle and the baths. This cubic coupling induces non-linear dissipation and noise terms in the influence functional/master equation of the particle. Its effect on the Out-of-Time-Ordered Correlators (OTOCs) of the particle cannot be captured by the conventional Feynman-Vernon formalism.We derive the generalised influence functional which correctly encodes the physics of OTO fluctuations, response, dissipation and decoherence. We examine an example where Markovian approximation is valid for the OTO dynamics. If the original cubic coupling has a definite time-reversal parity, the leading order OTO influence functional is completely determined by the couplings in the usual master equation via OTO generalisation of Onsager-Casimir relations. New OTO fluctuation-dissipation relations connect the non-Gaussianity of the thermal noise to the thermal jitter in the damping constant of the Brownian particle.

cond-mat.stat-mech↗

arXiv2019

Probing Out-of-Time-Order Correlators

We present a method to probe the Out-of-Time-Order Correlators (OTOCs) of a general system by coupling it to a harmonic oscillator probe. When the system's degrees of freedom are traced out, the OTOCs imprint themselves on the generalized influence functional of the oscillator. This generalized influence functional leads to a local effective action for the probe whose couplings encode OTOCs of the system. We study the structural features of this effective action and the constraints on the couplings from microscopic unitarity. We comment on how the OTOCs of the system appear in the OTOCs of the probe.

hep-th↗

arXiv2018

Classification of out-of-time-order correlators

The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n=2,3,4) to exemplify the general statements.

hep-th↗