arXiv subjects

Mukund Rangamani

Publications and source records attributed to Mukund Rangamani.

At least 37 records · Page 2Linked to original sources

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.

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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.

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arXiv2022

Snowmass white paper: Quantum information in quantum field theory and quantum gravity

We present a summary of recent progress and remaining challenges in applying the methods and ideas of quantum information theory to the study of quantum field theory and quantum gravity. Important topics and themes include: entanglement entropy in QFTs and what it reveals about RG flows, symmetries, and phases; scrambling, information spreading, and chaos; state preparation and complexity; classical and quantum simulation of QFTs; and the role of information in holographic dualities. We also highlight the ways in which quantum information science benefits from the synergy between the fields.

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arXiv2022

Baby Universes and Worldline Field Theories

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT.

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arXiv2021

A 3d disordered superconformal fixed point

We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $\mathcal{N}=2$ large $N$ Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large $N$ spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.

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arXiv2021

Real-time gravitational replicas: Low dimensional examples

We continue the study of real-time replica wormholes initiated in arXiv:2012.00828. Previously, we had discussed the general principles and had outlined a variational principle for obtaining stationary points of the real-time gravitational path integral. In the current work we present several explicit examples in low-dimensional gravitational theories where the dynamics is amenable to analytic computation. We demonstrate the computation of Rényi entropies in the cases of JT gravity and for holographic two-dimensional CFTs (using the dual gravitational dynamics). In particular, we explain how to obtain the large central charge result for subregions comprising of disjoint intervals directly from the real-time path integral.

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arXiv2021

Real-time gravitational replicas: Formalism and a variational principle

This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called `splitting surface'. This feature is an important hallmark of unitarity in a field theory dual.

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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.

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arXiv2020

Hawking radiation from AdS black holes

We study Hartle-Hawking-like states of quantum field theories on asymptotically AdS black hole backgrounds, with particular regard to the phase structure of interacting theories. By a suitable analytic continuation we show that the equilibrium dynamics of field theories on large asymptotically AdS black holes can be related to the low temperature states of the same field theory on the AdS soliton (or pure AdS) background. This allows us to gain insight into Hartle-Hawking-like states on large-radius Schwarzschild- or rotating-AdS black holes. Furthermore, we exploit the AdS/CFT correspondence to explore the physics of strongly coupled large N theories on asymptotically AdS black holes. In particular, we exhibit a plausibly complete set of phases for the M2-brane world-volume superconformal field theory on a BTZ black hole background. Our analysis partially resolves puzzles previously raised in connection with Hawking radiation on large AdS black holes.

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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.

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arXiv2020

Petz reconstruction in random tensor networks

We illustrate the ideas of bulk reconstruction in the context of random tensor network toy models of holography. Specifically, we demonstrate how the Petz reconstruction map works to obtain bulk operators from the boundary data by exploiting the replica trick. We also take the opportunity to comment on the differences between coarse-graining and random projections.

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arXiv2020

Superbalance of Holographic Entropy Inequalities

The domain of allowed von Neumann entropies of a holographic field theory carves out a polyhedral cone -- the holographic entropy cone -- in entropy space. Such polyhedral cones are characterized by their extreme rays. For an arbitrary number of parties, it is known that the so-called perfect tensors are extreme rays. In this work, we constrain the form of the remaining extreme rays by showing that they correspond to geometries with vanishing mutual information between any two parties, ensuring the absence of Bell pair type entanglement between them. This is tantamount to proving that besides subadditivity, all non-redundant holographic entropy inequalities are superbalanced, i.e. not only do UV divergences cancel in the inequality itself (assuming smooth entangling surfaces), but also in the purification thereof.

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arXiv2019

The quantum marginal independence problem

We investigate whether the presence or absence of correlations between subsystems of an N-partite quantum system is solely constrained by the non-negativity and monotonicity of mutual information. We argue that this relatively simple question is in fact very deep because it is sensitive to the structure of the set of N-partite states. It can be informed by inequalities satisfied by the von Neumann entropy, but has the advantage of being more tractable. We exemplify this by deriving the explicit solution for N=4, despite having limited knowledge of the entropic inequalities. Furthermore, we describe how this question can be tailored to the analysis of more specialized classes of states such as classical probability distributions, stabilizer states, and geometric states in the holographic gauge/gravity duality.

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arXiv2019

Supersymmetric Landau-Ginzburg Tensor Models

We study two dimensional $\mathcal{N} = (2, 2)$ Landau-Ginzburg models with tensor valued superfields with the aim of constructing large central charge superconformal field theories which are solvable using large $N$ techniques. We demonstrate the viability of such constructions and motivate the study of anisotropic tensor models. Such theories are a novel deformation of tensor models where we break the continuous symmetries while preserving the large $N$ solvability. Specifically, we examine theories with superpotentials involving tensor contractions chosen to pick out melonic diagrams. The anisotropy is introduced by further biasing individual terms by different coefficients, all of the same order, to retain large $N$ scaling. We carry out a detailed analysis of the resulting low energy fixed point and comment on potential applications to holography. Along the way we also examine gauged versions of the models (with partial anisotropy) and find generically that such theories have a non-compact Higgs branch of vacua.

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arXiv2019

Topological string entanglement

We investigate how topological entanglement of Chern-Simons theory is captured in a string theoretic realization. Our explorations are motivated by a desire to understand how quantum entanglement of low energy open string degrees of freedom is encoded in string theory (beyond the oft discussed classical gravity limit). Concretely, we realize the Chern-Simons theory as the worldvolume dynamics of topological D-branes in the topological A-model string theory on a Calabi-Yau target. Via the open/closed topological string duality one can map this theory onto a pure closed topological A-model string on a different target space, one which is related to the original Calabi-Yau geometry by a geometric/conifold transition. We demonstrate how to uplift the replica construction of Chern-Simons theory directly onto the closed string and show that it provides a meaningful definition of reduced density matrices in topological string theory. Furthermore, we argue that the replica construction commutes with the geometric transition, thereby providing an explicit closed string dual for computing reduced states, and Renyi and von Neumann entropies thereof. While most of our analysis is carried out for Chern-Simons on S^3, the emergent picture is rather general. Specifically, we argue that quantum entanglement on the open string side is mapped onto quantum entanglement on the closed string side and briefly comment on the implications of our result for physical holographic theories where entanglement has been argued to be crucial ingredient for the emergence of classical geometry.

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arXiv2019

Spinning constraints on chaotic large $c$ CFTs

We study out-of-time ordered four-point functions in two dimensional conformal field theories by suitably analytically continuing the Euclidean correlator. For large central charge theories with a sparse spectrum, chaotic dynamics is revealed in an exponential decay; this is seen directly in the contribution of the vacuum block to the correlation function. However, contributions from individual non-vacuum blocks with large spin and small twist dominate over the vacuum block. We argue, based on holographic intuition, that suitable summations over such intermediate states in the block decomposition of the correlator should be sub-dominant, and attempt to use this criterion to constrain the OPE data with partial success. Along the way we also discuss the relation between the spinning Virasoro blocks and the on-shell worldline action of spinning particles in an asymptotically AdS spacetime.

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arXiv2018

The holographic entropy arrangement

We develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in arXiv:1808.07871, of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign-definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5-party entropy cone. We work with explicit configurations in arbitrary (time-dependent) states leading to both simple derivations and an intuitive picture of the entanglement pattern.

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arXiv2018

On Melonic Supertensor Models

We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large $N$ limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for $SL(2,{\mathbb R})$ wavefunctions for fermionic excitations.

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