Effective field theory of stochastic diffusion from gravity

TL;DR

This work develops a universal holographic framework for open quantum systems with memory by introducing a designer scalar with a tunable Markovianity index $\mathscr{M}$. Quasinormal and Hawking fluctuations in planar Schwarzschild-AdS backgrounds are mapped to gauge-invariant scalar, gauge, and gravity probes, enabling a gradient-expansion treatment that cleanly separates fast (Markovian) and slow (non-Markovian) modes. A Wilsonian Schwinger-Keldysh (WIF) action is constructed to describe fluctuating hydrodynamics, diffusion constants, and Hawking-noise correlations for both charge/momentum diffusion and their gravitational counterparts, including hyperscaling-violating backgrounds. The framework recovers known diffusion poles, KMS relations, and the shear viscosity bound in a unified, gauge-invariant fashion, while clarifying the role of memory through a hydrodynamic moduli space and analytic continuation in $\mathscr{M}$. These results illuminate how holography encodes long-term black hole memory into open EFTs and provide a concrete template for analyzing memory-bearing open quantum systems in strongly coupled plasmas.

Abstract

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.

Figures (1)

• Figure 1: The complex $r$ plane with the locations of the two boundaries and the horizon marked. The grSK contour is a codimension-1 surface in this plane (drawn at fixed $v$). As indicated the direction of the contour is counter-clockwise and it encircles the branch point at the horizon.