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.
Highlights
Black holes when disturbed settle down after classically ringing in quasinormal modes [1, 2]
How should we characterize the effective dynamics of a probe system coupled to the conserved currents of the dual field theory? 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-anti-de Sitter (AdS) black hole can be efficiently captured by such designer scalars
Summary
Black holes when disturbed settle down after classically ringing in quasinormal modes [1, 2]. The quasinormal modes signify dissipation into a medium and the Hawking modes correspond to the attendant quantum statistical fluctuations. Quasinormal modes of AdS black holes correspond to thermalization rates of the dual field theory [4]. Massless spin-1 and spin-2 fields in planar AdS black holes have long-lived quasinormal modes with dispersions that are characteristic of hydrodynamic fluctuations [5,6,7]. Correspond to the charge and momentum diffusion, and (attenuated) sound waves in the dual field theory plasma One can trace their origins to the underlying gauge invariance of massless spin-1 and spin-2 fields manifested as global conservation laws for charge currents and energy-momentum tensor. Our goal in this work is to provide a unified treatment of the diffusive modes of AdS black holes and obtain an effective action governing their dynamics
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have