Abstract
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 quasi- normal 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.
Highlights
Insight into observables e.g., correlation functions, von Neumann entropy, etc., of the dual strongly coupled QFT
In addition to shedding light on open quantum systems coupled to strongly correlated thermal environments, our results provide a principled computation of Schwinger-Keldysh observables in gravity and holography
We wish to argue here that black holes provide a playground for the exploration of a much richer set of dynamics, viz., that of an open quantum field theory, where the degrees of freedom of the quantum system are non-trivially entangled with some external environment degrees of freedom
Summary
Our goal is to construct the open effective field theory of a single scalar degree of freedom coupled to a holographic thermal field theory. We will start by describing the general set-up and specialize to the case of two dimensional theories. We will first begin our description by focusing on the ‘bath/environment’ theory with a holographic dual and how its real-time correlators can be computed via AdS/CFT. We will describe how this computation amounts to deriving the open effective theory for the probe
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