Open quantum systems and Schwinger-Keldysh holograms

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 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.

Holographic KMS relations at finite density

“…Thus, when written in the RA basis, the two combinations of sources precisely multiply the ingoing/quasinormal bulk-to-boundary propagator and the outgoing bulk-to-boundary propagator respectively. This is analogous to the corresponding statements at zero chemical potential [2][3][4]7]. As pointed out in [2], the above fact can be used to argue why the generating function of correlations computed using our holographic prescription satisfy both the Schwinger-Keldysh collapse rules as well as the KMS conditions, i.e., the generating function cannot contain terms with only ψP or terms with only ψF .…”

“…held at a finite temperature and chemical potential. Our prescription is a straightforward generalisation of the original grSK prescription [1][2][3][4]. In this geometry, we describe how to obtain the outgoing or Hawking modes from the ingoing quasi-normal modes via a CP T transformation.…”

“…There is however a technical obstacle to such an endeavour: one needs a practical formalism to compute interactions between ingoing quasi-normal modes and the outgoing Hawking fluctuations. Recently, a gravitational Schwinger-Keldysh (grSK) geometry [3,4] has emerged as an arena where such computations can be performed with ease. This prescription is built on earlier work on real time holography [1,[5][6][7][8][9][10][11][12][13][14][15][16].…”

“…This is the gravitational Schwinger-Keldysh (grSK) geometry alluded to above. While an ab initio derivation of this prescription is still not known, its validity and efficacy have been demonstrated in several instances [1][2][3][4].…”

Real-time gravitational replicas: formalism and a variational principle

“…In the 7 Real-time correlation functions in thermal states of holographic field theories have also been argued to be computed on complex gravitational Schwinger-Keldysh geometries [46]. But while detailed analysis of observables shows consistency with field theory expectations [47,48], a first-principles argument that they are unique saddle point of the gravitational path integral does not yet exist. Nevertheless, we will argue in appendix B that these geometries do provide an useful arena to illustrate some of the ideas we discuss.…”