  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.
