A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems

TL;DR

This paper introduces a gravity-based method for calculating real-time correlation functions in non-equilibrium systems via a novel analytic continuation in dynamical black hole geometries, simplifying complex computations.

Contribution

It presents a new prescription for holographic Schwinger-Keldysh contours involving an analytic continuation in dynamical black holes, enabling easier calculation of non-equilibrium correlation functions.

Findings

Derived two-point functions for scalar operators.

Connected gravity calculations to non-equilibrium effective actions.

Simplified computations using derivative expansion in slowly varying horizons.

Abstract

We develop a prescription for computing real-time correlation functions defined on a Schwinger-Keldysh contour for non-equilibrium systems using gravity. The prescription involves a new analytic continuation procedure in a black hole geometry which can be dynamical. For a system with a slowly varying horizon, the continuation enables computation of the Schwinger-Keldysh generating functional using derivative expansion, drastically simplifying calculations. We illustrate the prescription with two-point functions for a scalar operator. We then use it to derive from gravity the recently proposed non-equilibrium effective action for diffusion.