Schwinger-Keldysh Propagators from AdS/CFT Correspondence

TL;DR

This paper develops a method to compute real-time Green's functions at finite temperature in field theories using their AdS gravity duals, successfully reproducing the Schwinger-Keldysh propagator and clarifying boundary condition issues.

Contribution

It introduces a new approach to derive Lorentzian signature correlators in AdS/CFT, including the full Schwinger-Keldysh matrix, resolving previous boundary condition challenges.

Findings

Reproduces Schwinger-Keldysh propagator from gravity calculations

Clarifies boundary condition subtleties in Lorentzian AdS/CFT

Method applicable to higher point correlators

Abstract

We demonstrate how to compute real-time Green's functions for a class of finite temperature field theories from their AdS gravity duals. In particular, we reproduce the two-by-two Schwinger-Keldysh matrix propagator from a gravity calculation. Our methods should work also for computing higher point Lorentzian signature correlators. We elucidate the boundary condition subtleties which hampered previous efforts to build a Lorentzian-signature AdS/CFT correspondence. For two-point correlators, our construction is automatically equivalent to the previously formulated prescription for the retarded propagator.