Schwinger-Keldysh Propagators from AdS/CFT Correspondence
C. P. Herzog, D. T. Son
TL;DR
The paper addresses how to obtain real-time, finite-temperature Green's functions from AdS/CFT, proposing a Lorentzian holographic prescription that uses Kruskal-like coordinates to impose horizon boundary conditions. By solving bulk fields in asymptotically AdS black hole backgrounds and evaluating the boundary action, the authors reproduce the full Schwinger-Keldysh (2×2) propagator matrix, including both the original field and its doubling partner, and show equivalence with the retarded propagator for two-point functions. The method extends to higher-point correlators and clarifies boundary-condition ambiguities that hindered previous approaches, while reducing to the standard zero-temperature Wick-rotated prescription in the appropriate limit. This work provides a consistent framework for computing Minkowski-signature correlators in holographic finite-temperature theories and deepens the connection between black hole thermodynamics and thermal behavior in the dual field theory.
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.