Real-time gauge/gravity duality and ingoing boundary conditions

TL;DR

This paper clarifies how to compute real-time correlation functions in gauge/gravity duality, deriving ingoing boundary conditions at horizons and extending the method to higher-point functions and regions beyond the horizon.

Contribution

It provides a detailed derivation of ingoing boundary conditions for bulk fields in real-time holography, generalizing previous prescriptions to higher-point functions and beyond the horizon.

Findings

Derived ingoing boundary conditions at the horizon for bulk fields.

Extended the real-time holography prescription to higher-point functions.

Clarified the role of regions beyond the horizon in correlation functions.

Abstract

In arXiv:0805.0150 [hep-th] and arXiv:0812.2909 [hep-th] a general prescription was presented for the computation of real-time correlation functions using the gauge/gravity duality. I apply this prescription to the specific case of retarded thermal correlation functions and derive the usual ingoing boundary conditions at the horizon for bulk fields. The derivation allows me to clarify various issues, in particular the generalization to higher-point functions and the relevance of including the regions beyond the horizon.