Thermal three-point functions from holographic Schwinger-Keldysh contours

TL;DR

This paper calculates retarded scalar three-point functions in holographic conformal field theories at finite temperature using real-time holography, revealing resonant quasinormal mode excitations and establishing a method involving mixed-signature spacetimes.

Contribution

It introduces a novel holographic method to compute three-point functions at finite temperature via mixed-signature spacetimes and connects this to ingoing boundary conditions on black hole backgrounds.

Findings

Resonant poles linked to quasinormal modes identified.

Equivalence of mixed-signature spacetime construction to ingoing boundary conditions shown.

Retarded correlators with stress-tensor insertions computed via Ward identities.

Abstract

We compute fully retarded scalar three-point functions of holographic CFTs at finite temperature using real-time holography. They describe the nonlinear response of a holographic medium under scalar forcing, and display single and higher-order poles associated to resonant QNM excitations. This involves computing the bulk-to-bulk propagator on a piecewise mixed-signature spacetime, the dual of the Schwinger-Keldysh contour. We show this construction is equivalent to imposing ingoing boundary conditions on a single copy of a black hole spacetime, similar to the case of the two-point function. We also compute retarded scalar correlators with stress-tensor insertions in general CFTs by solving Ward identities on the Schwinger-Keldysh contour.