Thermal three-point functions from holographic Schwinger-Keldysh contours

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.