Conformal quantum mechanics and holographic quench

TL;DR

This paper explores how holographic quenches in AdS-Vaidya backgrounds relate to conformal quantum mechanics, deriving and comparing non-equilibrium two-, three-, and four-point functions with a focus on the 3-point Witten diagram.

Contribution

It introduces a Hamiltonian-based approach to incorporate quenches into correlation functions in conformal quantum mechanics and verifies results with holographic computations.

Findings

Rederived known two-point functions in conformal quantum mechanics.

Computed non-equilibrium three- and four-point functions.

Matched the 3-point Witten diagram with conformal quantum mechanics results.

Abstract

Recently, there has been much interest in holographic computations of two-point non-equilibrium Green functions from AdS-Vaidya backgrounds. In the strongly coupled quantum field theory on the boundary, the dual interpretation of the background is an equilibration process called a holographic quench. The two dimensional AdS-Vaidya spacetime is a special case, dual to conformal quantum mechanics. We study how the quench is incorporated into a Hamiltonian $H + \theta(t) \Delta H$ and into correlation functions. With the help of recent work on correlation functions in conformal quantum mechanics, we first rederive the known two point functions, and then compute non-equilibrium 3- and 4-point functions. We also compute the 3-point function Witten diagram in the two-dimensional AdS-Vaidya background, and find agreement with the conformal quantum mechanics result.