Holographic real-time non-relativistic correlators at zero and finite temperature

TL;DR

This paper calculates real-time non-relativistic correlation functions at zero and finite temperature using holography, verifying results with non-relativistic AdS/CFT and extending to thermal backgrounds.

Contribution

It provides a systematic method to compute non-relativistic real-time correlators at finite temperature within holographic duality, including three-point functions, verifying consistency with known relations.

Findings

Derived non-relativistic correlators from relativistic ones via Fourier transform.

Computed thermal two and three-point correlators in Schrödinger spacetime backgrounds.

Confirmed that correlators satisfy Kallen-Lehmann relations.

Abstract

We compute a variety of two and three-point real-time correlation functions for a strongly-coupled non-relativistic field theory. We focus on the theory conjectured to be dual to the Schr\"{o}dinger-invariant gravitational spacetime introduced by Balasubramanian, McGreevy, and Son, but our methods apply to a large class of non-relativistic theories. At zero temperature, we obtain time-ordered, retarded, and Wightman non-relativistic correlators for scalar operators of arbitrary conformal dimension directly in field theory by applying a certain lightlike Fourier transform to relativistic conformal correlators, and we verify that non-relativistic AdS/CFT reproduces the results. We compute thermal two and three-point real-time correlators for scalar operators dual to scalar fields in the black hole background which is the finite temperature generalization of the Schr\"{o}dinger spacetime. This is done by first identifying thermal real-time bulk-to-boundary propagators, which combined with Veltman's circling rules, yield two and three-point correlators. The two-point correlators we obtain satisfy the Kallen-Lehmann relations. We also give retarded and time-ordered three-point correlators.