Correlation Functions in Non-Relativistic Holography

TL;DR

The paper investigates correlation functions in non-relativistic holography with Schrödinger symmetry by mapping the problem to AdS via a mass-Fourier transform. Using this reduction, it constructs the bulk-to-boundary and bulk-to-bulk propagators for a scalar field in the Schrödinger background and computes three- and four-point functions via holographic Witten diagrams, deriving explicit forms and regulator schemes. The results show that the gravity-side correlators satisfy the constraints of Schrödinger invariance, including explicit dependence on time differences and mass conservation, and they extend to general $n$-point structures. This work strengthens the non-relativistic AdS/CFT program by providing concrete, analytics-based NRCFT correlators and clarifying how Schrödinger invariance constrains higher-point functions.

Abstract

Recently constructed gravity solutions with Schrodinger symmetry provide a new example of AdS/CFT-type dualities for the type of non-relativistic field theories relevant to certain cold atom systems. In this paper we use the gravity side to calculate n-point correlation functions of scalar fields by reducing the computation to that in ordinary AdS space via a particular Fourier transform. We evaluate the relevant integrals for 3- and 4-point functions and show that the results are consistent with the requirements of Schrodinger invariance, the implications of which we also work out for general n-point functions.