Holographic stress tensor for non-relativistic theories

TL;DR

This paper develops a method to compute the stress tensor in non-relativistic holographic duals, specifically for Schrödinger and Lifshitz geometries, and verifies its physical consistency through solutions and comparisons.

Contribution

It introduces a new definition of the non-relativistic stress tensor complex for Schrödinger and Lifshitz duals, including an action principle for Lifshitz and validation against known solutions.

Findings

Stress tensor is finite on-shell for Lifshitz backgrounds.

Method reproduces known results for Schrödinger black holes.

Provides a consistent framework for non-relativistic holographic stress tensors.

Abstract

We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schrodinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schrodinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.