Holography for Schrodinger backgrounds

TL;DR

This paper explores holographic dualities involving Schrodinger backgrounds in massive gravity and vector theories, establishing the correspondence with non-relativistic conformal field theories and computing correlation functions.

Contribution

It develops the holographic dictionary for Schrodinger backgrounds and demonstrates the matching of 2-point functions between holographic and field theory calculations.

Findings

Holographic duals are described by deformations of conformal field theories respecting Schrodinger symmetry.

Holographic renormalization involves non-local counterterms in the lightcone direction.

Agreement between holographic and field theory 2-point functions is established.

Abstract

We discuss holography for Schrodinger solutions of both topologically massive gravity in three dimensions and massive vector theories in (d+1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrodinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k_v. We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction.