Lifshitz Space-Times for Schroedinger Holography

TL;DR

This paper demonstrates that Lifshitz space-times are holographically dual to field theories with Schrödinger symmetry, providing a detailed correspondence including sources, vevs, and Ward identities, thus advancing the understanding of non-relativistic holography.

Contribution

It provides a complete holographic dictionary for Lifshitz space-times dual to Schrödinger-invariant theories, including boundary sources, vevs, and Ward identities.

Findings

Identified boundary sources as torsional Newton-Cartan geometry.

Constructed the boundary energy-momentum tensor and mass current.

Showed Ward identities are organized by the Schrödinger algebra.

Abstract

We show that asymptotically locally Lifshitz space-times are holographically dual to field theories that exhibit Schroedinger invariance. This involves a complete identification of the sources, which describe torsional Newton-Cartan geometry on the boundary and transform under the Schroedinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy-momentum tensor and mass current and show that these obey Ward identities that are organized by the Schroedinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2, it can be expressed in terms of computable vev/source pairs.