Non-relativistic Holography and Singular Black Hole

TL;DR

This paper develops a covariant framework for non-relativistic holography based on Bargmann lift and null-like Kaluza-Klein reduction, constructs a singular black hole solution, and analyzes its thermodynamics and viscosity properties.

Contribution

It introduces a covariant action principle for non-relativistic holography, explains the co-dimension 2 nature, and constructs a singular black hole solution with consistent thermodynamics.

Findings

Reproduces zero temperature results for non-relativistic holography.

Constructs a black hole with a curvature singular horizon.

Derives consistent thermodynamics for the dual non-relativistic CFT.

Abstract

We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be nonzero.