Lifshitz from AdS at finite temperature and top down models

TL;DR

This paper analytically constructs Lifshitz black branes with a small deviation from z=1 in Einstein-Proca models, explores their holographic duals as deformations of CFTs, and discusses stability issues in top-down models.

Contribution

It provides an analytical Lifshitz black brane solution with a small dynamical exponent deviation and analyzes the holographic dual QFT deformations and stability constraints.

Findings

Thermodynamic quantities match Lifshitz invariance predictions.

The dual QFT is a vector-deformed CFT with a VEV for the vector operator.

Top-down models exhibit modes violating the Breitenlohner-Freedman bound.

Abstract

We construct analytically an asymptotically Lifshitz black brane with dynamical exponent z=1+epsilon^2 in an Einstein-Proca model, where epsilon is a small parameter. In previous work we showed that the holographic dual QFT is a deformation of a CFT by the time component of a vector operator and the parameter epsilon is the corresponding deformation parameter. In the black brane background this operator additionally acquires a vacuum expectation value. We explain how the QFT Ward identity associated with Lifshitz invariance leads to a conserved mass and compute analytically the thermodynamic quantities showing that they indeed take the form implied by Lifshitz invariance. In the second part of the paper we consider top down Lifshitz models with dynamical exponent close to one and show that they can be understood in terms of vector deformations of conformal field theories. However, in all known cases, both the conformal field theory and its Lifshitz deformations have modes that violate the Breitenlohner-Freedman bound.