Lifshitz from AdS at finite temperature and top down models

TL;DR

This paper addresses finite-temperature Lifshitz holography by treating Lifshitz spacetimes as vector deformations of AdS, and it constructs analytic Lifshitz black branes with $z=1+\epsilon^2$ in Einstein-Proca theory. It develops the holographic dictionary for these near-AdS Lifshitz systems, derives renormalized one-point functions and Ward identities, and computes thermodynamic quantities that obey Lifshitz scaling relations. The authors then connect these bottom-up results to top-down Lifshitz solutions from Romans gauged supergravity, showing that such $z\sim 1$ theories are in the same universality class as vector-deformed CFTs but suffer Breitenlohner-Freedman instabilities in both the AdS and Lifshitz sectors. The findings highlight a universal mechanism for realizing near-relativistic Lifshitz dynamics via vector deformations, while also emphasizing stability challenges in current string theory embeddings and motivating the search for stable, supersymmetric realizations.

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.