An analytic Lifshitz black hole

TL;DR

The paper constructs an analytic Lifshitz black hole in four dimensions with $d=2$, $z=2$, asymptotic to Lifshitz spacetime by extending simple gravity-matter models. It provides the Lifshitz vacuum and an analytic black-hole solution, analyzes thermodynamics via holographic renormalization, and solves the scalar wave equation exactly to obtain retarded Green's functions. The scalar correlators resemble 2D CFT structures at a formal level but feature nontrivial pole structure and lack ultralocality at finite temperature, highlighting distinctive Lifshitz-like holographic dynamics. The work advances concrete holographic control of Lifshitz theories while acknowledging the need for a UV-complete embedding and inviting further connections to Lifshitz-like field theories.

Abstract

A Lifshitz point is described by a quantum field theory with anisotropic scale invariance (but not Galilean invariance). In arXiv:0808.1725, gravity duals were conjectured for such theories. We construct analytically a black hole which asymptotes to a vacuum Lifshitz solution; this black hole solves the equations of motion of some simple (but somewhat strange) extensions of the models of arXiv:0808.1725. We study its thermodynamics and scalar response functions. The scalar wave equation turns out to be exactly solvable. Interestingly, the Green's functions do not exhibit the ultralocal behavior seen previously in the free Lifshitz scalar theory.