Lifshitz-like black brane thermodynamics in higher dimensions

TL;DR

This paper investigates Lifshitz-like black brane solutions in higher-dimensional gravity models, analyzing their thermodynamics, stability, and interpolation between Lifshitz and AdS behaviors, with implications for holographic duals of critical phenomena.

Contribution

It provides a numerical study of dilaton-Einstein-Maxwell backgrounds with Lifshitz-like solutions, exploring their thermodynamic properties and interpolations across different regimes and dimensions.

Findings

No thermal instability observed across regimes.

Solutions smoothly interpolate between Lifshitz and AdS behaviors.

Entropy density follows a power law with temperature and chemical potential.

Abstract

Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent z\geq 1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. Such backgrounds are characterized by a temperature T and chemical potential \mu, and we find how to embed these solutions into AdS for a range of values of z and d. We find no thermal instability going from the (T\ll\mu) to the (T\gg\mu) regimes, regardless of the dimension, and find that the solutions smoothly interpolate between the Lifshitz-like behaviour and the relativistic AdS-like behaviour. We exploit some conserved quantities to find a relationship between the energy density E, entropy density s, and number density n, E=\frac{d}{d+1}(Ts+n\mu), as is required by the isometries of AdS_{d+2}. Finally, in the (T\ll\mu) regime the entropy density is found to satisfy a power law s \propto c T^{d/z} \mu^{(z-1)d/z}, and we numerically explore the dependence of the constant c, a measure of the number of degrees of freedom, on d and z.