# Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries - High Energy Physics - Theory

Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: Several classes of gravitational backgrounds in $3+1$ dimensions have beenproposed as holographic duals to Lifshitz-like theories describing criticalphenomena in $2+1$ dimensions with critical exponent $z\geq 1$. We numericallyexplore one such model, characterized by a temperature $T$ and chemicalpotential $\mu$, and find how to embed these solutions into AdS for a range ofvalues of $z$. We find no phase transition going from the $T\ll\mu$ to the$T\gg \mu$ regimes, and find that the solutions smoothly interpolate betweenthe Lifshitz-like behavior and the relativistic AdS-like behavior. Finally, weexploit some conserved quantities to find a relationship between the energydensity $\mc E$, entropy density $s$, and number density $n$, $\mcE=\frac{2}{3} \leftTs+\mu n ight$. We show that this result is expected fromgeneral scaling arguments, and generalizes to $\mc E= \frac{d}{d+1}\leftTs+\mun ight$ for a theory dual to AdS$ {d+2}$ Poincar\-e patch asymptotics witha local $U1$ gauge invariance.

Author: ** Gaetano Bertoldi, Benjamin A. Burrington, Amanda W. Peet**

Source: https://arxiv.org/