Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries

Gaetano Bertoldi; Benjamin A. Burrington; Amanda W. Peet

doi:10.1103/PhysRevD.82.106013

paper

Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries

arXiv:1007.1464 · doi:10.1103/PhysRevD.82.106013

Abstract

Several classes of gravitational backgrounds in $3 + 1$ dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in $2 + 1$ dimensions with critical exponent $z \geq 1$ . We numerically explore one such model, characterized by a temperature $T$ and chemical potential $μ$ , and find how to embed these solutions into AdS for a range of values of $z$ . We find no phase transition going from the $T ≪ μ$ to the $T ≫ μ$ regimes, and find that the solutions smoothly interpolate between the Lifshitz-like behavior and the relativistic AdS-like behavior. Finally, we exploit some conserved quantities to find a relationship between the energy density $\mc E$, entropy density $s$ , and number density $n$ , $\mc E=\frac{2}{3} \left(Ts+μn\right)$. We show that this result is expected from general scaling arguments, and generalizes to $\mc E= \frac{d}{d+1}\left(Ts+μn\right)$ for a theory dual to AdS $_{d + 2}$ (Poincaré patch) asymptotics with a local $U (1)$ gauge invariance.

arXiv comment26 pages, 4 figures

Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries

Abstract

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