Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-07-27
Phys.Rev.D80:126004,2009
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, references added and regrouped
Scientific paper
10.1103/PhysRevD.80.126004
Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where $\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the entropy density. This matches the expected behavior for a 2+1 dimensional theory with a scaling symmetry $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to \lambda^z t$.
Bertoldi Gaetano
Burrington Benjamin A.
Peet Amanda W.
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