Abstract
In this work we will study black brane solutions that are not translationally invariant in the spatial directions along which it extends. Instead, we require homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. We find Einstein-Maxwell black hole solutions whose near horizon geometry correspond to Solv (Bianchi $V1_{-1}$), Nil (Bianchi $II$) or $SL_2({\cal R})$ (Bianchi $VIII$). Interestingly we observe that at intermediate temperatures our solutions have an scaling regime where different spacetime directions scale differently. We also compute the DC conductivities for these charged solutions and study how they scale in this intermediate regime.
Highlights
Quantum critical points and novel phases of matter with unconventional scalings are systems of which the degrees of freedom are believed to be in a strongly coupled regime
There is an effort to classify phase structures, in particular, in the deep IR regime. The result of such efforts was the appearance of novel renormlization group (RG) flow geometries with intermediate scalings, which are useful to model the behavior of conformal field theories around quantum critical points
The parameters at1, f0, and h0 are the independent coefficients of the functions expanded around the horizon, and h∞, h∞4, g∞, g∞4, and f∞ are the corresponding ones when the expansion is around the UV. These boundary conditions imply that our black hole solutions have the same scaling for the metric in all the directions, which is an important difference with respect to previous works [11–13]
Summary
Quantum critical points and novel phases of matter with unconventional scalings are systems of which the degrees of freedom are believed to be in a strongly coupled regime. In the context of the AdS=CFT approach to studying condensed matter physics, there has been significant recent interest in the construction of black hole solutions dual to conformal field theories (CFTs) deformed by operators that break translational invariance. This is because these systems allow momentum to dissipate, giving room to study more realistic transport properties. Having the translational symmetry broken, the dual field theories will have finite dc transport coefficients We can read such coefficients directly from the horizon metric following the method developed in Ref. V, we summarize our results and discuss possible future directions
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