Aspects of holography for theories with hyperscaling violation

Abstract

Abstract We analyze various aspects of the recently proposed holographic theories with general dynamical critical exponent z and hyperscaling violation exponent θ. We first find the basic constraints on z, θ from the gravity side, and compute the stress-energy tensor expectation values and scalar two-point functions. Massive correlators exhibit a nontrivial exponential behavior at long distances, controlled by θ. At short distance, the two-point functions become power-law, with a universal form for θ > 0. Next, the calculation of the holographic entanglement entropy reveals the existence of novel phases which violate the area law. The entropy in these phases has a behavior that interpolates between that of a Fermi surface and that exhibited by systems with extensive entanglement entropy. Finally, we describe microscopic embeddings of some θ ≠ 0 metrics into full string theory models — these metrics characterize large regions of the parameter space of Dp-brane metrics for p ≠ 3. For instance, the theory of N D2-branes in IIA super gravity has z = 1 and θ = −1/3 over a wide range of scales, at large g s N.