Aspects of holography for theories with hyperscaling violation

TL;DR

This paper explores holographic theories with hyperscaling violation, analyzing constraints, correlators, entanglement entropy, and string theory embeddings, revealing novel phases and universal behaviors.

Contribution

It provides a comprehensive analysis of holographic theories with hyperscaling violation, including constraints, correlator behaviors, entanglement entropy phases, and string theory embeddings.

Findings

Massive correlators show exponential behavior at long distances.

Holographic entanglement entropy reveals phases violating the area law.

Certain metrics with hyperscaling violation embed into string theory models like Dp-branes.

Abstract

We analyze various aspects of the recently proposed holographic theories with general dynamical critical exponent z and hyperscaling violation exponent $\theta$. We first find the basic constraints on $z, \theta$ 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 $\theta$. At short distance, the two-point functions become power-law, with a universal form for $\theta > 0$. 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 $\theta \neq 0$ metrics into full string theory models -- these metrics characterize large regions of the parameter space of Dp-brane metrics for $p\neq 3$. For instance, the theory of N D2-branes in IIA supergravity has z=1 and $\theta = -1/3$ over a wide range of scales, at large $g_s N$.