Aspects of holography for theories with hyperscaling violation

TL;DR

The paper advances holographic understanding of theories with dynamical exponent z and hyperscaling violation θ by deriving gravity-side constraints, correlator behavior, and entanglement structure for a broad class of scale-covariant metrics. It shows that θ qualitatively changes two-point functions, induces novel entanglement entropy phases, and yields finite-temperature crossovers, while establishing a string-theory embedding via Dp-branes that realizes z=1 and θ≠0 over wide scale ranges. The work identifies θ≈d−1 as a local minimum of entanglement, suggestive of Fermi-surface-like physics, and analyzes stability constraints that disfavour θ>d, linking bulk instabilities to boundary observables. Together, these results illuminate how hyperscaling violation shapes scaling dimensions, entanglement, thermodynamics, and UV/IR completions in holographic theories, with potential applications to strongly correlated quantum matter.

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 $θ\neq 0$ 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 $θ= -1/3$ over a wide range of scales, at large $g_s N$.