On holographic entanglement entropy of non-local field theories

TL;DR

This paper investigates holographic entanglement entropy in non-local field theories using gravity duals characterized by a parameter, analyzing behavior at extremality and finite temperature, and revealing volume law scaling and universal conditions.

Contribution

It provides exact solutions for holographic entanglement entropy in non-local theories at various temperatures, clarifies universality conditions, and explores special cases like w=1.

Findings

Volume law behavior for small entangling regions

Analytic expressions at high and low temperatures

Finite extremal entanglement entropy related to zero temperature limit

Abstract

We study holographic entanglement entropy of non-local field theories both at extremality and finite temperature. The gravity duals, constructed in arXiv:1208.3469 [hep-th], are characterized by a parameter $w$. Both the zero temperature backgrounds and the finite temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples with the entangling regions being a strip and a sphere. We find that the leading order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading order result is universal. For the finite temperature case we obtain the analytic expressions both in the high temperature limit and in the low temperature limit. In the former case the leading order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when $w=1$.