Holographic entanglement entropy probes (non)locality

TL;DR

This paper investigates how holographic entanglement entropy behaves in theories with intrinsic nonlocality, revealing a transition from area to volume law at certain scales, influenced by UV/IR mixing and symmetry considerations.

Contribution

It demonstrates the violation of the area law in nonlocal theories using holographic methods and analyzes the impact of UV/IR mixing and Lorentz symmetry on entanglement entropy.

Findings

Area law is violated at nonlocality scales in these models.

Volume law replaces area law at short distances.

UV/IR mixing affects the critical length scale in noncommutative theories.

Abstract

We study the short-distance structure of geometric entanglement entropy in certain theories with a built-in scale of nonlocality. In particular we examine the cases of Little String Theory and Noncommutative Yang-Mills theory, using their AdS/CFT descriptions. We compute the entanglement entropy via the holographic ansatz of Ryu and Takayanagi to conclude that the area law is violated at distance scales that sample the nonlocality of these models, being replaced by an extensive volume law. In the case of the noncommutative model, the critical length scale that reveals the area/volume law transition is strongly affected by UV/IR mixing effects. We also present an argument showing that Lorentz symmetry tends to protect the area law for theories with field-theoretical density of states.