Holographic entanglement entropy in nonlocal theories

TL;DR

This paper investigates holographic entanglement entropy in nonlocal theories, revealing volume and area law behaviors, phase transitions, and UV/IR mixing effects, with implications for thermalization in strongly coupled nonlocal field theories.

Contribution

It provides the first detailed holographic analysis of entanglement entropy in dipole and noncommutative SYM theories, highlighting novel behaviors due to nonlocality and non-asymptotic AdS geometries.

Findings

Dipole theory exhibits a volume law for small regions, transitioning smoothly to an area law.

Noncommutative theory shows a volume law up to a critical scale, then a phase transition to an area law.

UV cutoff affects the critical length scale, indicating UV/IR mixing and volume law persistence.

Abstract

We compute holographic entanglement entropy in two strongly coupled nonlocal field theories: the dipole and the noncommutative deformations of SYM theory. We find that entanglement entropy in the dipole theory follows a volume law for regions smaller than the length scale of nonlocality and has a smooth cross-over to an area law for larger regions. In contrast, in the noncommutative theory the entanglement entropy follows a volume law for up to a critical length scale at which a phase transition to an area law occurs. The critical length scale increases as the UV cutoff is raised, which is indicative of UV/IR mixing and implies that entanglement entropy in the noncommutative theory follows a volume law for arbitrary large regions when the size of the region is fixed as the UV cutoff is removed to infinity. Comparison of behaviour between these two theories allows us to explain the origin of the volume law. Since our holographic duals are not asymptotically AdS, minimal area surfaces used to compute holographic entanglement entropy have novel behaviours near the boundary of the dual spacetime. We discuss implications of our results on the scrambling (thermalization) behaviour of these nonlocal field theories.