Extremal Surfaces and Thin-shell Wormholes

TL;DR

This paper investigates extremal surfaces in traversable wormhole geometries within AdS/CFT, analyzing holographic entanglement entropy and phase transitions, revealing how thin-shell wormholes influence the entanglement structure and phase behavior of the dual theory.

Contribution

It introduces the study of extremal surfaces in stable thin-shell wormholes in AdS, exploring their impact on holographic entanglement entropy and phase transitions in the dual CFT.

Findings

Holographic entanglement entropy results are consistent with the dual picture.

Thin-shell wormholes cause cusps in the phase space diagram.

Phase transitions occur for disconnected boundary regions.

Abstract

We study extremal surfaces in a traversable wormhole geometry that connects two locally AdS$_5$ asymptotic regions. In the context of the AdS/CFT correspondence, we use these to compute the holographic entanglement entropy for different configurations: First, we consider an extremal surface anchored at the boundary on a spatial $2$-sphere of radius $R$. The other scenario is a slab configuration which extends in two of the boundary spacelike directions while having a finite size $L$ in the third one. We show that in both cases the divergent and the finite pieces of the holographic entanglement entropy give results consistent with the holographic picture and this is used to explore the phase transitions that the dual theory undergoes. The geometries we consider here are stable thin-shell wormholes with flat codimension-one hypersurfaces at fixed radial coordinate. They appear as electrovacuum solutions of higher-curvature gravity theories coupled to Abelian gauge fields. The presence of the thin-shells produces a refraction of the extremal surfaces in the bulk, leading to the presence of cusps in the phase space diagram. Further, the traversable wormhole captures a phase transition for the subsystems made up of a union of disconnected regions in different boundaries. We discuss these and other features of the phase diagram.