Entanglement wedge cross section inequalities in AdS/BCFT

TL;DR

This paper investigates the inequalities of the entanglement wedge cross section in AdS/BCFT, demonstrating that these inequalities hold similarly to those in AdS/CFT, despite complex phase structures introduced by boundaries.

Contribution

It provides a universal algebraic proof of entanglement wedge cross section inequalities in AdS/BCFT, extending known results from AdS/CFT to boundary scenarios.

Findings

Entanglement wedge cross section satisfies similar inequalities in AdS/BCFT and AdS/CFT.

The proof is algebraic, applicable across all phase structures.

Boundary presence leads to rich phase structures in the entanglement wedge.

Abstract

The entanglement wedge cross section in holographic picture provides a geometrical description of the entanglement for mixed states. In this paper we study the inequalities for the entanglement wedge cross section in AdS/BCFT duality. In the presence of the boundary in conformal field theory (CFT), the dual entanglement wedge cross section exhibits abundant phase structures since the extremal surface may end on the brane. We present a universal treatment which is applicable for all the possible phases such that the inequalities for the entanglement wedge cross section can be proved in an algebraic manner rather than a diagrammatic manner. We show that the entanglement wedge cross section in AdS/BCFT satisfies the same inequalities as in AdS/CFT.