Holographic Mutual Information for Singular Surfaces

TL;DR

This paper investigates corner effects on holographic mutual information in 3D conformal field theories, revealing divergences and phase transitions, and explores implications for higher dimensions and other geometries.

Contribution

It provides new insights into corner contributions and divergences in holographic mutual information for disjoint regions, including tripartite information behavior.

Findings

Mutual information exhibits a first order phase transition.

Tripartite information is divergent for disjoint sectors.

Corner effects are local, confirmed by separated region analysis.

Abstract

We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in three-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information between regions separated by a sharp annular region. Possible extensions to higher dimensions and hyperscaling violating geometries is also considered for disjoint sectors.