Holographic Mutual Information at small separations

TL;DR

This paper investigates the behavior of holographic mutual information at small separations in 2+1 dimensions, proposing universality in the leading term and extending conjectures to higher dimensions and conformal field theories.

Contribution

It provides an exact analysis of minimal surfaces in AdS4 for small separations and suggests a universal form for the mutual information's short-distance expansion.

Findings

Universal leading term in short-distance expansion of holographic mutual information.

Conjecture extending the universality to higher dimensions (d > 2).

Comments on analogous behavior in conformal field theories.

Abstract

The holographic mutual information for the small separation of two circles and two strips in 2+1 dimensional space-time is considered based on the known exact minimal surfaces spanning the boundaries on AdS4. The results suggest a universality for the leading term in the short-distance expansion of holographic mutual information. A conjecture for a similar result for d > 2 is also presented, as well as comments about the analogous expansion in conformal field theory.