Exact Mutual Information Difference: Scalar vs. Maxwell Fields

TL;DR

This paper derives exact formulas for the difference in mutual Re9nyi information between scalar and Maxwell fields in four dimensions, revealing the convergence properties of their series expansions.

Contribution

It provides an exact computation of mutual information differences for scalars and Maxwell fields across all Re9nyi indices, using a novel dimensional reduction approach.

Findings

Exact difference computed for all Re9nyi indices

Series converges only for integer n>1

Asymptotic series for n=1 and non-integer n

Abstract

We compute, for any R\'enyi index $n$, the exact difference between the mutual R\'enyi informations of a pair of free massless scalars and that of a Maxwell field in $d=4$ dimensions. Using the standard dimensional reduction method in polar coordinates, the problem is mapped to that of a single scalar field in $d=2$ with Dirichlet boundary conditions, which in turn can be conveniently related to the algebra of a chiral current on the full line. This latter identification, which maps algebras on an interval to two-interval algebras, yields exact results that clarify the structure of the long-distance OPE perturbative expansion of the mutual information. We find that this series has a finite radius of convergence only for integer $n>1$, while it becomes only asymptotical for $n=1$ and general non-integer values of $n$.