Exact mutual information difference: Scalar vs Maxwell fields

Abstract

We compute, for any Rényi index 𝑛, the exact difference between the mutual Rényi information 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 operator algebras on an interval to two-interval operator algebras, yields exact results that clarify the structure of the long-distance, perturbative operator product 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 noninteger values of 𝑛.