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Exact mutual information difference: Scalar vs Maxwell fields

Nicolás Abate, Horacio Casini, Marina Huerta, and Leandro Martinek

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Phys. Rev. D 113, 125014 – Published 11 June, 2026

DOI: https://doi.org/10.1103/y84p-sbbx

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.

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Outline

Information

Phys. Rev. D 113, 125014– Published 11 June, 2026
  • Received 19 February 2026
  • Accepted 11 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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