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  • Letter
  • Open Access

Mutual information from modular flow in general conformal field theories

César A. Agón1,*, Pablo Bueno2,†, Adem Deniz Piskin3,4,‡, and Guido van der Velde2,§

  • *Contact author: cesar.agon@upct.es
  • †Contact author: pablobueno@ub.edu
  • ‡Contact author: a.d.piskin@tudelft.nl
  • §Contact author: guidovandervelde@icc.ub.edu
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Phys. Rev. D 114, L041704 – Published 25 August, 2026

DOI: https://doi.org/10.1103/pwmb-pl64

Abstract

The vacuum mutual information (MI) of subregion algebras provides a universal window into the data of general conformal field theories (CFTs). Exploiting the geometric nature of the modular flow associated to ball-shaped regions and the operator product expansion of twist operators implementing the replica symmetry in an n-fold version of a CFT, it is possible to construct a hierarchy of increasingly refined approximations to the full MI. In this letter, we use the two-point functions of primaries of arbitrary spin in the replicated theory to constrain the twist operators, and find their contribution to the MI of arbitrarily boosted balls in any d-dimensional CFT. When the two-point functions involve the primary with the lowest scaling dimension, our result provides the most precise approximation for the long-distance behavior of the MI, superseding all previous expansions. Building upon this result and certain universal properties of the short- and long-distance regimes, we put forward a new high-precision analytic approximation to the MI for arbitrary separations. The accuracy of our approach is validated against exact d=2 and lattice d=3 results. We further apply it to characterize the MI of a d=4 Maxwell field, a case for which no prior results are available.

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Phys. Rev. D 114, L041704– Published 25 August, 2026
  • Received 14 May 2026
  • Accepted 30 July 2026
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