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arXiv · 2604.19860

Mutual Information from Modular Flow in General CFTs

César A. Agón·Pablo Bueno·Adem Deniz Piskin·Guido van der Velde
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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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César A. Agón, Pablo Bueno, Adem Deniz Piskin, Guido van der Velde. 2026-04-21. Mutual Information from Modular Flow in General CFTs. https://arxiv.org/abs/2604.19860

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