Mutual Information from Modular Flow in General CFTs

TL;DR

This paper develops a high-precision analytical approximation for the mutual information in general conformal field theories, utilizing modular flow and operator product expansion, validated against known results and applied to Maxwell fields.

Contribution

It introduces a novel hierarchy of approximations to mutual information in CFTs using modular flow and twist operators, improving long-distance behavior predictions.

Findings

Provides the most precise long-distance MI approximation when involving the lowest-dimension primary.

Validates the approximation against exact 2D and lattice 3D results.

Applies the method to the Maxwell field in 4D, a previously unexplored case.

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.