Mutual information from modular flow in CFTs

Abstract

The operator product expansion (OPE) of twist operators in the replica trickframework enables a long-distance expansion of the mutual information (MI) in conformalfield theories (CFTs). In this expansion, the terms are labeled by primary operators, ascontributions from descendant operators can be resummed into conformal blocks. However,for the MI, the expansion involves primaries from the multi-replica theory, which includes farmore operators than those in the original theory. In this work, we develop a method to resumthis series, yielding an expansion in terms of the primaries of the original theory, specificallyrestricted to the two-copy sector. This is achieved by expressing the twist operators in anon-local manner across different replicas and using a modular flow representation to obtainthe n → 1 limit of the Rényi index. We explicitly compute the resulting “enhanced conformalblocks,” which, surprisingly, provide excellent approximations to the MI of generalized freefields across the full range of cross ratios. Remarkably, this approximation appears to beexact in the limit of large spacetime dimensions.