Mutual information in deformed conformal field theories

Abstract

The operator product expansion of twist operators within the replica trick framework has become a central tool for computing entanglement entropies in conformal field theories. Recent advances have successfully applied this formalism to the two-copy sector of a single scalar primary operator, retaining only the contributions from the twist operator that involve correlations across two replica copies. This provides a tractable approximation that captures a universal contribution to mutual information in the ground state of any conformal field theory with a scalar primary in its spectrum. In this work, we extend this result by incorporating scalar conformal perturbations into the computation. We continue to work within the two-copy sector and carry out the analytic continuation on the number of replicas, taking the n → 1 limit. This enables us to explore how conformal perturbations modify the entanglement structure of the theory. A central technical achievement of this analysis is the development of new methods for solving Lorentzian integral equations that arise from the modular flow. These techniques enable us to work in the Lorentzian signature and perturb the two-copy formalism away from conformality, thereby opening the door to systematic studies of entanglement entropy in a broader class of theories.