CFT Correlators for Cardy Bulk Fields via String-Net Models

Abstract

We show that string-net models provide a novel geometric method to construct invariants of mapping class group actions. Concretely, we consider string-net models for a modular tensor category 𝒞. We show that the datum of a specific commutative symmetric Frobenius algebra in the Drinfeld center 𝛧(𝒞) gives rise to invariant string-nets. The Frobenius algebra has the interpretation of the algebra of bulk fields of the conformal field theory in the Cardy case.