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 Z(C) gives rise to invariant string-nets. The Frobe-nius algebra has the interpretation of the algebra of bulk fields of the conformal field theory in the Cardy case.