CFT Correlators for Cardy Bulk Fields via String-Net Models

TL;DR

This paper introduces a geometric approach using string-net models to construct invariants of mapping class group actions, linking algebraic structures in conformal field theory to topological invariants.

Contribution

It demonstrates how a specific Frobenius algebra in the Drinfeld center yields invariant string-net models for CFT correlators in the Cardy case.

Findings

String-net models produce mapping class group invariants.

Frobenius algebra encodes bulk field data in CFT.

Geometric construction connects algebraic and topological aspects.

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 ${\mathcal C}$. We show that the datum of a specific commutative symmetric Frobenius algebra in the Drinfeld center $Z(\mathcal{C})$ 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.