CFT correlators and mapping class group averages

TL;DR

This paper establishes a connection between mapping class group averages in 3D gravity and correlators in 2D rational CFTs using topological field theories, extending previous results to Ising-type categories.

Contribution

It demonstrates that Ising-type modular fusion categories meet the necessary properties for this correspondence on various surfaces, broadening the scope of previous work.

Findings

Ising-type categories satisfy the required properties

Extension of results to surfaces with/without field insertions

Absence of invertible global symmetries in these models

Abstract

Mapping class group averages appear in the study of 3D gravity partition functions. In this paper, we work with 3D topological field theories to establish a bulk-boundary correspondence between such averages and correlators of 2D rational CFTs whose chiral mapping class group representations are irreducible and satisfy a finiteness property. We show that Ising-type modular fusion categories satisfy these properties on surfaces with or without field insertions, extending results in [Jian et al., JHEP 10 (2020) 129], and we comment on the absence of invertible global symmetries in the examples we consider.