String-net models for pivotal bicategories

TL;DR

This paper extends string-net models to pivotal bicategories, providing a graphical calculus and demonstrating how these models relate to conformal field theory correlators, thus broadening the algebraic framework for topological quantum field theories.

Contribution

It introduces a string-net construction for pivotal bicategories, expanding the algebraic structures used in topological quantum field theory beyond spherical fusion categories.

Findings

Develops a graphical calculus for pivotal bicategories.

Constructs bicategorical string-net spaces as colimits over surfaces.

Shows functoriality and compatibility with mapping class group actions.

Abstract

We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category. An essential ingredient in our construction is a graphical calculus for pivotal bicategories, which we express in terms of a category of colored corollas. The globalization of this calculus to oriented surfaces yields the bicategorical string-net spaces as colimits. We show that every rigid separable Frobenius functor between strictly pivotal bicategories induces linear maps between the corresponding bicategorical string-net spaces that are compatible with the mapping class group actions and with sewing. Our results are inspired by and have applications to the description of correlators in two-dimensional conformal field theories.