Higher fusion categories and their fusion rings

Abstract: Higher fusion categories are certain algebraic gadgets which capture some of the behavior of topological operators/defects in higher-dimensional quantum field theories.

In the first part of this talk, I will give an introduction to the basic concepts of higher fusion category theory and overview some key examples. If time permits, I will then explain how every fusion n-category C has associated `homotopy sets' pi_k C, defined as a certain quotient of the set of (k+1)-codimensional operators. I will sketch how these sets pi_k C carry a kind of fusion ring structure and how in the modular case this fusion ring structure can be recovered from a higher-dimensional Verlinde formula.

The first part of this talk is based on arXiv:1812.11933 (joint with Christopher Douglas), the second part is based on ongoing joint work with Theo Johnson-Freyd.

MathematicsPhysics

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.