Non-invertible Symmetries of Class $\mathcal{S}$ Theories

Understand

We study the non-invertible symmetries of class $\mathcal{S}$ theories obtained by compactifying the type $\mathfrak{a}_{p-1}$ 6d (2,0) theory on a genus $g$ Riemann surface with no punctures.

• After setting up the general framework, we describe how such symmetries can be classified up to genus 5.
• Of central interest to us is the question of whether a non-invertible symmetry is "intrinsic," i.e.
• whether it can be related to an invertible symmetry by discrete gauging.