Unifying Constructions of Non-Invertible Symmetries

Understand

In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d\geq 3$ have appeared.

• In this paper we provide a unified perspective on these constructions.
• Central to this framework are so-called theta defects, which generalize the notion of theta-angles, and allow the construction of universal and non-universal topological symmetry defects.
• We complement this physical analysis by proposing a mathematical framework (based on higher-fusion categories) that converts the physical construction of non-invertible symmetries into a concrete computational scheme.