Representation theory for categorical symmetries

Understand

This paper addresses the question of how categorical symmetries act on extended operators in quantum field theory.

• Building on recent results in two dimensions, we introduce higher tube categories and algebras associated to higher fusion category symmetries.
• We show that twisted sector extended operators transform in higher representations of higher tube algebras and interpret this result from the perspective of the sandwich construction of finite symmetries via the Drinfeld center.
• Focusing on three dimensions, we discuss a variety of examples to illustrate the general constructions.