Description
The action of generalized symmetries on an n-dimensional quantum field theory can be conveniently encoded by realizing it as a boundary of a topological field theory in one dimension higher, called the symmetry TQFT, using a sandwich construction. The extended operators of the symmetry TQFT give a concrete implementation of the categorical symmetry of the boundary. In fully local topological quantum field theories, there exists an operator–state correspondence, which identifies the possible extended operators with the higher categories of states that the TQFT assigns to manifolds of lower codimension. Taking unitarity into account in this setting requires the symmetry TQFT to be unitary and fully extended, which in turn calls for a not-yet-fully-developed theory of unitary higher categories. In my talk, I will explain some recent progress towards the definition and classification of unitary fully local topological quantum field theories. This is based on several joint works, involving (in part) Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd, Cameron Krulewski, Nivedita, David Penneys, David Reutter, Claudia Scheimbauer, Luuk Stehouwer, and Chetan Vuppulury, as well as ongoing work with Theo Johnson-Freyd, Cameron Krulewski, and Luuk Stehouwer.