Generalized symmetries of quantum field theory
I will discuss joint work with Oscar Randal-Williams and Joe Tooby-Smith in which QFTs are formulated rigorously using the language of infinity categories. Doing so allows one to define a `space’ of QFTs and study generalized symmetries in a systematic way. In the special case of topological field theories, for example, the `space’ X of theories is in fact a homotopy type and the n-form symmetry group of a theory x \in X is given by the (n+1)-th homotopy group of X at x.
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