Description
In the modern perspective, the generalized global symmetries of a quantum field theory (QFT) are encoded in the spectrum of its (extended) topological operators. Finite symmetries, in particular, are expected to be captured by higher fusion categories. The Symmetry Topological Field Theory (SymTFT) provides a powerful framework for analyzing many facets of these symmetry structures.
While categorical methods and SymTFT techniques are by now well established for finite symmetries, a complete and systematic framework for continuous symmetries is still being developed. In these lectures, I will present some features of SymTFTs for continuous symmetries from a physicist’s perspective. As a complementary approach to better understanding the properties of symmetry operators associated with continuous symmetries, I will also discuss aspects of their realization in holography and string theory.