The Symmetry Topological Field Theory (SymTFT) is a realization of the philosophy that symmetries in Quantum Field Theory (QFT) can be studied using tools from Topological Quantum Field Theory (TQFT). In this talk, I will introduce this topic and motivate the construction of the SymTFT for a d-dimensional QFT as a (d+1)-dimensional topological field theory. I will explain how this (d+1)-dimensional theory is completely determined by the global symmetries of the d-dimensional QFT, making it "universal" for all d-dimensional theories sharing the same symmetries. A significant advantage of the SymTFT is its ability to separate kinematical aspects from dynamical ones. This separation enables the analysis of the constraints imposed by a given symmetry structure on the dynamics, with a prime example being 't Hooft anomalies, using only TQFT tools and observables.
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Slava Rychkov