Patrick Jefferson (UMass Physics): Symmetries in QFT, Part 3

I will continue last week's discussion where we left off, beginning with some examples of 0-form and higher-form symmetries. Having introduced the traditional formulation of symmetries in quantum field theory (QFT), I will continue the discussion by reviewing the key result of Gaiotto, Kapustin, Seiberg and Willet (2015), which asserts that symmetries in QFT are associated to topological operators. I will show that this paradigm encompasses conventional symmetries as well as "higher-form" symmetries, focusing in particular on examples of the latter in gauge theories. Time permitting, I will also begin reviewing some general properties of QFTs intimately related to symmetries, such as anomalies and gauging, and I will explain how for a given QFT many of these properties are elegantly captured by an associated topological field theory of one dimension higher.