Week 24.04.2023 – 30.04.2023

These three lectures will aim to provide a pedagogical introduction to the dynamics of N=2 supersymmetric gauge theory and the work of Seiberg and Witten. We will assume only basic knowledge of supersymmetry.

Generalised notions of symmetries have received widespread attention in recent years. Though exotic, such generalised symmetries have been shown to naturally arise for instance as dual symmetries upon gauging ordinary symmetries. In this talk, I will present a systematic framework to investigate dualities of quantum lattice models and study the resulting generalised symmetries. I will illustrate this framework in the context of familiar spin models.

Using the BF formulation of JT gravity, we will extend the factorisation techniques in BF theory with compact groups to non-compact ones. The Euclidean path integral formulation of these theories provides some locality interpretation of these results in terms of gravitational edge modes. We shall comment on how to extend these ideas to 3d gravity. We will aim to stress differences occurring between gauge and gravity theories already in these low dimensional examples.

These three lectures will aim to provide a pedagogical introduction to the dynamics of N=2 supersymmetric gauge theory and the work of Seiberg and Witten. We will assume only basic knowledge of supersymmetry.