Eric Sharpe (Virginia Tech)
In this talk we will discuss various advances in Seiberg-like dualities in two-dimensional gauge theories with (2,2) and (0,2) supersymmetry. We begin with a quick review of the (2,2) supersymmetric CP^n model and nonabelian analogues, and review other (2,2) and (0,2) dualities, such as in gauge theories with both fundamentals and antifundamentals. In two dimensions, the gauge field has no dynamics, so it is possible to get a very concrete handle on IR behaviors, and also to see some phenomena one would not expect in four dimensions, such as dualities between abelian and nonabelian gauge theories. In addition, techniques such as supersymmetric localization enable for example exact partition function computations, which form a powerful tool for checking dualities, as we shall discuss. If time permits, we will also discuss `decomposition,' relating two-dimensional nonabelian gauge theories with center-invariant matter to disjoint unions of nonabelian gauge theories with variable discrete theta angles.