Chennai Mathematical Institute


Classification of 4d N=2 gauge theories

Lakshya Bhardwaj
Chennai Mathematical Institute.


In the last 20 years, people have developed many mutually complementary methods to obtain the Seiberg-Witten solutions of N=2 gauge theories. However, none of them applies to arbitrary N=2 gauge theories, and each of the methods have strengths and weaknesses depending on the type of gauge theories. It would be interesting to know if the methods obtained so far are powerful enough to solve all N=2 UV-complete gauge theories, and if not, to develop new methods to solve them. Ideally, one might want to find a general method to solve all such theories.
A first step in this direction would be to classify all N=2 UV-complete gauge theories. However, recently, many mysterious non-Lagrangian gauge theories were found. Still, N=2 supersymmetric UV-complete gauge theories composed of gauge groups and hypermultiplets form a nice traditional subclass of all possible four-dimensional N=2 supersymmetric systems. The main aim of this talk is to classify all such traditional theories.