Partition functions, BPS states and abelianization

Abstract: In this talk I will re-express the Nekrasov-Shatashvili partition function for a four-dimensional N=2 gauge theory as an integral of a ratio of Wronskians of solutions to the relevant oper equation, with the AD2 theory and the pure SU(2) theory as two main examples. This motivates the definition of a generalized Nekrasov-Shatashvili partition function for any four-dimensional N=2 theory of class S, and makes a connection with abelianization and exact WKB analysis. We will end with some remarks regarding the five-dimensional generalization and the relation to similar mathematical structures underlying the topological string partition function. This talk is based on 2109.14699 and work in progress.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.