Speaker
Description
I will talk about three-dimensional N=2 supersymmetric gauge theories on M_{g,p}, a circle bundle of degree p over a genus g Riemann surface. We compute the supersymmetric partition functions on M_{g,p} and correlation functions of BPS loop operators. We also consider four-dimensional uplift of this construction, which computes the generalized index of N=1 gauge theories defined on elliptic fibration over genus g Riemann surface. We find that the partition function or index can be written as a sum over "Bethe vacua” of two-dimensional A-twisted theory obtained by compactification. With this framework, we will see how the partition functions on manifolds with different topologies are related to each other. It also provides a novel tool to study various supersymmetric dualities, which allows us to study the action of the dualities on the co-dimension two BPS operators.
