Mathematics

Supersymmetric intersecting surface defects in four-dimensional N=2 theories can be viewed as coupled 4d/2d/0d supersymmetric systems preserving two supercharges. Their partition functions are expected to match with Liouville/Toda correlators via a generalization of AGT correspondence. In this talk, we will start by reviewing some relevant back- grounds. Then we move on to two simple systems of free hypermultiplets in the presence of intersecting defects. We present their partition functions, match them with Liouville four-point functions, and discuss a Seiberg-like duality. We will also discuss a Higgsing procedure, which is a straightforward way to computing partition functions in the presence of (intersecting) surface defects. We will then summarize and propose a set of conjectures.