High Energy Theory Seminar

I discuss the partition functions of supersymmetric gauge theories on Seifert manifolds. First we consider the case of 3d N=2 theories on a three-manifold $M_{g,p}$, a degree-p principal U(1) bundle over a smooth, genus-g Riemann surface. This includes the topological index and the three-sphere and lens space partition functions as special cases. The computation can be performed using a 3d uplift of the A-twist on the underlying Riemann surface. A similar calculation for 4d N=1 theories on $M_{g,p}$ x $S^1$ is also described. I discuss several applications of these computations, and briefly comment on the extension to arbitrary Seifert manifolds, i.e., circle bundles over orbifolds.