In two-dimensional N=(2,2) R-symmetric theories of vector and chiral multiplets on the two-sphere, the partition function as well as expectation values of supersymmetric operators can be computed with localization techniques. Depending on the choice of localizing term, the partion function can be expressed either as an integral over the Coulomb branch, or as a sum over a discrete Higgs branch of a vortex times an antivortex partition functions. As applications, I will discuss mirror symmetry, I will show equality of the path integrals for “Seiberg-like” dual theories in two dimensions, and present a novel way of computing Gromow-Witten invariants of Calabi-Yau manifolds.

Simons Center, SUNY, Stony Brook