Exact results in d = 2 supersymmetric gauge theories,” 2012. Talk given at the conference

We compute exactly the partition function of two dimensional N = (2, 2) gauge theories on S2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on the Higgs branches of the theory. We further demonstrate that correlation func-tions in two dimensional Liouville/Toda CFT compute the S2 partition function for a class of N = (2, 2) gauge theories, thereby uncovering novel modular prop-erties in two dimensional gauge theories. Some of these gauge theories flow in the infrared to Calabi-Yau sigma models – such as the conifold – and the topology changing flop transition is realized as crossing symmetry in Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited by demonstrating that the partition function of conjectured Seiberg dual pairs are the same