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2012

Exact Results in D=2 Supersymmetric Gauge Theories

Doroud, Nima, Gomis, Jaume, Floch, Bruno Le et al.

Understand

We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 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 functions in two dimensional Liouville/Toda CFT compute the S^2 partition function for a class of N=(2,2) gauge theories, thereby uncovering novel modular properties 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.