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arXiv · 1206.2606

Exact Results in D=2 Supersymmetric Gauge Theories

Nima Doroud·Jaume Gomis·Bruno Le Floch·Sungjay Lee
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Abstract

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.

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Nima Doroud, Jaume Gomis, Bruno Le Floch, Sungjay Lee. 2016-11-12. Exact Results in D=2 Supersymmetric Gauge Theories. https://doi.org/10.1007/jhep05(2013)093

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