Abstract
We compute exactly the partition function of two dimensional \( \mathcal{N} \) = (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 \( \mathcal{N} \) = (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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Doroud, N., Gomis, J., Le Floch, B. et al. Exact results in D = 2 supersymmetric gauge theories. J. High Energ. Phys. 2013, 93 (2013). https://doi.org/10.1007/JHEP05(2013)093
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DOI: https://doi.org/10.1007/JHEP05(2013)093