Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$

Abstract

We apply the method of Higgs branch localization to the $\mathcal{N}=1$ supersymmetric partition function on $S^3\times S^1.$ As a result, we show that it can be written as the product of an elliptic vortex and anti-vortex partition function summed over a finite number of Higgs vacua.

29 pages; v2: minor improvements, references added

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• Superconformal indices of three-dimensional theories related by mirror symmetry
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• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
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• Modularity of supersymmetric partition functions
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• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
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• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality