Ellipsoid partition function from Seiberg-Witten monopoles

Abstract

We study Higgs branch localization of N=2 supersymmetric theories placed on compact Euclidean manifolds. We analyze the resulting localization equations in detail on the four-sphere and find that in this case the path integral is dominated by vortex-like configurations as well as singular Seiberg-Witten monopoles located at the north and south pole. The partition function is written accordingly.

37 pages; v2: minor typos corrected, published version

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• A slow review of the AGT correspondence
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• Chiral Algebras, Localization and Surface Defects
• Supersymmetric localization in two dimensions
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• 3d Mirror Symmetry from S-duality
• AGT/Z${}_2$
• 3d Expansions of 5d Instanton Partition Functions
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Supersymmetric vortex defects in two dimensions
• Vortex-Strings in N=2 SQCD and Bulk-String Decoupling
• Bootstrapping the $S^5$ partition function
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Intersecting Surface defects and 3d Superconformal indices
• Vortex-strings in N=2 quiver X U(1) theories