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arXiv · 1406.5236

5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry

Yiwen Pan
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Abstract

In this paper we apply the idea of Higgs branch localization to 5d supersymmetric theories of vector multiplet and hypermultiplets, obtained as the rigid limit of $\mathcal{N} = 1$ supergravity with all auxiliary fields. On supersymmetric K-contact/Sasakian background, the Higgs branch BPS equations can be interpreted as 5d generalizations of the Seiberg-Witten equations. We discuss the properties and local behavior of the solutions near closed Reeb orbits. For $U(1)$ gauge theories, we show the suppression of the deformed Coulomb branch, and the partition function is dominated by 5d Seiberg-Witten solutions at large $ζ$-limit. For squashed $S^5$ and $Y^{pq}$ manifolds, we show the matching between poles in the perturbative Coulomb branch matrix model, and the bound on local winding numbers of the BPS solutions.

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Yiwen Pan. 2015-05-29. 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry. https://doi.org/10.1007/jhep01(2015)145

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