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

TL;DR

This paper extends Higgs branch localization to 5d supersymmetric theories, revealing that BPS equations resemble 5d Seiberg-Witten equations and analyzing their solutions on specific manifolds.

Contribution

It introduces 5d generalizations of Seiberg-Witten equations within Higgs branch localization and explores their solutions on K-contact and Sasakian backgrounds.

Findings

Partition function dominated by 5d Seiberg-Witten solutions at large 

Suppression of Coulomb branch in U(1) theories

Matching poles in matrix model with BPS solution bounds

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 $\zeta$-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.