5d Higgs branch localization, Seiberg-Witten equations and contact geometry

摘要

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, which can be straight-forwardly generalized to theories whose gauge group can be completely broken, we show the suppression of the deformed Coulomb branch, and the partition function is dominated by 5d Seiberg-Witten solutions. 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.