Higgs branches of 5d rank-zero theories from geometry

TL;DR

This paper investigates the Higgs branches of specific 5d rank-zero theories derived from M-theory on non-toric Calabi-Yau threefolds, revealing their structure as orbifolds of quaternionic varieties.

Contribution

It introduces a geometric approach to analyze Higgs branches of 5d theories from non-toric Calabi-Yau threefolds using IIA reductions and T-brane configurations.

Findings

Higgs branches are characterized as orbifolds of quaternionic varieties.

Discrete gauge groups emerge in partially Higgsed theories.

The method applies to non-toric, non-compact Calabi-Yau threefolds.

Abstract

We study the Higgs branches of five-dimensional N=1 rank-zero theories obtained from M-theory on two classes non-toric non-compact Calabi-Yau threefolds: Reid's pagodas, and Laufer's examples. Our approach consists in reducing to IIA with D6-branes and O6-planes, and computing the open-string spectra giving rise to hypermultiplets. Starting with the seven-dimensional worldvolume theories, we switch on T-brane backgrounds to give rise to bound states with angles. We observe that the resulting partially Higgsed 5d theories have discrete gauge groups, from which we readily deduce the geometry of the Higgs branches as orbifolds of quaternionic varieties.