Higgs branches of 5d rank-zero theories from geometry

A bstract We study the Higgs branches of five-dimensional $$ \mathcal{N} 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 O6-planes, computing open-string spectra giving rise hypermultiplets. Starting seven-dimensional worldvolume theories, we switch T-brane backgrounds give bound states angles. observe that resulting partially Higgsed 5d have discrete gauge groups, which readily deduce geometry as orbifolds quaternionic varieties.