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 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.

We study the dynamics of M-theory on isolated non-toric Calabi-Yau threefold singularities of type (Aj, Al) and (Ak, Dn), engineering five-dimensional rank-zero SCFTs. Our approach consists in mapping these backgrounds to type IIA string theory with D6 branes at angles and O6− planes, computing the five-dimensional open string modes located at the brane intersections. This permits us to characterize the Higgs Branches of these theories as algebraic varieties, determine the flavour and gauge group and inspect subtleties related to T-branes. Our methods apply for all the considered singularities: we give a closed formula for the (Aj, Al) Higgs Branches, and tables for the Higgs Branches of the (Ak, Dn) series.

The conifold is a basic example of a noncompact Calabi-Yau threefold that admits a simple flop, and in M-theory, gives rise to a 5d hypermultiplet at low energies, realized by an M2-brane wrapped on the vanishing sphere. We develop a novel gauge-theoretic method to construct new classes of examples that generalize the simple flop to so-called length ℓ = 1, . . . , 6. The method allows us to naturally read off the Gopakumar-Vafa invariants. Although they share similar properties to the beloved conifold, these threefolds are expected to admit M2-bound states of higher degree ℓ. We demonstrate this through our computations of the GV invariants. Furthermore we characterize the associated Higgs branches by computing their dimensions and flavor groups. With our techniques we extract more refined data such as the charges of the hypers under the flavor group.

We classify rank zero 5d SCFTs geometrically engineered from M-theory on quasi-homogeneous compound Du Val isolated threefold singularities. For all such theories, we characterize the Higgs Branch, by computing the dimension, the continuous and discrete symmetry groups, as well as more refined details such as the charges of the hypermultiplets under these groups. We derive these data by means of a gauge-theoretic method, that we have recently introduced, based on establishing a correspondence between an adjoint Higgs field and the M-theory geometry. As a byproduct, this further allows us to construct several T-brane backgrounds, that yield inequivalent 5d spectra but are associated with the same geometry.

collinucci dot phys at gmail dot com mdemarco at sissa dot it andrea dot sangiovanni at phd dot units dot it roberto dot valandro at ts dot infn dot it