5D and 6D SCFTs from C3 orbifolds

We study the orbifold singularities X = C-3/Gamma where Gamma is a finite subgroup of SU (3). M-theory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods. The first approach is via 3d McKay correspondence which relates the group theoretic data of Gamma to the physical properties of the 5d SCFT. In particular, the 1-form symmetry of the 5d SCFT is read off from the McKay quiver of Gamma in an elegant way. The second method is to explicitly resolve the singularity X and study the Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric hypersurface and complete intersection cases. Many new theories are constructed, either with or without an IR quiver gauge theory description. We find that many resolved Calabi-Yau threefolds, (X) over tilde, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of Gamma, the orbifold singularity C-3/Gamma can be embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank-1 6d SCFTs without a gauge group, which are potentially different from the rank-1 E-string theory.

Automated summary

This study investigates orbifold singularities X = C-3/Gamma, where Gamma is a finite subgroup of SU (3). The M-theory on this orbifold singularity gives rise to a 5d SCFT, which is explored using two different methods. The first method involves the 3d McKay correspondence, which relates the group theoretic data of Gamma to the properties of the 5d SCFT. The second method involves explicitly resolving the singularity X and studying the Coulomb branch information of the 5d SCFT. Several new theories are constructed, some with IR quiver gauge theory descriptions and some without. Additionally, certain cases of Gamma can be embedded in an elliptic model and give rise to a 6d (1,0) SCFT in F-theory construction.