5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds

Abstract

We study the orbifold singularities X=\mathbb{C}^3/\GammaX=ℂ3/Γ where \GammaΓ is a finite subgroup of SU(3)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 \GammaΓ 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 \GammaΓ in an elegant way. The second method is to explicitly resolve the singularity XX 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, \widetilde{X}X̃, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of \GammaΓ, the orbifold singularity \mathbb{C}^3/\Gammaℂ3/Γ 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.