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

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