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

Jiahua Tian, Yi-Nan Wang

SciPost Phys. 12, 127 (2022) · published 12 April 2022

- doi: 10.21468/SciPostPhys.12.4.127
- Submissions/Reports

### Abstract

We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ 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, $\widetilde{X}$, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of $\Gamma$, the orbifold singularity $\mathbb{C}^3/\Gamma$ 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.

### Cited by 24

### Authors / Affiliations: mappings to Contributors and Organizations

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^{1}Jiahua Tian, -
^{2}^{3}Yi-Nan Wang

^{1}Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]^{2}University of Oxford^{3}北京大学 / Peking University [PKU]