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

Journal article

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

Authors: Tian, J; Wang, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: SciPost
• Journal: SciPost Physics
• Volume: 12
• Issue: 4
• Pages: 127
• Publication date: 2022-04-12
• DOI: 10.21468/scipostphys.12.4.127
• EISSN: 2542-4653
• ISSN: 2542-4653
• Language: Latvian
• Keywords: Physics; Artificial intelligence; Computer science; Orbifold; Mathematical physics; Algorithm