Tinkertoys for the Z3-twisted D4 Theory

Abstract

Among the simple Lie algebras, $D_4$ is distinguished as the unique one whose group of outer-automorphisms is bigger than ${\mathbb{Z}}_2$. We study the compactifications of the $D_4$ (2,0) Theory on a punctured Riemann surface, $C$, with outer-automorphism twists around cycles of $C$ lying in ${\mathbb{Z}}_3\subset \text{Aut}(D_4)=S_3$. The resulting 4D $\mathcal{N}=2$ SCFTs have a number of new and interesting properties. As byproduct, we discover a new rank-1 $\mathcal{N}=2$ SCFT with flavour symmetry group $SU(4)$.

28 pages, 71 figures