Tinkertoys for the Z3-twisted D4 Theory

TL;DR

This paper explores the compactification of the $D_4$ (2,0) theory with outer-automorphism twists, revealing new 4D $ ext{N}=2$ SCFTs and discovering a novel rank-1 SCFT with $SU(4)$ flavor symmetry.

Contribution

It introduces a new class of 4D $ ext{N}=2$ SCFTs from twisted compactifications of the $D_4$ theory, including a previously unknown rank-1 SCFT with $SU(4)$ flavor symmetry.

Findings

Discovery of new 4D $ ext{N}=2$ SCFTs with outer-automorphism twists.

Identification of a new rank-1 $ ext{N}=2$ SCFT with $SU(4)$ flavor symmetry.

Analysis of properties of theories arising from $D_4$ with $ ext{Z}_3$ twists.

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 $SU(4)$.