Tinkertoys for the twisted D-series

We study 4D N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 superconformal field theories that arise from the compactification of 6D N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = (2, 0) theories of type DN on a Riemann surface, in the presence of punctures twisted by a ℤ2 outer automorphism. Unlike the untwisted case, the family of SCFTs is in general parametrized, not by ℳg,n, but by a branched cover thereof. The classification of these SCFTs is carried out explicitly in the case of the D4 theory, in terms of three-punctured spheres and cylinders, and we provide tables of properties of twisted punctures for the D5 and D6 theories. We find realizations of Spin(8) and Spin(7) gauge theories with matter in all combinations of vector and spinor representations with vanishing β-function, as well as Sp(3) gauge theories with matter in the 3-index traceless antisymmetric representation.