Tinkertoys for the Twisted D-Series

TL;DR

The paper extends the class-S program to Z2-twisted D_N theories, systematically classifying twisted punctures and their local data via Hitchin system boundary conditions. It develops a detailed framework for pole structures, constraints, and collisions, and analyzes gauge-coupling spaces and ramification patterns, including atypical degenerations that yield branched coverings of moduli spaces. Focusing on the D4 case, it provides a comprehensive catalog of regular and irregular punctures, cylinders, and fixtures, and demonstrates a variety of new gauge-theory realizations (Spin(8), Spin(7), Sp(3)) with vanishing beta functions, including intricate S-dual descriptions. The work also computes Hall-Littlewood indices to identify global symmetries and confirms enhancements, connecting twisted-sector fixtures to known SCFTs such as Sp(4)×SU(2) and E8-related theories, and extends the analysis to higher genus with ramifications of twists on the moduli space and duality structure.

Abstract

We study 4D N=2 superconformal field theories that arise from the compactification of 6D N=(2,0) theories of type D_N on a Riemann surface, in the presence of punctures twisted by a Z_2 outer automorphism. Unlike the untwisted case, the family of SCFTs is in general parametrized, not by M_{g,n}, but by a branched cover thereof. The classification of these SCFTs is carried out explicitly in the case of the D_4 theory, in terms of three-punctured spheres and cylinders, and we provide tables of properties of twisted punctures for the D_5 and D_6 theories. We find realizations of Spin(8) and Spin(7) gauge theories with matter in all combinations of vector and spinor representations with vanishing beta-function, as well as Sp(3) gauge theories with matter in the 3-index traceless antisymmetric representation.