Tinkertoys for the Twisted D-Series

TL;DR

This paper classifies twisted 4D N=2 superconformal field theories derived from 6D D_N theories on Riemann surfaces, revealing new gauge theory realizations with specific matter content and detailed puncture properties.

Contribution

It provides an explicit classification of twisted SCFTs for D_4, D_5, and D_6 theories, including tables of puncture properties and new gauge theory constructions.

Findings

Classified twisted SCFTs for D_4, D_5, D_6 theories.

Identified gauge theories with matter in various representations.

Provided detailed properties of twisted punctures.

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.