Gaiotto Duality for the Twisted A_{2N-1} Series
Oscar Chacaltana, Jacques Distler, Yuji Tachikawa
TL;DR
This work extends the 6D (2,0) construction to A_{2N-1} theories with Z_2-twisted punctures, enabling a complete classification of 4D N=2 SCFTs via three-punctured spheres and cylinders. It develops explicit algorithms to compute local puncture data, including pole structures, graded Coulomb branch dimensions, and constraint structures (c- and a-constraints) from B-partitions, and demonstrates atypical degenerations where gauge couplings can reside at interior moduli-space points. The paper then applies these tools to realize D_n-shaped quivers, analyze S-duality for SU(4) and Sp(2) theories, and realize all rank-1 SCFTs (including a Δ=3 theory) from twisted A-series constructions. Collectively, these results provide new duality frames, novel fixture-based gauge theories, and a richer map between 6D twisted data and 4D SCFT phenomena, with implications for Lagrangian and non-Lagrangian quivers, moduli-space structure, and rank-1 theory classifications.
Abstract
We study 4D N=2 superconformal theories that arise from the compactification of 6D N=(2,0) theories of type A_{2N-1} on a Riemann surface C, in the presence of punctures twisted by a Z_2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A_3, and provide tables of properties of twisted defects up through A_9. We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space. As applications, we study: i) 6D representations of 4D superconformal quivers in the shape of an affine/non-affine D_n Dynkin diagram, ii) S-duality of SU(4) and Sp(2) gauge theories with various combinations of fundamental and antisymmetric matter, and iii) realizations of all rank-one SCFTs predicted by Argyres and Wittig.