Gaiotto Duality for the Twisted A_{2N-1} Series

TL;DR

This paper classifies twisted A_{2N-1} 4D N=2 superconformal theories from 6D compactifications, revealing new degenerations and exploring dualities, gauge theories, and rank-one SCFT realizations.

Contribution

It provides a complete classification of twisted A_{2N-1} SCFTs via three-punctured spheres, including explicit tables and analysis of atypical degenerations and their physical implications.

Findings

Classification of twisted A_{2N-1} theories achieved

Identification of atypical degenerations with fixed gauge couplings

Connections to 6D representations, S-duality, and rank-one SCFTs

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.