We study the local properties of a class of codimension-2 defects of the 6d N =(2, 0) theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra g, where g is determined by J and the outer-automorphism twist around the defect. This class is a natural generalisation of the defects of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the 4d central charges a and c, and to the flavour central charge k.

We describe a procedure for classifying N = 2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A N −1 SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N = 5, and for several families of SCFTs for arbitrary N . These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N = 2 SCFTs.

We describe a procedure for classifying 4D N = 2 superconformal theories of the type introduced by Davide Gaiotto. Any punctured curve, C, on which the 6D (2, 0) SCFT is compactified, may be decomposed into 3-punctured spheres, connected by cylinders. The 4D theories, which arise, can be characterized by listing the "matter" theories corresponding to 3-punctured spheres, the simple gauge group factors, corresponding to cylinders, and the rules for connecting these ingredients together. Different pants decompositions of C correspond to different S-duality frames for the same underlying family of 4D N = 2 SCFTs. In a previous work [1], we developed such a classification for the A N −1 series of 6D (2, 0) theories. In the present paper, we extend this to the D N series. We outline the procedure for general D N , and construct, in detail, the classification through D 4 . We discuss the implications for S-duality in Spin(8) and Spin(7) gauge theory, and recover many of the dualities conjectured by Argyres and Wittig [2].arXiv:1106.5410v3 [hep-th]

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 β-function, as well as Sp(3) gauge theories with matter in the 3-index traceless antisymmetric representation.

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.