Tinkertoys for the D_N series

TL;DR

This paper extends the classification of 4D N=2 superconformal theories from the A_{N-1} series to the D_N series, providing a systematic method to understand their S-duality frames via punctured curves and decompositions.

Contribution

It introduces a procedure for classifying D_N series theories, generalizing previous work on A_{N-1} theories, and explores implications for S-duality in Spin groups.

Findings

Classification of D_N theories via punctured curves and decompositions

Explicit construction for D_4 case

Identification of S-duality frames in Spin(8) and Spin(7) theories

Abstract

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 $ 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].