Tinkertoys for the D_N series
Oscar Chacaltana, Jacques Distler
TL;DR
This work extends the Gaiotto class S program to the $D_N$ theories by developing a tinkertoy-like construction for 4D $\mathcal{N}=2$ SCFTs arising from compactifications of the 6D $\mathcal{N}=(2,0)$ theory on punctured Riemann surfaces. The authors introduce the Spaltenstein map to relate Nahm and Hitchin data for $D_N$ punctures, analyze regular and irregular punctures, and derive central charges and Coulomb-branch structures, culminating in a complete D4 catalogue and partial progress for higher $D_N$. A central result is the identification of new non-Lagrangian SCFTs, such as $Sp(4)_8\times Sp(2)_7$ and $Sp(5)_7$, along with extensive S-duality analyses for Spin(8) and Spin(7) gauge theories and their dual frames, enriched by explicit Seiberg-Witten curves. The findings extend the scope of class S, revealing intricate dualities and non-Lagrangian sectors in theories with orientifold-related origins and providing concrete tools for computing conformal data in these $D_N$ 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].