Tinkertoys for the D_N series

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].

53 pages, 268 figures, LaTeX2e, utarticle class. Version 3: JHEP version, with a few typos in the tables corrected. Version 2: global symmetries corrected, for 7 entries in table of interacting SCFTs in D4 theory. Thanks to Simone Giacomelli and Yuji Tachikawa for alerting us to the problem in version 1

References in corpus (10)

• S-duality in N=2 supersymmetric gauge theories
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Mirrors of 3d Sicilian theories
• Tinkertoys for Gaiotto Duality
• The gravity duals of N=2 superconformal field theories
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Gauge Theory, Ramification, And The Geometric Langlands Program
• More Three Dimensional Mirror Pairs
• Gaiotto Duality for the Twisted A_{2N-1} Series
• N=2 S-duality via Outer-automorphism Twists

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