# Tinkertoys for Gaiotto duality

 Title: Tinkertoys for Gaiotto duality Author: Chacaltana Alarcon, Oscar Chacaltana 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 C correspond to different S -duality frames for the same underlying family of 4D \mathcal{N}=2 SCFTs . We developed such a classification for the A _{N -1} and the D _N series of 6D (2 ,0 ) theories . We outline the procedure for general A _{N -1} and D _N , and construct , in detail , the classification through A _4 and D _4 , respectively . URI: http : / /hdl .handle .net /2152 /ETD -UT -2011 -08 -4359 Date: 2011-09-28

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