Amihay Hanany, Yang-Hui He, Chuang Sun, Spyros Sypsas
We derive necessary and sufficient conditions in the form of Diophantine equations for N=1, (3+1)-dimensional, block quiver gauge theories to have non trivial infra-red superconformal fixed points. Techniques from representation theory of quivers are used in order to generalize known results for theories with a small number of gauge groups factors to arbitrary block quiver gauge theories. The latter can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate these theories to certain subsets of imaginary roots. These methods also allow for an interpretation of Seiberg duality as the action of the affine Weyl group on the root lattice.
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http://arxiv.org/abs/1211.6111
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