Superconformal block quivers, duality trees and Diophantine equations View Full Text


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Article Info

DATE

2013-11

AUTHORS

Amihay Hanany, Yang-Hui He, Chuang Sun, Spyros Sypsas

ABSTRACT

We generalize previous results on = 1, (3 + 1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e. that the beta and gamma functions vanish in addition to anomaly cancellation, translate to a Diophantine equation in terms of the quiver data. We re-derive results for low block numbers revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points of such theories. After explicitly computing the five block case Diophantine equation, we use this structure to reorganize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate them 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. More... »

PAGES

17

References to SciGraph publications

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  • 2004-12-18. D-branes on vanishing del Pezzo surfaces in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2001-12-03. Toric duality is Seiberg duality in JOURNAL OF HIGH ENERGY PHYSICS
  • 2006-01-19. Brane dimers and quiver gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 1999-02-17. Non-abelian finite gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-03. Probing the space of toric quiver theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-07-29. Duality cascades and duality walls in JOURNAL OF HIGH ENERGY PHYSICS
  • 2003-01-31. On Berenstein-Douglas-Seiberg Duality in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-07-30. The holographic Weyl anomaly in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01. On the classification of brane tilings in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-09-02. Seiberg duality is an exceptional mutation in JOURNAL OF HIGH ENERGY PHYSICS
  • 2003-02-27. Quiver theories, soliton spectra and Picard-Lefschetz transformations in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2006-04-19. New results on superconformal quivers in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-01. Symmetries of abelian orbifolds in JOURNAL OF HIGH ENERGY PHYSICS
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  • Identifiers

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    DOI

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    DIMENSIONS

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