Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models

Details Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models

2003-07-04

arxiv.org/abs/hep-th/0307054v2

JHEP 0309 (2003) 063

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 2 figures, JHEP style. v2: references added

Scientific paper

10.1088/1126-6708/2003/09/063

We study the phases and geometry of the N=1 A_2 quiver gauge theory using matrix models and a generalized Konishi anomaly. We consider the theory both in the Coulomb and Higgs phases. Solving the anomaly equations, we find that a meromorphic one-form sigma(z)dz is naturally defined on the curve Sigma associated to the theory. Using the Dijkgraaf-Vafa conjecture, we evaluate the effective low-energy superpotential and demonstrate that its equations of motion can be translated into a geometric property of Sigma: sigma(z)dz has integer periods around all compact cycles. This ensures that there exists on Sigma a meromorphic function whose logarithm sigma(z)dz is the differential. We argue that the surface determined by this function is the N=2 Seiberg-Witten curve of the theory.

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