We study the phases and geometry of the N = 1 A2 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 σ(z)dz is naturally defined on the curve ς 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 ς: σ(z)dz has integer periods around all compact cycles. This ensures that there exists on ς a meromorphic function whose logarithm σ(z)dz is the differential. We argue that the surface determined by this function is the N = 2 Seiberg-Witten curve of the theory.
Phases and geometry of the N=1 A(2) quiver gauge theory and matrix models
TRINCHERINI, ENRICO
2003
Abstract
We study the phases and geometry of the N = 1 A2 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 σ(z)dz is naturally defined on the curve ς 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 ς: σ(z)dz has integer periods around all compact cycles. This ensures that there exists on ς a meromorphic function whose logarithm σ(z)dz is the differential. We argue that the surface determined by this function is the N = 2 Seiberg-Witten curve of the theory.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
