Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory

Details Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory

2003-09-04

arxiv.org/abs/hep-th/0309049v1

Phys.Lett. B578 (2004) 432-442

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 7 figures

Scientific paper

A hermitian one-matrix model with an even quartic potential exhibits a third-order phase transition when the cuts of the matrix model curve coalesce. We use the known solutions of this matrix model to compute effective superpotentials of an N=1, SU(N) supersymmetric Yang-Mills theory coupled to an adjoint superfield, following the techniques developed by Dijkgraaf and Vafa. These solutions automatically satisfy the quantum tracelessness condition and describe a breaking to SU(N/2) x SU(N/2) x U(1). We show that the value of the effective superpotential is smooth at the transition point, and that the two-cut (broken) phase is more favored than the one-cut (unbroken) phase below the critical scale. The U(1) coupling constant diverges due to the massless monopole, thereby demonstrating Ferrari's general formula. We also briefly discuss the implication of the Painleve II equation arising in the double scaling limit.

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