Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory
arXiv:hep-th/0309049 · doi:10.1016/j.physletb.2003.10.098
Abstract
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.
15 pages, 7 figures
References in corpus (13)
- Chiral Rings and Anomalies in Supersymmetric Gauge Theory
- A Perturbative Window into Non-Perturbative Physics
- Perturbative Computation of Glueball Superpotentials
- Phases of N=1 Supersymmetric Gauge Theories and Matrices
- N=1 and N=2 Geometry from Fluxes
- Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
- On exact superpotentials in confining vacua
- Comments on Effective Superpotentials via Matrix Models
- Branches of N=1 Vacua and Argyres-Douglas Points
- Gravity Induced C-Deformation
- Konishi anomaly approach to gravitational F-terms
- The C-Deformation of Gluino and Non-planar Diagrams
- Matrix Models, Argyres-Douglas singularities and double scaling limits
Cited by in corpus (6)
- Liouville Field Theory -- A decade after the revolution
- An Introduction to Supersymmetric Gauge Theories and Matrix Models
- Properties of Higher-Order Phase Transitions
- Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models
- The Matrix Model Curve Near the Singularities
- Fermionic Matrix Models and Bosonization