$\mathcal{N}=1$ Theories and a Geometric Master Field

Abstract

We study the large $N$ limit of the class of U(N) ${\CN}=1$ SUSY gauge theories with an adjoint scalar and a superpotential $W(\P )$. In each of the vacua of the quantum theory, the expectation values $\la$Tr${\Phi }^p$$\ra$ are determined by a master matrix ${\Phi }_0$ with eigenvalue distribution ${\rho }_{GT}(ł)$. ${\rho }_{GT}(ł)$ is quite distinct from the eigenvalue distribution ${\rho }_{MM}(ł)$ of the corresponding large $N$ matrix model proposed by Dijkgraaf and Vafa. Nevertheless, it has a simple form on the auxiliary Riemann surface of the matrix model. Thus the underlying geometry of the matrix model leads to a definite prescription for computing ${\rho }_{GT}(ł)$, knowing ${\rho }_{MM}(ł)$.

16 pages; v2. Further elaboration in Sec. 5 on the relation between gauge and matrix eigenvalue distributions, v3: Minor changes

References in corpus (16)

• On Geometry and Matrix Models
• Matrix models vs. Seiberg-Witten/Whitham theories
• S-duality of the Leigh-Strassler Deformation via Matrix Models
• Exact Superpotentials for Theories with Flavors via a Matrix Integral
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• On exact superpotentials in confining vacua
• Exact Superpotentials from Matrix Models
• Effective matter superpotentials from Wishart random matrices
• The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation
• Quantum moduli spaces from matrix models
• Exact superpotentials in N=1 theories with flavor and their matrix model formulation
• Konishi anomaly and N=1 effective superpotentials from matrix models
• Massive Vacua of N=1* Theory and S-duality from Matrix Models
• Comments on Effective Superpotentials via Matrix Models
• Perturbative Derivation of Exact Superpotential for Meson Fields from Matrix Theories with One Flavour
• Adding flavor to Dijkgraaf-Vafa

Cited by in corpus (17)

• Penner Type Matrix Model and Seiberg-Witten Theory
• Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• Seiberg Duality in Matrix Models II
• Super Yang-Mills With Flavors From Large N_f Matrix Models
• Cubic curves from matrix models and generalized Konishi anomalies
• Whitham Prepotential and Superpotential
• Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Exact U(N_c)-> U(N_1)xU(N_2) factorization of Seiberg-Witten curves and N=1 vacua
• Improved matrix-model calculation of the N=2 prepotential
• On the Geometry of Matrix Models for N=1*
• Solving matrix models using holomorphy
• On toric geometry, Spin(7) manifolds, and type II superstring compactifications
• Factorization of Seiberg-Witten Curves with Fundamental Matter
• On Geometric Transitions in String Compactifications