${\cal N}=1$ Theories and a Geometric Master Field
arXiv:hep-th/0211100 · doi:10.1088/1126-6708/2003/05/033
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 $W(¶)$. In each of the vacua of the quantum theory, the expectation values $\la$Tr$Φ^p$$\ra$ are determined by a master matrix $Φ_0$ with eigenvalue distribution $Ï_{GT}(Å)$. $Ï_{GT}(Å)$ is quite distinct from the eigenvalue distribution $Ï_{MM}(Å)$ 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 $Ï_{GT}(Å)$, knowing $Ï_{MM}(Å)$.
16 pages; v2. Further elaboration in Sec. 5 on the relation between gauge and matrix eigenvalue distributions, v3: Minor changes