Explicit factorization of Seiberg–Witten curves with matter from random matrix models

Abstract

Within the Dijkgraaf-Vafa correspondence, we study the complete factorization of the Seiberg-Witten curve for U (N c ) gauge theory with N f < N c massive flavors. We obtain explicit expressions, from random matrix theory, for the moduli, parametrizing the curve. These moduli characterize the submanifold of the Coulomb branch where all monopoles become massless. We find that the matrix model reveals some nontrivial structures of the gauge theory. In particular the moduli are additive with respect to adding extra matter and increasing the number of colors.

Supersymmetric gauge theories with flavors and matrix models

“…Furthermore, one can show that both (3.6) and (3.4) for K = 0 are exactly the same as the one given by the strong coupling analysis in [16] and the weak coupling analysis in [28,29]. 6 As we mentioned before, for m f = 0 the allowed Higgs branch requires K ≤ N f but the strong coupling analysis gives K ≤ N f /2.…”

“…f for any K. In other words, all K-th branches collapse 16 to the same branch under the constraint (4.3). Figure 6: Under the constraint (4.3), contours C 1 and C 2 become degenerate:…”

Exact Superpotentials, Theories with Flavor and Confining Vacua

“…The exact effective superpotential was computed in [17] for a pure gauge theory using the "integrating in" procedure. The addition of fundamental matter was considered in [10,33] for the particular case of a quadratic tree level superpotential, W tree = 1 2 trΦ 2 , and in [30], using random matrix models, for a more general tree level superpotential. The method described in this section shows that in order to obtain the exact superpotential with fundamental matter in the maximally degenerating point of the moduli space we just need to compute, within the matrix model formulation, vacuum expectation values of several operators.…”

“…1 The generalization of (3.4) to the case with matter has been addressed in [30,32,31], and the expressions for the moduli that factorize the curve (3.3) become very complicated compared to the pure gauge theory case. However, for the computation of the exact effective superpotential that we develop in this section, we just need the simple form of (3.4).…”

“…The fact that in the results presented in [30] the dependence on the glueball superfield enters in a highly non-linear way in the JHEP06 (2004)051 equation for the effective superpotential, makes it very complicated to compare both results. Nevertheless, we can check our result by comparing it with the one obtained in [10] for the particular case of a quadratic tree level superpotential, W tree = 1 2 trΦ 2 .…”