Comments on Effective Superpotentials via Matrix Models

Abstract

Dijkgraaf and Vafa have conjectured that the effective superpotentials for N = 1 four-dimensional supersymmetric gauge theories can be given by the planar diagrams of matrix models. We examine some special models with cubic and quartic tree level superpotentials for adjoint chiral superfield Φ. We consider the effective superpotentials for the classical vacuum Φ = 0 for U (N ) and SO(N )/Sp(N ) gauge theories. We evaluate the effective superpotentials exactly in terms of the matrix model and in terms of closed string theory on Calabi-Yau geometry with fluxes. As a result we find their perfect agreements.

Exact Superpotentials, Theories with Flavor and Confining Vacua

“…The main difference in both expressions for the exact superpotential is that in [17] the dependence of the superpotential in the glueball superfield S is given in an implicit way, whereas here we write that dependence in an explicit way. The results presented here also agree with the ones appearing in [28,29] for the special cases of quadratic and quartic tree level superpotentials. The expression (3.15) is valid for an arbitrary tree level superpotential.…”

Phases of SO(Nc) gauge theories with flavors

“…Keeping the second and third terms of (4.18) we have one solution of c ∼ Λ 12 , which gives the one vacuum of SO(4) × U(1) where SO(4) is at the Special branch 22 . Now we consider other special cases.…”

An exact relation for orientifold field theories with arbitrary superpotential

“…However, Refs. [31,32] deal with U(N) group rather than SU(N), and, therefore, we need to translate their results from U(N) to SU(N). This translation, together with the relations…”

“…This result can be expressed as follows: the effective superpotentials in both theories take the same form, except for an anticipated overall factor (we use the notation of Ref. [31]),…”