Cubic curves from matrix models and generalized Konishi anomalies

We study the matrix model/gauge theory connection for three different N=1models: U(N) x U(N) with matter in bifundamental representations, U(N) withmatter in the symmetric representation, and U(N) with matter in theantisymmetric representation. Using Ward identities, we explicitly show thatthe loop equations of the matrix models lead to cubic algebraic curves. We thenestablish the equivalence of the matrix model and gauge theory descriptions intwo ways. First, we derive generalized Konishi anomaly equations in the gaugetheories, showing that they are identical to the matrix-model equations.Second, we use a perturbative superspace analysis to establish the relationbetween the gauge theories and the matrix models. We find that the gaugecoupling matrix for U(N) with matter in the symmetric or antisymmetricrepresentations is_not_ given by the second derivative of the matrix-model freeenergy. However, the matrix-model prescription can be modified to give thegauge coupling matrix.Comment: 27 pages, 2 figures; v2: minor corrections and clarifications; v3: published versio