Chiral field theories, Konishi anomalies and matrix models

We study a chiral N=1, U(N) field theory in the context of the Dijkgraaf-Vafacorrespondence. Our model contains one adjoint, one conjugate symmetric and oneantisymmetric chiral multiplet, as well as eight fundamentals. We compute thegeneralized Konishi anomalies and compare the chiral ring relations they inducewith the loop equations of the (intrinsically holomorphic) matrix model definedby the tree-level superpotential of the field theory. Surprisingly, we findthat the matrix model is well-defined only if the number of flavors equals two!Despite this mismatch, we show that the 1/N expansion of the loop equationsagrees with the generalized Konishi constraints. This indicates that the matrixmodel - gauge theory correspondence should generally be modified when appliedto theories with net chirality. We also show that this chiral theory producesthe same gaugino superpotential as a nonchiral SO(N) model with a singlesymmetric multiplet and a polynomial superpotential.Comment: 43 page