Notes on anomalies, baryons, and Seiberg duality

We consider an N=1 SU(N_c) SUSY gauge theory with N_f \geq N_c matter multiplets transforming in the fundamental and antifundamental representations of the gauge group. Using the Konishi anomaly and a non-anomalous conservation law, we derive a system of partial differential equations that determine the low energy effective superpotential as a function of the mesonic and baryonic vacuum expectation values. We apply the formalism to the cases of N_f = N_c and N_f = N_c +1 where the equations are easily integrated and recover the known results. We further apply the formalism to derive a system of partial differential equations to determine the low energy effective superpotential for the Seiberg dual theories. Finally we briefly discuss the associated matrix models via the Dijkgraaf-Vafa conjecture.