On singular effective superpotentials in supersymmetric gauge theories


Using the generalized Konishi anomaly equation in the chiral ring of a four dimensional N=1 SU(N) supersymmetric gauge theory with fundamental and anti-fundamental matters, we derive the large N_f effective superpotentials of the theory. These superpotentials are singular when expressed in terms of local gauge-invariant chiral fields. We show that these effective superpotentials, despite being singular, are perfectly sensible, i.e. they correctly describe the moduli space of vacua, are consistent under RG flow to fewer flavors upon turning on masses, and also (in the case of SU(2) gauge group) reproduce by a tree-level calculation all the higher-derivative F-terms recently calculated by Beasley and Witten by instanton methods.