Positivity constraints on anomalies in supersymmetric gauge theories

The relation between the trace and R-current anomalies in supersymmetric theories implies that the U(1)RF², U(1)R, and U(1)R³ anomalies which are matched in studies of $N=1$ Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as four-dimensional generalizations of the Zamolodchikov c theorem. These constraints are tested in a large number of $N=1$ supersymmetric gauge theories in the non-Abelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomaly-free R current, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient aUV-aIR is always positive, as conjectured by Cardy.