Positivity Constraints on Anomalies and Supersymmetry

The relation between the trace and R-current anomalies in 4D supersymmetric theories implies that the U(1)$_R$F$^2$, U(1)$_R$ and U(1)$^3_R$ anomalies which matched in studies of N=1 Seiberg duality satisfy positivity constraints. 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, $a_{UV}-a_{IR}$, is always positive, as conjectured by Cardy.