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) ₑF^2, U (1) ₑ, and U (1) ₑ^3 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 aₔₕ-a₈ₑ is always positive, as conjectured by Cardy.