Positivity Constraints on Anomalies and Supersymmetry

Abstract

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)${}_R^3$ 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.

8 pages, uses sprocl.sty, talk given at PASCOS-98