Positivity Constraints on Anomalies in Supersymmetric Gauge Theories

Abstract

The relation between the trace and R-current anomalies in supersymmetric theories implies that the U$(1{)}_R{F}^2$, U$(1{)}_R$ and U$(1{)}_R^3$ 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, $a_{UV}-a_{IR}$, is always positive, as conjectured by Cardy.

latex, 36 pages

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