Positivity Constraints on Anomalies and Supersymmetry

TL;DR

This paper explores positivity constraints on anomalies in 4D supersymmetric theories, confirming that the flow of the Euler anomaly coefficient is always positive, supporting Cardy's conjecture across various models.

Contribution

It demonstrates that positivity constraints on anomalies hold in numerous N=1 supersymmetric gauge theories and confirms the positivity of the Euler anomaly flow, supporting a key conjecture.

Findings

Positivity constraints are satisfied in all tested models.

The flow of the Euler anomaly coefficient is always positive.

Constraints hold even with accidental symmetries.

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)$^3_R$ 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.