Positivity Constraints on Anomalies in Supersymmetric Gauge Theories

TL;DR

This paper investigates positivity constraints on anomalies in N=1 supersymmetric gauge theories, confirming that certain anomaly-related quantities always satisfy positivity conditions, including the conjectured positivity of the Euler anomaly difference.

Contribution

It establishes positivity constraints on anomalies in supersymmetric theories and verifies them across many models, supporting the conjecture that the Euler anomaly difference is always positive.

Findings

Anomaly constraints are satisfied in all tested models.

The flow of the Euler anomaly coefficient is always positive.

Rigorous and conjectured positivity constraints hold in various supersymmetric theories.

Abstract

The relation between the trace and R-current anomalies in supersymmetric theories implies that the U$(1)_RF^2$, 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.