An anomalous breaking of supersymmetry in supersymmetric gauge theories with local coupling

TL;DR

This paper investigates an anomalous supersymmetry breaking in Super-Yang-Mills theories with local gauge coupling, revealing a one-loop order anomaly that influences higher-order gauge beta functions and cannot be removed by counterterms.

Contribution

It introduces a framework extending gauge coupling to a superfield, identifies an anomaly in supersymmetry breaking, and links it to the two-loop gauge beta function in pure Super-Yang-Mills theories.

Findings

Anomaly appears at one-loop order and vanishes with constant coupling.

The anomaly is gauge and scheme independent, arising from non-local contributions.

The anomaly influences the two-loop order of the gauge beta function.

Abstract

We extend the gauge coupling of Super-Yang-Mills theories to an external superfield composed out of a chiral and an antichiral superfield and perform renormalization in the extended model. In one-loop order we find an anomalous breaking of supersymmetry which vanishes in the limit to constant coupling. The anomaly arises form non-local contributions and its coefficient is gauge and scheme independent and strictly of one-loop order. In the perturbative framework of the construction the anomaly cannot be absorbed as a counterterm to the classical action. With local gauge coupling the symmetric counterterms with chiral integration are holomorphic functions and this property is independent from the specific regularization scheme. Thus, the symmetric counterterm to the Yang-Mills part is of one-loop order only - and it is the anomaly which gives rise to the two-loop order of the gauge $\beta$-function in pure Super-Yang-Mills theories and to its closed all-order expression.