An Anomalous Breaking of Supersymmetry in Super-Yang-Mills Theories with Local Coupling and its Implications

We extend the gauge coupling of Super-Yang-Mills theories to an external superfield and find an anomalous breaking of supersymmetry in one-loop order. The anomaly is the variation of a gauge invariant field monomial depending on the logarithm of the coupling. Since the perturbative expansion and all loop diagrams are power series in the coupling, the anomaly cannot be absorbed as a counterterm to the action. We prove that the coefficient of the anomaly is gauge- and scheme-independent and strictly of one-loop order.

With local coupling the symmetric counterterms to the Yang-Mills part are exhausted in one-loop order and it is the anomaly, which gives rise to the two-loop order of the beta-function in pure Super-Yang-Mills theories.