The Power of the Anomaly Consistency Condition for the Master Ward Identity: Conservation of the Non-Abelian Gauge Current

Abstract Extending local gauge transformations in a suitable way to Faddeev–Popov ghost fields, one obtains a symmetry of the total action, i.e., the Yang–Mills action plus a gauge fixing term (in a $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> -gauge) plus the ghost action. The anomalous Master Ward Identity (for this action and this extended, local gauge transformation) states that the pertinent Noether current—the interacting “gauge current”—is conserved up to anomalies. It is proved that, apart from terms being easily removable (by finite renormalization), all possible anomalies are excluded by the consistency condition for the anomaly of the Master Ward Identity, recently derived in Brunetti et al. (Ann Henri Poincaré, 2023, https://doi.org/10.1007/s00023-023-01388-w ).