Renormalization of gauge invariant operators and anomalies in Yang-Mills theory

TL;DR

This paper proves a conjecture about the structure of gauge invariant operators in Yang-Mills theory and derives the general form of anomalies using a cohomological approach without power counting.

Contribution

It establishes a long-standing conjecture on the structure of renormalized gauge invariant operators and derives the anomaly consistency condition through a purely cohomological method.

Findings

Confirmed the structure of renormalized gauge invariant operators.

Derived the general solution for anomalies with sources.

Utilized a cohomological approach without power counting.

Abstract

A long-standing conjecture on the structure of renormalized, gauge invariant, integrated operators of arbitrary dimension in Yang-Mills theory is established. The general solution of the consistency condition for anomalies with sources included is also derived. This is achieved by computing explicitely the cohomology of the full unrestricted BRST operator in the space of local polynomial functionals with ghost number equal to zero or one. The argument does not use power counting and is purely cohomological. It relies crucially on standard properties of the antifield formalism.