A general non renormalization theorem in the extended antifield formalism

TL;DR

This paper develops a general non-renormalization theorem within the extended antifield formalism, providing conditions for vanishing beta functions in gauge theories without relying on power counting or gauge fixing specifics.

Contribution

It introduces a broad non-renormalization theorem applicable to gauge theories, extending the algebraic renormalization framework to derive anomaly and beta function conditions.

Findings

Derived general anomaly consistency conditions

Established criteria for beta function vanishing

Applicable to arbitrary non anomalous symmetries

Abstract

In the context of algebraic renormalization, the extended antifield formalism is used to derive the general forms of the anomaly consistency condition and of the Callan-Symanzik equation for generic gauge theories. A local version of the latter is used to derive sufficient conditions for the vanishing of beta functions associated to terms whose integrands are invariant only up to a divergence for an arbitrary non trivial non anomalous symmetry of the Lagrangian. These conditions are independent of power counting restrictions and of the form of the gauge fixation.