Massive Yang-Mills Theory in Abelian Gauges

TL;DR

This paper proves the perturbative renormalizability of SU(2) Yang-Mills theory in abelian gauges with mass terms, analyzing the implications for Slavnov-Taylor identities and renormalization group equations.

Contribution

It demonstrates the renormalizability of massive Yang-Mills theory in abelian gauges and explores the conditions for finite renormalized masses in the infrared limit.

Findings

Mass terms preserve Slavnov-Taylor identities with modified BRST variations.

Renormalization group equations describe effective action variation with masses.

Finite renormalized masses are achievable under specific wave function renormalization conditions.

Abstract

We prove the perturbative renormalisability of pure SU(2) Yang-Mills theory in the abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow to preserve the standard form of the Slavnov-Taylor identities (but with modified BRST variations), mass terms for the diagonal gauge fields require the study of modified Slavnov-Taylor identities. We comment on the renormalization group equations, which describe the variation of the effective action with the different masses. Finite renormalized masses for the charged gauge fields, in the limit of vanishing bare mass terms, are possible provided a certain combination of wave function renormalization constants vanishes sufficiently rapidly in the infrared limit.