Ward Identities for Yang-Mills Theory in Abelian Gauges: Abelian Dominance at High Energies

TL;DR

This paper derives Ward identities for Yang-Mills theory in Abelian gauges, showing that at high energies, the theory exhibits Abelian dominance and asymptotic freedom can be understood through an effective Abelian framework.

Contribution

It establishes all-order Ward identities in Abelian gauges, demonstrating that the high-energy behavior of Yang-Mills theory is effectively Abelian, supporting Abelian dominance.

Findings

Coupling constant renormalized only via Abelian two-point function

Asymptotic freedom explained by effective Abelian theory

Ward identities valid to all orders in perturbation theory

Abstract

We consider Yang-Mills theory in a general class of Abelian gauges. Exploiting the residual Abelian symmetry on a quantum level, we derive a set of Ward identities in functional form, valid to all orders in perturbation theory. As a consequence, the coupling constant is only renormalised through the Abelian two-point function. This implies that asymptotic freedom in all Abelian gauges can be understood from an effective Abelian theory alone, which can be interpreted as Abelian dominance in the high energy regime.