The Most General and Renormalizable Maximal Abelian Gauge

TL;DR

This paper develops the most general form of the Maximal Abelian gauge for SU(2) Yang-Mills theory, analyzes its symmetries, simplifies it, and computes key renormalization group functions to understand low-energy QCD physics.

Contribution

It introduces the most general gauge fixing with eleven parameters, reduces it using symmetries, and connects it to previous models, providing one-loop renormalization group calculations.

Findings

Identified the most general Maximal Abelian gauge with eleven parameters.

Reduced parameters using symmetry considerations to simpler forms.

Calculated beta functions and anomalous dimensions at one-loop order.

Abstract

We construct the most general gauge fixing and the associated Faddeev-Popov ghost term for the SU(2) Yang-Mills theory, which leaves the global U(1) gauge symmetry intact (i.e., the most general Maximal Abelian gauge). We show that the most general form involves eleven independent gauge parameters. Then we require various symmetries which help to reduce the number of independent parameters for obtaining the simpler form. In the simplest case, the off-diagonal part of the gauge fixing term obtained in this way is identical to the modified maximal Abelian gauge term with two gauge parameters which was proposed in the previous paper from the viewpoint of renormalizability. In this case, moreover, we calculate the beta function, anomalous dimensions of all fields and renormalization group functions of all gauge parameters in perturbation theory to one-loop order. We also discuss the implication of these results to obtain information on low-energy physics of QCD.