Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

TL;DR

This paper investigates two known solutions of Yang-Mills theory in Landau gauge using stochastic quantization and effective action formalism, revealing their gauge dependence and stability, with implications for understanding confinement.

Contribution

It demonstrates how stochastic quantization affects the existence of scaling and massive solutions and shows the massive solution's robustness outside Landau gauge.

Findings

Scaling solution disappears with soft gauge-fixing in stochastic quantization.

Massive solution persists outside Landau gauge.

Massive solution minimizes the quantum effective action in a bare vertex approximation.

Abstract

Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for high (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as "scaling" features an infrared power law for the gluon and ghost propagators, the "massive" solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quantization. What we find, in four dimensions and in a rainbow approximation, is that stochastic quantization supports both solutions in Landau gauge but the scaling solution abruptly disappears when the parameter controlling the drift force is separated from zero (soft gauge-fixing), recovering only the perturbative propagators; the massive solution seems to survive the extension outside Landau gauge. These results are consistent with the scaling solution being related to the existence of a Gribov horizon, with the massive one being more general. We also examine the effective action in Faddeev-Popov quantization that generates the rainbow and we find, for a bare vertex approximation, that the the massive-type solutions minimise the quantum effective action.