On the Infrared Behaviour of Landau Gauge Yang-Mills Theory with Differently Charged Scalar Fields

TL;DR

This paper explores the infrared behavior of Landau gauge Yang-Mills theory with scalar fields, suggesting a universal confinement mechanism in the gauge sector that applies to both quarks and scalars, based on functional equations.

Contribution

It demonstrates that the confinement mechanism via infrared singularities extends to scalar fields, indicating universality in the gauge sector within functional approaches.

Findings

Infrared singularities can confine scalar fields similarly to quarks.

Color algebra leads to cancellations in Dyson-Schwinger equations.

Confinement mechanism may be universal across matter fields.

Abstract

Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhibiting interesting cancelations purely due to colour algebra.