On Confinement, Chiral Symmetry Breaking, and the UA(1) anomaly in Functional Approaches

TL;DR

This paper reviews functional approaches to Landau gauge Yang-Mills theory, highlighting how different solutions relate to confinement, chiral symmetry breaking, and the UA(1) anomaly, emphasizing the universality of confinement in the gauge sector.

Contribution

It clarifies the connection between confinement, chiral symmetry breaking, and the UA(1) anomaly within the framework of functional equations, especially for the scaling solution.

Findings

Positivity violation indicates gluon confinement.

Infrared singularities in the quark-gluon vertex signal quark confinement.

Scaling solution relates confinement phenomena to chiral symmetry breaking.

Abstract

The so-called decoupling and scaling solutions of functional equations of Landau gauge Yang-Mills theory are briefly reviewed. In both types of solutions the positivity violation seen in the gluon propagator is taken as an indication of gluon confinement. In the scaling solution the resulting infrared singularities of the quark-gluon vertex are responsible for the linear potential between static quarks and are therefore signaling quark confinement. A corresponding description of the UA(1) anomaly in functional approaches is only known for the scaling solution. Nevertheless, it seems puzzling at first sight that quark confinement is related to the dynamical and anomalous breaking of chiral symmetry in a self-consistent manner: One obtains either all these phenomena or none. For the scaling solution also fundamental scalar fields are confined. This provides evidence 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.