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

Understand

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.