Infrared behavior of the gluon propagator in Yang–Mills theory

The Dyson–Schwinger equation in a lightlike gauge and the Slavnov–Taylor identities are used to investigate the possible realization of a power-law infrared asymptotic behavior of the type $(p^{-2})^{\alpha+1}$ for the gluon propagator. Such behavior is shown to becompatible with the equation only for $\alpha=1$. By a suitable choice of the transverse part of the three-gluon vertex function, the Dyson–Schwinger equation is solved in the infrared region. The solution corresponds to a combination of a linearly increasing potential and a Coulomb potential.