Ultraviolet behavior of the gluon propagator in the maximal Abelian gauge

The ultraviolet asymptotic behavior of the gluon propagator is evaluated in the maximal Abelian gauge in the $SU(2)$ gauge theory on the basis of the renormalization-group improved perturbation theory at the one-loop level. Square-root singularities obtained in the Euclidean domain are attributed to artifacts of the one-loop approximation in the maximal Abelian gauge and the standard normalization condition for the propagator used in our study. It is argued that this gauge is essentially nonperturbative.

Figure 1

Polarization operator of the diagonal gluon.

Figure 2

Polarization operator of the “off-diagonal” gluon.

Figure 3

Projection of characteristic curves onto the $(\alpha ,g)$ plane.

Figure 4

Projection of characteristic curves onto the $(\alpha ,g)$ plane.