On the dependence of the Landau gauge ghost-gluon-vertex on the number of flavors

Abstract

The gauge-boson, ghost and fermion propagators as well as the gauge-boson--ghost vertex function are studied for SU(N), Sp(2N) and SO(N) gauge groups. We solve a set of coupled Dyson-Schwinger equations in Landau gauge for a variable, fractional number $N_f$ of massless fermions in the fundamental representation. For large $N_f$ we find a phase transition from a chirally broken into a chirally symmetric phase that is consistent with the behavior expected inside the conformal window. Even in the presence of fermions the gauge-boson--ghost-vertex dressing remains small. In the conformal window this vertex shows the expected power law behavior. It does not assume its tree-level value in the far infrared, but the respective dressing function is a constant greater than one.

Comments: 10 pages, 8 figures, 4 tables; v2: changed title, added discussion on the vertex' Nc dependence, added Fig.4,6,7,8, further minor changes