Dependence of the Landau gauge ghost-gluon-vertex on the number of flavors

The gauge-boson, ghost and fermion propagators as well as the gauge-boson-ghost vertex function are studied for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>SU</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>Sp</e:mi><e:mo stretchy="false">(</e:mo><e:mrow><e:mn>2</e:mn><e:mi>N</e:mi></e:mrow><e:mo stretchy="false">)</e:mo></e:mrow></e:math>, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>SO</i:mi><i:mo stretchy="false">(</i:mo><i:mi>N</i:mi><i:mo stretchy="false">)</i:mo></i:mrow></i:math> gauge groups. We solve a set of coupled Dyson-Schwinger equations in Landau gauge for a variable, fractional number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>N</m:mi><m:mi>f</m:mi></m:msub></m:math> of massless fermions in the fundamental representation. For large <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>N</o:mi><o:mi>f</o:mi></o:msub></o:math> 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 1. Published by the American Physical Society 2024