  We study the gluon sector in pure Yang-Mills theories via the computation of
two, three and four point Landau gauge gluon correlation functions via LQCD
using the Wilson action for Monte-Carlo simulations. The first goal was to use
lattice tensor representations for the propagator in four dimensions to
understand/quantify deviations of the lattice propagator from its continuum
form. We also identified classes of kinematic configurations where these
deviations are minimal and the continuum description of lattice tensors is
improved. These tensor structures also allow to verify that the continuum
Slavnov-Taylor identity for the propagator is is fulfilled, with good accuracy,
on the lattice. The computation of the three gluon vertex served to explore the
so-called zero crossing, a property related to the ghost dominance at the
infrared scales that restricts the behaviour of the three gluon vertex. We also
explore the possible existence of a ghost mass preventing the IR divergence.
Functional forms were used to model the lattice data and explore the two
different possibilities for the IR behaviour. In the first case we estimate the
mass scale associated with the crossing and search for a possible sign of the
divergence. Secondly, we study the possibility of a sign change and a finite
zero momentum value of the vertex. A last topic is the calculation of the four
gluon vertex. A suitable choice of kinematics allows to eliminate the unwanted
contributions from lower order functions while large statistical fluctuations
hinder the precise computation of this object. Our investigation is a proof of
concept, we show that the lattice computation of the four gluon correlation
function is feasible with reasonable computational resources. An increase in
statistics is necessary to provide a clearer signal on the complete correlation
function and to compute the one particle irreducible function.
