This thesis is devoted to the study of Yang-Mill theories with fermions in the ad-joint representation. Through numerical Monte-Carlo simulations, we investigated non-perturbative phenomena such as confinement and chiral symmetry breaking. We studied three theories closely related to each other but that differ on the fermionic mattter content. First, we considered Yang-Mills theory coupled to an adjoint Dirac fermion, Nf = 1 adjQCD. We focused on studying the IR physics of the theory, which must be close to the lower end of the conformal window, making the theory appealing for composite Higgs models. Our simulations explore a polynomial approximation of the Overlap Dirac operator, which preserves a modified chiral symmetry on the lattice. With this implementation, we confirmed the existence of a non-vanishing chiral condensate, pointing to an scenario where both confinement and spontaneous chiral symmetry breaking are realized. By taking the infinite mass limit of one Weyl component of the adjoint Dirac Fermion, Nf = 1 adjQCD is mapped to N = 1 SYM; the supersymmetric extension of the strong force in the standard model. Even though the lattice explicitly breaks supersymmetry, N = 1 SYM has been simulated successfully. It has been shown that a correct tuning of the fermion mass to the chiral point suffices to recover supersymmetry in the continuum. For theories with a larger parameter space, the tuning point of the parameters is unclear. In this work, we investigated whether the tuning can be performed using results from perturbation theory. We used a gauge independent renormalization scheme (GIRS) suitable for both perturbative computations and lattice simulations. This way we could determined and compared the results from perturbation theory and from the lattice. Finally, we considered the case of pure Yang-Mills theories and the role that pseudoparticles can play in confinement. Some models have been proposed where fractional instantons could explain the properties of the vacuum of pure Yang-Mills theory. In this work, we used a method based on zero modes of the adjoint Dirac operator to reveal the instantons present in Monte-Carlo generated configurations. With this methodology, models for confinement based on instantons can be tested on the lattice.
Ivan Soler Calero (Wed,) studied this question.