Gauge theories with dyamical adjoint fermions at large-N

This thesis explores the study of Yang-Mills theories with matter in the adjoint representation, focusing on the limit of large number of colors (large-Nc). The research leverages the property of Eguchi- Kawai reduction, where the theory becomes independent of the torus size in the large-Nc limit, facilitating simulation as a matrix model on a lattice with a single spacetime point. Key to this approach is the application of twisted boundary conditions (TEK reduction), providing a solid and efficient way to formulate and simulate Yang-Mills theory, including its extension with matter in the adjoint representation. The thesis provides a comprehensive overview of the lattice formulation of volume-reduced theories, presenting a review of pertinent concepts. It then presents a collection of results that encompass various research areas, offering insights into multiple topics of investigation. The primary field of application is the pure Yang-Mills theory in the large-Nc limit, of which we present a tree-level improved methodology to perform the scale setting. Furthermore, we present a preliminary calculation of the Λ-parameter in the MS scheme and the chiral condensate of the theory. Moving on to the case of N=1 SUSY Yang-Mills theory, we conducted simulations featuring a single Majorana adjoint fermion. Consistent results were obtained by determining lattice spacing through various observables. We then studied the supersymmetric limit and extrapolated the lattice scale in the massless gluino limit, revealing the expected dependence on bare couplings in the supersymmetric theory.