Phd in PHYSICS

Thesis title: Non-planar large-N Yang-Mills theory and QCD

We study the ultraviolet asymptotics and renormalization in large-N Yang-Mills theory and QCD. Specifically, we compute to the lowest order in perturbation theory n-point correlators of twist-2 gluonic gauge-invariant operators, both in coordinate and momentum representation. We also study their ultraviolet asymptotics by means of renormalization-group improved perturbation theory. We construct the generating functional of the aforementioned correlators. By the fundamental principles of large-N Yang-Mills theory, the generating functional of the nonplanar renormalization-group improved correlators must be asymptotic to the glueball 1-loop effective action. We provide a spectacular check of this statement by showing that the generating functional has indeed the structure of a 1-loop functional determinant. Finally, we study the nonperturbative renormalization of large-N QCD and provide a diagrammatic interpretation in terms of the glueball and meson effective action. The information contained in the aforementioned correlators, effective action and renormalization poses the strongest constraints on any candidate solution of large-N QCD and may also be a powerful guide in the search of such a solution.