Large-N QCD-like gauge theories

In this thesis we study some properties of N = 1 supersymmetric SU(N) Yang-Mills (SYM) theory and pure SU(N) Yang-Mills (YM) theory in ’t Hooft large-N limit. First, to say it in a nutshell, we work out in a closed form the asymptotic renormalization-group improved generating functional of the connected correlators of superfield twist-2 operators in N = 1 SYM theory in Euclidean superspace and its planar and leading nonplanar parts in the large-N expansion. We verify – as originally predicted in [1] and checked in the component formalism [2–5] – that the leading nonplanar asymptotic RG-improved generating functional matches the structure of logarithm of a functional superdeterminant of the corresponding nonperturbative object arising from the glueball/gluinoball one-loop effective action [1–5], which should be asymptotic to at short distances because of the asymptotic freedom. Hence, our large-N computation sets strong ultraviolet asymptotic constraints on the yet-to-come nonperturbative solution of large-N N = 1 SYM theory that may be a pivotal guide for the search of such a solution. Second, we provide a detailed proof of the triviality of the v.e.v. of twistor Wilson loops [6], a class of Wilson loops in the planar limit of pure SU(N) YM theory previously defined by means of a noncommutative deformation of the theory in which the coordinates are promoted to noncommuting operators. These observables define a trivial topological field theory (TFT) at all energy scale underlying the large-N limit of pure SU(N) YM theory [6] that at next-to-leading order has been conjectured to capture some nonperturbative aspects of the theory [1].