ar X iv : h ep - l at / 9 80 90 72 v 1 1 1 Se p 19 98 1 The large - N phase transition of lattice SU ( N ) gauge theories

The large-N limit of SU(N) gauge theories is of considerable interest from the phenomenological point of view, and is one of our sources of understanding of non-perturbative QCD. The theoretical side is no less interesting, allowing e.g. to establish precise relationships between Yang-Mills theories and string theories. A crucial property of large-N field theories is factorization: connected Green’s functions of invariant quantities are suppressed with respect to the corresponding disconnected parts by powers of 1/N . One of the most notable consequences of factorization is the possibility of constructing reduced models, i.e. single-site models which reproduce a lattice gauge theory in the N → ∞ limit [1,2]. Despite the considerable simplifications occurring for large N , many interesting models have not been solved analytically; therefore we must resort to approximate techniques, such as numerical simulations.