Large Nc physics from the lattice

Abstract

I summarise what lattice methods can contribute to our understanding of the phenomenology of QCD at large Nc and describe some recent work on the physics of SU(Nc) gauge theories. These non-perturbative calculations show that there is indeed a smooth Nc -> infinity limit and that it is achieved by keeping g.g.Nc fixed, confirming the usual diagrammatic analysis. The lattice calculations support the crucial assumption that the theory remains linearly confining at large Nc. Moreover we see explicitly that Nc=3 is `close to' Nc=infinity for many physical quantities. We comment on the fate of topology and the deconfining transition at large Nc. We find that multiple confining strings are strongly bound. The string tensions, K(k), of these k-strings are close to the M(-theory)QCD-inspired conjecture as well as to `Casimir scaling' with the most accurate recent calculations favouring the former. We point out that closed k-strings provide a natural way for non-perturbative effects to introduce O(1/Nc) corrections into the pure gauge theory, in contradiction to the conventional diagrammatic expectation.