Reliable semiclassical computations in QCD

Abstract

We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For $N_f>N$, a systematic computation is possible; for $N_f<N$, it is not. $N_f=N$ is a borderline case. In our analysis, we see explicitly the exponential suppression of instanton effects at large $N$. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit.