The sigma model of a field in SU(N) in 1+1 dimensions 1) is asymptotically free and 2) has applications in the study of gauge theories (massive gauge theory in 1+1 dimensions, q-qbar potentials in 2+1-dimensional Yang-Mills). The large-N Feynman diagrams of this sigma model are planar, hence mean-field/saddle-point methods do not work. Exact correlators were eventually found by combining large-N methods with the form-factor boot- strap. Until recently, the behavior of these expressions was known in the infrared, but not tested in the ultraviolet. In this talk, I will describe the asymptotic ultraviolet form of the two-point function $C(x)$ of the scaling field. Although no perturbation theory was used in its derivation, its form: $C(x)\approx C_{2}\ln^{2}(mx)$ confirms the result of the perturbative renormalization group. The coefficient $C_{2}$ is $1/16\pi=0.01989$.