Seeing asymptotic freedom in an exact correlator of a large- N matrix field theory

Exact expressions for correlation functions are known for the large-N (planar) limit of the (1 + 1)-dimensional SU(N) x SU(N) principal chiral sigma model. These were obtained with the form-factor bootstrap, an entirely nonperturbative method. The large-N solution of this asymptotically free model is far less trivial than that of the O(N) sigma model (or other isovector models). Here we study the Euclidean two-point correlation function N super(-1)[left angle bracket]Tr [Phi](0) super([dagger])[Phi](x )[right angle bracket], where [Phi](x) ~ Z super(-1/2)U (x) is the scaling field and U(x) [setmembership] SU(N) is the bare field. We express the two-point function in terms of the spectrum of the operator [radical]-d super(2)/du super(2), where u [setmembership] (-1, 1). At short distances, this expression perfectly matches the result from the perturbative renormalization group.