Exact Results for the SU(∞) Principal Chiral Model

Exact correlation functions of N × N matrix-valued quantized fields are not generally known, even as N approaches infinity (the planar limit). This is in stark contrast to isovector field theories, which have straightforward 1/N-expansions. I review the method by which exact correlation functions of the large-N limit (1 + 1)-dimensional sigma model with SU(N) × SU(N) symmetry. This field theory is asymptotically free, with a dynamically generated mass gap. The technique is a combination of the 1/N-expansion of the S matrix and Smirnov's form-factor axioms. I briefly discuss how to extract the short-distance behavior of the exact correlation function, which can be compared with perturbation theory.