The 't Hooft Expansion for the Principal Chiral Model

The principal chiral model (PCM) is a quantum field theory in 1+1 dimesions. Its local field is an SU(N) matrix. The 1/N-expansion is much harder to solve than that of isovector (e.g. CP(N), O(N)) models, because the fundamental field is a matrix, not an isovector. The large-N diagrams of the PCM are planar, rather than linear. Notheless, exploiting integrability and the form factor bootstrap, the 1/N expansion can be made to work. Exact expressions for correlation functions have been obtained; their behavior has been found in both infrared and ultraviolet limits. The latter limit is consistent with the asymptotic freedom of the PCM.