Reduced chiral U(N)×U(N) model

We investigate analytically the reduced chiral model for any N and any dimension d. The relevant group integral for computing the free energy and correlation functions is performed in the semiclassical approximation which becomes exact for d = 1 any N, and some special values of N for any d. The quenching procedure is described and the appropriate expressions, which should be investigated in the large-N limit are written down. For the one-dimensional case the free energy is computed and it agrees with the exact result. The relevance of this reduced model for the underlying continuum chiral theory is discussed and the structure of the vacuum is analyzed.