Principal chiral field at large N

We present an exact and explicit solution of the principal chiral field in two dimensions for a group manifold with infinitely large rank. The energy of the ground state is explicitly found for the external Noether fields of arbitrary magnitude. The exact Gell-Mann-Low function exhibits asymptotic freedom behaviour at large value of the field in agreement with perturbative calculations. Coefficients of the perturbative expansion in the renormalized charge are calculated. They grow factorially with the order showing the presence of renormalons. At small field we found an inverse logarithmic singularity in the ground-state energy at the mass gap which indicates that at N=∞ the spectrum of the theory contains extended objects rather than pointlike particles. ((orig.))