2D Principal Chiral Field at Large N as a Possible Solvable 2D String Theory

We present the exact and explicit solution of the principal chiral field in two dimensions for an infinitely large rank group manifold. The energy of the ground state is explicitly found for the external Noether’s fields of an arbitrary magnitude. 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. 1 Unité Propre du Centre National de la Recherche Scientifique, associée à l’École Normale Supérieure et à l’Université de Paris-Sud.