THE EXACT MASS GAP OF THE O(N) SIGMA-MODEL FOR ARBITRARY N-GREATER-THAN-OR-EQUAL-TO-3 IN D = 2

Starting from the exact S-matrix of the O(N) model we derive an integral equation, which determines the free energy as the function of the chemical potential coupled to a Noether charge. For N = 3 and 4 the equation agrees with that obtained earlier by Polyakov and Wiegmann with Bethe Ansatz for the related fermionic models. Using a method discussed in a recent paper by M. Maggiore and the authors, this integral equation predicts for the mass gap m = ( 8 e) 1 (N-2) × [ 1 Γ ( 1 + 1 (N - 2))] ΛMS. © 1990.