On the ground state and infrared divergences of Goldstone bosons in two dimensions

We study the O(N) invariant Goldstone field theory in two dimensions where rigorous theorems forbid the occurrence of spontaneous symmetry breaking. We argue that for computation of the ground state energy at weak coupling it is still the standard Goldstone perturbation expansion that is applicable. This happens due to cancellation of infrared divergences and we demonstrate this fact explicitly at the two-loop level.