A two-dimensional integrable axionic σ-model and T-duality

An S-matrix is proposed for the two dimensional O(3) σ-model with a dynamical θ-term (axion model). Exploiting an Abelian T-duality transformation connecting the axion model to an integrable SU(2)×U(1) symmetric principal σ-model, strong evidence is presented for the correctness of the proposed S-matrix by comparing the perturbatively calculated free energies with the ones previously obtained by the Thermodynamical Bethe Ansatz. This T-duality transformation also leads to a new Lax-pair for both models. The quantum non-integrability of the O(3) σ-model with a constant θ-term, in contradistinction to the axion model, is illustrated by calculating the 2→3 particle production amplitude to lowest order in θ.