Dualised σ-models at the two-loop order Original Research Article

We adress ourselves the question of the quantum equivalence of non-abelian dualised σ-models on the simple example of the T-dualised SU(2) σ-model. This theory is classically canonically equivalent to the standard chiral SU(2) σ-model. It is known that the equivalence also holds at the first order in perturbations with the same β functions. However, this model has been claimed to be non-renormalisable at the two-loop order. The aim of the present work is the proof that it is — at least up to this order — still possible to define a correct quantum theory. Its target space metric being only modified in a finite manner, all divergences are reabsorbed into coupling and fields (infinite) renormalisations.