On conformal properties of the dualized sigma-models

We have calculated the first-order β-functions for a σ-model (with dilaton) dualized with respect to an arbitrary Lie group that acts without isotropy. We find that non-abelian duality preserves conformal invariance for semi-simple groups, but in general there is an extra contribution to the β-function proportional to the trace of the structure constants, which cannot be absorbed into an additional dilaton shift. Two particular examples, a Bianchi V cosmological background and the G ⊗ G WZW model, are discussed.