Perturbative Quantum (In)equivalence of Dual $\sigma$ Models in $2$   dimensions
  Various examples of target space duality transformations are investigated up to two loop order in perturbation theory. Our results show that when using the tree level (`naive') transformation rules the dual theories are in general {\it inequivalent} at two loops to the original ones, (both for the Abelian and the non Abelian duality). 
J. Balog, P. Forg\'acs, Z. Horv\'ath and L. Palla