Quantum structure of T-dualized models with symmetry breaking

We study the principal σ-models defined on any group manifold GLxGR/GD with breaking of GR, and their T-dual transforms. For arbitrary breaking we can express the torsion and Ricci tensor of the dual model in terms of the frame geometry of the initial principal model. Using these results we give necessary and sufficient conditions for the dual model to be torsionless and prove that the one-loop renormalizability of a given principal model is inherited by its dual partner, who shares the same β functions. These results are shown to hold also if the principal model is endowed with torsion. As an application we compute the β functions for the full Bianchi family and show that for some choices of the breaking parameters the dilaton anomaly is absent: for these choices the dual torsion vanishes. For the dualized Bianchi V model (which is torsionless for any breaking), we take advantage of its simpler structure, to study its two-loops renormalizability