Renormalisability of T-dualised non-homogeneous sigma-models

Abstract

The quantum equivalence between $\sigma$-models and their non-abelian T-dualised partners is examined for a large class of four dimensional non-homogeneous and quasi-Einstein metrics with an isometry group $SU(2)\times U(1)$. We prove that the one-loop renormalisability of the initial torsionless $\sigma$-models does still imply the one-loop renormalisability of the T-dualised torsionful model. A kind of new ``dilaton anomaly'' appears for T-dualised quasi-Einstein metrics which never occurs in the framework of T-dualised homogeneous Einstein metrics