We show that in a two-dimensional σ model whose fields only depend on one target space coordinate, the $O(d,d)\mathrm{}$ invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion).

• Received 11 November 1999

DOI:https://doi.org/10.1103/PhysRevD.62.026003