Chern-Simons terms in the sigma model for the heterotic string

The gauge anomalous contributions to the two-loop beta functions in the non-linear sigma model for the heterotic string moving in a curved background with torsion, are calculated explicitly, using a well-defined regularization scheme. It is shown that these contributions to both the beta functions for the metric and the antisymmetric tensor field are absorbed exactly by the addition of the full gauge Chern-Simons form to the torsion. The circumstances under which there is an analogous cancellation in the Lorentz sector is discussed and it is shown to depend on the choice of fermionic quantum variables. (orig.)