Heterotic string in background gauge fields

The higher order corrections to the two-dimensional nonlinear σ-model for the heterotic string are considered. The divergent parts of the effective action are calculated explicitly to two-loop order in the presence of arbitrary background gauge fields. It is shown that the full gauge Chern-Simons term appears in the divergent terms. We also discuss its relevance to the equations of motion for the massless modes of the heterotic string with emphasis on the local gauge invariance of the heterotic string theory.