Equations of Motion for the Heterotic String Theory from the Conformal Invariance of the Sigma Model

In the presence of arbitrary background gauge, gravitational, and antisymmetric tensor fields, the heterotic string may be described by a two-dimensional local field theory. It is conjectured, and verified to a certain approximation, that the conditions on the background fields for this model to have vanishing $\beta$ function are identical to the equations of motion for the massless fields. In particular, the appearance of the Chern-Simons three-forms in the classical equations of motion is shown to be related to the chiral anomaly in two-dimensional gauge theories.