Higher order corrections to supersymmetry and compactifications of the heterotic string

Starting from the known form of the order α'3 corrections to the effective action for the heterotic string, the modifications to the compactified solutions at this order are discussed. The corrections to the spacetime supersymmetry transformations necessary for consistency with N=1 supersymmetry in the modified vacuum are derived. Although the holonomy group of the modified solutions is U(3), consistency in the gluino sector requires the embedding of only an SU(3) connection in the Yang-Mills gauge group. The original embedding of the spin connection in the gauge group must therefore be modified appropriately. In the case of the E8xE8 heterotic string, this means that the residual gauge group in four dimensions is still E6xE8. (orig.)