Higher order terms in an improved heterotic M theory
  Curvature squared terms are added to a consistent formulation of supergravity on manifolds with boundary which is meant to represent the low energy limit of the strongly coupled heterotic string. These terms are necessary for the cancellation of gravitational anomalies and for reduction to lower dimensions with broken chiral symmetry. The consequences of anomaly cancellation when flux and extrinsic curvature terms are taken into account have yet to be fully exploited, but some implications for flux terms are discussed. 
Ian G Moss