The Ten-dimensional Effective Action of Strongly Coupled Heterotic String Theory

We derive the ten-dimensional effective action of the strongly coupled heterotic string as the low energy limit of M-theory on S^1/Z_2. In contrast to a conventional dimensional reduction, it is necessary to integrate out nontrivial heavy modes which arise from the sources located on the orbifold fixed hyperplanes. This procedure, characteristic of theories with dynamical boundaries, is illustrated by a simple example. Using this method, we determine a complete set of R^4, F^2R^2, and F^4 terms and the corresponding Chern-Simons and Green-Schwarz terms in ten dimensions. As required by anomaly cancelation and supersymmetry, these terms are found to exactly coincide with their weakly coupled one-loop counterparts.