Strong Coupling Expansion Of Calabi-Yau Compactification

In a certain strong coupling limit, compactification of the $E_8\times E_8$ heterotic string on a Calabi-Yau manifold $X$ can be described by an eleven-dimensional theory compactified on $X\times \S^1/\Z_2$. In this limit, the usual relations among low energy gauge couplings hold, but the usual (problematic) prediction for Newton's constant does not. In this paper, the equations for unbroken supersymmetry are expanded to the first non-trivial order, near this limit, verifying the consistency of the description and showing how, in some cases, if one tries to make Newton's constant too small, strong coupling develops in one of the two $E_8$'s. The lower bound on Newton's constant (beyond which strong coupling develops) is estimated and is relatively close to the actual value.