Conway Subgroup Symmetric Compactifications Of Heterotic String

We investigate special compactifications of the heterotic string for which the space of half-BPS states is, in a natural way, a representation of various subgroups of the Conway group. These compactifications provide a useful framework for analyzing the action of some of the large symmetry groups appearing in discussions of Moonshine in the physics literature. We investigate toroidal compactifications of heterotic string with sixteen supersymmetries as well as asymmetric toroidal orbifolds with $N=2$ supersymmetry in four dimensions that arise as $K3 \times T^2$ compactifications. The latter Conway subgroup symmetric compactifications of the heterotic string might have some interesting implications for D-brane bound states on Calabi-Yau manifolds.