  The structure of heterotic string target space compactifications is studied
using the formalism of the noncommutative geometry associated with lattice
vertex operator algebras. The spectral triples of the noncommutative spacetimes
are constructed and used to show that the intrinsic gauge field degrees of
freedom disappear in the low-energy sectors of these spacetimes. The quantum
geometry is thereby determined in much the same way as for ordinary superstring
target spaces. In this setting, non-abelian gauge theories on the classical
spacetimes arise from the K-theory of the effective target spaces.
