Limitations of Heterotic-Superstring Phenomenology

The low-energy effective theory arising from compactification of the $E_8\otimes E_8^{\prime }$ heterotic superstring on $M_4\times K_6$ is discussed. Symmetry between the observed and shadow world will occur only for manifolds (of which no examples are yet known) with special values of $Tr\left(R\wedge R\right)$. Other scenarios are described in which no new gauge bosons or chiral fermions appear.