Maximally Supersymmetric String Theories inD<10

The existence of maximally supersymmetric solutions to heterotic string theory that are not toroidal compactifications of the ten-dimensional superstring is established. We construct an exact fermionic realization of an $N=1\mathrm{}$ supersymmetric string theory in $D=8\mathrm{}$ with non-simply-laced gauge group $\mathrm{Sp}\left(20\right)$. Toroidal compactification to six and four dimensions gives maximally extended supersymmetric theories with reduced rank $(4,12)$ and $(6,14)$, respectively.