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Maximally Supersymmetric String Theories in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">D</mml:mi><mml:mi /><mml:mo><</mml:mo><mml:mi /><mml:mn>10</mml:mn></mml:math>
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 $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ supersymmetric string theory in $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8$ with non-simply-laced gauge group $\mathrm{Sp}(20)$. Toroidal compactification to six and four dimensions gives maximally extended …