Asymmetric Orbifolds and Grand Unification

We generalize the rules for the free fermionic string construction to include other asymmetric orbifolds with world-sheet bosons. We use these rules to construct various grand unified string models that involve level-$3$ current algebras. We present the explicit construction of three classes of $3$-chiral-family grand unified models in the heterotic string theory. Each model has $5$ left-handed, and two right-handed families, and an adjoint Higgs. Two of them are $SO(10)$ and the third is $E_6$. With Wilson lines and/or varying moduli, we show how other $3$-family grand unified models, such as $SO(10)$ and $SU(5)$, may be constructed from them.