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-three current algebras. We present the explicit construction of three classes of three-chiral-family grand unified models in the heterotic string theory. Each model has five left-handed, and two right-handed families, and an adjoint Higgs representation. Two of them are SO(10) and the third is ${\mathrm{E}}_6$. With Wilson lines and/or varying moduli, we show how other three-family grand unified models, such as SO(10) and SU(5), may be constructed from them.

• Received 16 July 1996

DOI:https://doi.org/10.1103/PhysRevD.54.7520