A three-generation Pati–Salam model is constructed by compactifying the heterotic string on a particular Abelian symmetric orbifold with two discrete Wilson lines. The compactified space is taken to be the Lie algebra lattice G2⊕SU(3)⊕SO(4). When one dimension of the SO(4) lattice is large compared to the string scale, this model reproduces many features of a 5d SO(10) grand unified theory compactified on an orbifold. (Of course, with two large extra dimensions we can obtain a 6d SO(10) grand unified theory.) We identify the orbifold parities and other ingredients of the orbifold grand unified theories in the string model. Our construction provides a UV completion of orbifold grand unified theories, and gives new insights into both field theoretical and string theoretical constructions.
