Three-family SU(5) grand unification in string theory

We present two 3-family SU(5) grand unified models in the heterotic string theory. One model has 3 chiral families and 9 pairs of 5 + 5 Higgs fields, and an asymptotically-free SU(2) ⊗ SU(2) hidden sector, where the two SU(2)s have different matter contents. The other model has 6 left-handed and 3 right-handed 10s, 12 left-handed and 9 right-handed 5s, and an asymptotically-free SU(3) hidden sector. At the string scale, the gauge couplings g2 of the hidden sectors are three times as big as that of SU(5). In addition, both models have an anomalous U(1).