We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kahler modulus T. Using this mechanism it is shown that the Delta (54) non-Abelian discrete symmetry group originates from a SU(3) gauge symmetry, whereas the D-4 symmetry group is obtained from a SU(2) gauge symmetry

We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for Z 3 asymmetric orbifold construction. We also calculate gauge symmetry breaking patterns.

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Using Z 3 asymmetric orbifolds in heterotic string theory, we construct N = 1 SUSY three-generation models with the standard model gauge group SU(3) C × SU(2) L × U(1) Y and the left-right symmetric group SU(3)One of the models possesses a gauge flavor symmetry for the Z 3 twisted matter.

We investigate a gauge theory realization of non-Abelian discrete flavor symmetries and apply the gauge enhancement mechanism in heterotic orbifold models to fieldtheoretical model building. Several phenomenologically interesting non-Abelian discrete symmetries are realized effectively from a U (1) gauge theory with a permutation symmetry. We also construct a concrete model for the lepton sector based on a U (1) 2 ⋊ S 3 symmetry.