Gauge origin of discrete flavor symmetries in heterotic orbifolds

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 Kähler modulus T. Using this mechanism it is shown that the Δ(54) non-Abelian discrete symmetry group originates from a SU(3) gauge symmetry, whereas the D4 symmetry group is obtained from a SU(2) gauge symmetry.