Gauge extension of non-Abelian discrete flavor symmetry

We investigate a gauge theory realization of non-Abelian discrete flavor symmetries and apply the gauge enhancement mechanism in heterotic orbifold models to field-theoretical 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 $U(1)^2 rtimes S_3$ symmetry.

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 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.

Three-generation Asymmetric Orbifold Models from Heterotic String Theory

Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1 SUSY three-generation models with the standard model gauge group SU(3)_C times SU(2)_L times U(1)_Y and the left-right symmetric group SU(3)_C times SU(2)_L times SU(2)_R times U(1)_{B-L}. One of the models possesses a gauge flavor symmetry for the Z3 twisted matter.

Gauge Symmetries in Heterotic Asymmetric Orbifolds

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 Z3 asymmetric orbifold construction. We also calculate gauge symmetry breaking patterns.