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.

Chiral Four-Dimensional Heterotic Covariant Lattices

In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all right-mover lattices that can appear in such a chiral model, and to study the corresponding left-mover lattices using the theory of lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is employed to calculate a lower bound on the number of left-mover lattices. Also, the known relationship between asymmetric orbifolds and covariant lattices is considered in the context of our classification.

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.