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.Comment: 32 page

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 K\"ahler 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.Comment: 12 page

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.Comment: 24 page

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.Comment: 18 pages, 1 figur