Gauge Origin of Discrete Flavor Symmetries in Heterotic Orbifolds

TL;DR

This paper demonstrates that non-Abelian discrete symmetries in heterotic orbifold string models originate from gauge symmetries, specifically from enhanced gauge symmetries at special points in moduli space, which are broken to discrete groups by moduli VEVs.

Contribution

It reveals the gauge origin of non-Abelian discrete symmetries in heterotic orbifolds, linking them to specific gauge groups like SU(3) and SU(2).

Findings

$ ext{Delta}(54)$ arises from $SU(3)$ gauge symmetry.

$D_4$ symmetry originates from $SU(2)$ gauge symmetry.

Discrete symmetries are connected to symmetry-enhanced points in moduli space.

Abstract

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.