Gauge origin of discrete flavor symmetries in heterotic orbifolds

Florian Beye,Tatsuo Kobayashi,Shogo Kuwakino

doi:10.1016/j.physletb.2014.07.058

Gauge origin of discrete flavor symmetries in heterotic orbifolds

Florian Beye, Tatsuo Kobayashi + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2014.07.058

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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 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.

Highlights

It is important to understand the flavor structure of the standard model of particle physics
In this paper we point out that these non-Abelian discrete flavor symmetries originate from a gauge symmetry
We showed that non-Abelian discrete symmetries in heterotic orbifold models originate from a non-Abelian continuous gauge symmetry

Summary

Introduction

It is important to understand the flavor structure of the standard model of particle physics. In this paper we point out that these non-Abelian discrete flavor symmetries originate from a gauge symmetry. The effective action of this model can be derived from G gauge × G discrete symmetry invariance.2 This situation slightly changes if we set the model to be at a symmetry enhanced point in moduli space. The maximal rank of the enhanced gauge symmetry G enhanced is six, because we compactify six internal dimensions At this specific point in moduli space, orbifold fixed points are characterized by gauge charges of G enhanced , and the spectrum is extended by additional massless fields charged under G enhanced. The group G enhanced originates from a larger non-Abelian gauge symmetry that exists before the orbifolding. We will show this explicitly in the following

Gauge origin of non-Abelian discrete symmetry

D 4 non-Abelian discrete symmetry

Conclusion