Stringy origin of non-Abelian discrete flavor symmetries

TLDR: In this article, the origin of non-Abelian discrete flavor symmetries in superstring theory was studied and a simple geometric understanding of the realization of the non-abelian flavor symmetsries was given.

About: This article is published in Nuclear Physics.The article was published on 2007-04-16 and is currently open access. It has received 293 citations till now. The article focuses on the topics: Orbifold & Heterotic string theory.

Figures

Fig. 1. S1/Z2 orbifold. Points which are related by a reflection on the dashed line are identified. The fundamental region of the orbifold is an interval with the fixed points sitting at the boundaries.

Table 3 Character table for D4

Table 4 Character table of the group (54) (with ω= e2π i/3). The second row gives the number of elements in the certain class and the second column the dimension of the representation

Table 5 Decomposition of the 3 of (54) into irreps of the particular subgroup under the breaking

Table 2 Non-Abelian discrete flavor symmetries of the building blocks

Table 1 (a) ZN and (b) ZN ×ZM orbifold twists for 6D ZN orbifolds leading to N = 1 SUSY

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Stringy origin of non-abelian discrete flavor symmetries" ?

The authors study the origin of non-Abelian discrete flavor symmetries in superstring theory. The authors also study possible breaking patterns. The authors classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. 

Q2. What are the future works in "Stringy origin of non-abelian discrete flavor symmetries" ?

It should be interesting to study phenomenological applications of their results, such as the understanding of the observed Yukawa matrices of quarks and leptons in terms of spontaneously broken flavor symmetries, taking into account the mixing with vector-like states. 

Q3. What is the coupling strength between localized fields?

the coupling strength between localized fields is a function of geometrical features such as the distance between the fields. 

Q4. What is the important issue in contemporary particle physics?

One of the most important issues in contemporary particle physics is to understand the quark and lepton flavor structure, i.e. the origin of the number of generations, the observed mass hierarchies as well as the mixing angles. 

Q5. What is the reason for having less symmetry than what one would have for the product space?

The reason for having less symmetry than what one would have for the product space (S1/Z2) × (S1/Z2) (i.e. D4 × D4) is that in T2/Z2 the automorphism θ reflects both ei simultaneously. 

Q6. What are the characteristics of the heterotic orbifold?

Among the known string constructions, heterotic orbifold models [12,13] have a particularly simple geometric interpretation, and an encouraging phenomenology. 

Q7. what is the condition that requires(19)n = 3?

That requires(19)n = 3 × (integer), n∑j=1 m(j) 1 = 0 mod 3.The first condition is equivalent to demanding that the Lagrangian be invariant under(20) ⎛ ⎝ |(θ,0), . . .〉|(θ, e1), . . .〉|(θ,2e1), . . .〉⎞ ⎠ → ⎛ ⎝ω 0 00 ω 00 0 ω⎞ ⎠ ⎛ ⎝ |(θ,0), . . .〉|(θ, e1), . . .〉|(θ,2e1), . . .〉⎞ ⎠ ,with ω = e2π i/3. 

Q8. What is the only non-Abelian group obtained from the D3 symmetry?

The D3 symmetry is the only non-Abelian group obtained from (54) by a VEV of the 3 as shown in Appendix C. Recall that only triplets as well as trivial singlets appear as string fundamental states. 

Q9. What are the twists of the untwisted sector?

The states from the untwisted sector are bulk fields in the effective field theory whereas the twisted states are brane fields living at the fixed points or planes. 

Q10. What are the twisted sectors of the Hilbert space?

the Hilbert space of (massless) states decomposes in an untwisted and various twisted sectors, denoted by U and Tk , respectively. 

Q11. What is the role of the building blocks in the discussion of orbifold GUT limits?

These building blocks play an important role when discussing orbifold GUT limits [17,18,20,23,26], where one considers the effective field theory describing anisotropic orbifolds for energies between different compactification scales.