Kähler potential of heterotic orbifolds with multiple Kähler moduli

Abstract

Aiming at improving our knowledge of the low-energy limit of heterotic orbifold compactifications, we determine at lowest order the Kähler potential of matter fields in the case where more than three bulk Kähler moduli appear. Interestingly, bulk matter fields couple to more than one Kähler modulus, a subtle difference with models with only three Kähler moduli that may provide a tool to address the question of moduli stabilization in these models.1 See e.g. [1,2,3,4] for details on heterotic orbifold compactifications in the bosonic formulation. 2 Yet, despite the great progress on coupling selection rules [13,14,15,16], there remain some details to clarify.

Eclectic flavor groups

“…is nontrivial, there are outer automorphisms that might in principle lead to eclectic extensions of the traditional flavor symmetry ∆ (54). It turns out that ∆(54) can be extended only in two ways: either by the finite modular group Γ 3 ∼ = T in the case without CP or by Γ * 3 ∼ = SL(2, 3) in the case with CP.…”

“…In both cases, ρ(S) and ρ(T) generate the finite modular group Γ 2 ∼ = S 3 , where the triplet of ∆(27) builds a 2 ⊕ 1 of S 3 if α = 1, or 2 ⊕ 1 if α = −1. In both cases, the eclectic flavor group is ∆ (54).…”

“…→ ∆(54) ∼ =[54,8] (42a)τ = i : Ω(1) → Σ(36 × 3) ∼ = [108, 15] (42b) τ = exp ( 2πi /3) : Ω(1) →Ỹ (0) ∼ = [162, 10](42c)where the flavor groups are defined as follows:i) ∆(54) is generated by ρ(A), ρ(B) and ρ(C), ii) Σ(36 × 3) ∼ = [108, 15] is generated by ρ(A), ρ(B) and ρ(S) (see ref. [67]), and, finally, iii)Ỹ (0) ∼ = [162, 10] is generated by ρ(A), ρ(B), ρ(C) and ρ(S T) (see ref.…”

“…Surprisingly it turns out that many prominent traditional flavor symmetries, such as S 3 , D 12 ∼ = S 3 × Z 2 , T 7 , S 4 , Z 9 Z 3 , SL(2, 4) and A 5 , do not allow for any nontrivial modular extension and thus are not included in table 2. Among the groups we have studied, only Q 8 , Z 3 × Z 3 , A 4 , T , ∆(27) and ∆(54)…”

“…In contrast to modular forms Y (τ ), fields can have fractional weights as realized in string theory[52][53][54].…”