Siegel modular flavor group and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">CP</mml:mi></mml:math> from string theory

Baur, Alexander; Kade, Moritz; Nilles, Hans Peter; Ramos‐Sánchez, Saúl; Vaudrevange, Patrick K.S.

doi:10.1016/j.physletb.2021.136176

Cited by 38 publications

(19 citation statements)

References 17 publications

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“…In particular, CP transformation laws of the modulus τ, of chiral matter multiplets and of modular forms have been determined [48] and several models where CP is spontaneously broken have been constructed [48][49][50][51][52][53][54]. Within the more general case of a multidimensional moduli space, consistent CP definitions have been examined recently in the context of symplectic modular invariant theories, where the relevant flavour group is the Siegel modular group [55,56]. Ref.…”

Section: Introductionmentioning

confidence: 99%

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CP symmetry and symplectic modular invariance

2021

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We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus g\ge 3g≥3 the definition of CP is unique, while two independent possibilities are allowed when g\le 2g≤2. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.

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Section: Introductionmentioning

confidence: 99%

“…We show that for genus g ≥ 3 there is a unique automorphism suitable to be interpreted as CP, coinciding with the one identified in refs. [55,56]. On the other hand, for genus g ≤ 2 two possibilities are allowed 1 .…”

Section: Introductionmentioning

confidence: 99%

CP symmetry and symplectic modular invariance

2021

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“…This would require the embedding of SL(2, Z) T × SL(2, Z) U and mirror symmetry in the Siegel modular group Sp(4, Z), as discussed in ref. [18], see also refs. [16,17], where bottom-up model building based on Sp(4, Z) has been initiated.…”

Section: Jhep06(2021)110mentioning

confidence: 90%

“…(3.3) for the element M ∈ Sp(4, Z) that corresponds toΣ using again the dictionary of ref. [18]. It is important to note that the resulting automorphy factor will be independent of the specific choice n = n T or n = n U , since n T = n U mod 2.…”

Section: Automorphy Factors Of Modular Transformationsmentioning

confidence: 99%

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Completing the eclectic flavor scheme of the ℤ2 orbifold

Baur

Kade

Nilles³

et al. 2021

J. High Energ. Phys.

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We present a detailed analysis of the eclectic flavor structure of the two-dimensional ℤ2 orbifold with its two unconstrained moduli T and U as well as SL(2, ℤ)T× SL(2, ℤ)U modular symmetry. This provides a thorough understanding of mirror symmetry as well as the R-symmetries that appear as a consequence of the automorphy factors of modular transformations. It leads to a complete picture of local flavor unification in the (T, U) modulus landscape. In view of applications towards the flavor structure of particle physics models, we are led to top-down constructions with high predictive power. The first reason is the very limited availability of flavor representations of twisted matter fields as well as their (fixed) modular weights. This is followed by severe restrictions from traditional and (finite) modular flavor symmetries, mirror symmetry, $$ \mathcal{CP} $$ CP and R-symmetries on the superpotential and Kähler potential of the theory.

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