Classification of symmetric toroidal orbifolds

Fischer, Maximilian; Ratz, Michael; Torrado, Jesús; Vaudrevange, Patrick K.S.

doi:10.1007/jhep01(2013)084

Cited by 59 publications

(122 citation statements)

References 68 publications

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“…That is, we have used all possible geometries (ignoring roto-translations) of Z N orbifolds and only the simplest ones for Z N ×Z M orbifolds. Our results, that shall further detailed elsewhere, are statistically equivalent [27]. The third column displays the most common flavor symmetry appearing in promising models; the symmetries in squared brackets are non-Abelian flavor symmetries that appear less frequently in these models.…”

supporting

confidence: 53%

On flavor symmetries of phenomenologically viable string compactifications

Ramos‐Sánchez¹

2017

J. Phys.: Conf. Ser.

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Abstract. Heterotic orbifolds can explain the origin of flavor symmetries and the flavor representations of matter fields in particle physics as a result of the geometric properties of the associated string states in the compact space. After a review of the method to obtain flavor symmetries in these models, we determine the most frequent non-Abelian flavor symmetries appearing in promising Abelian heterotic orbifolds. Interestingly, these symmetries correspond only to D4, Δ(54) and products of these symmetries and Abelian factors. A large set of promising models exhibits purely Abelian flavor symmetries. We finally explore the phenomenological potential of a sample model endowed with Δ(54) assuming certain ad hoc flavon expectation values. IntroductionOne of the goals of flavor phenomenology is to discover the underlying structure in particle physics that may solve some questions left unanswered in the SM, such as the origin of the family replication, the patterns of quark and lepton mixing matrices, the origin of CP violation and the absence of flavor-changing neutral currents (FCNC). The field theoretic approach consists in first freely choosing a non-Abelian discrete symmetry within SU(3) 5 flavor , the largest global symmetry of the SM in the absence of Yukawa couplings, and then introducing a number of ad hoc matter fields, some of them with unjustified expectation values (VEVs), to fulfill different basic phenomenological constraints, such as the quark and lepton masses and mixings. Once these restrictions are met, this bottom-up approach delivers a number of consequences, which frequently include interesting new physics. There are plenty of useful symmetries which have been thoroughly studied (see e.g. [1, 2] for a review), and it is hard to learn which of them corresponds to the actual description of our Universe.Looking for the origin of such symmetries might at least reduce the number of possibilities. In particular, given the constraining environment of string theory, one may wonder what kind of flavor symmetries can emerge in string compactifications that reproduce many properties of the standard model (SM) or its minimal supersymmetric extension (MSSM). The first general studies of this question were [3,4], in the context of orbifold compactifications of the heterotic string perhaps due to their geometric simplicity. Around those studies, there has been some progress in understanding the qualities of flavor symmetries arising in some phenomenologically viable heterotic orbifolds [5,6,7], their enhancements [8] and their generalizations in models endowed with magnetic fluxes [9]. Recently, there has also been progress in the study of flavor symmetries from promising orientifold D-brane models [10,11].

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confidence: 53%

On flavor symmetries of phenomenologically viable string compactifications

Ramos‐Sánchez¹

2017

J. Phys.: Conf. Ser.

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“…Requiring unbroken supersymmetry in the effective 4D field theory as well as considering topological equivalences between compactifications with different geometries reduce greatly the number of allowed heterotic orbifolds. In fact, all possible 6D orbifolds of this type have been exhaustively classified [80], resulting in a small number of Abelian orbifolds and thus a small number of possible geometrical symmetries to be considered.…”

Section: Jhep12(2016)131mentioning

confidence: 99%

Δ(54) flavor phenomenology and strings

Carballo-Pérez

Peinado

Ramos‐Sánchez

2016

J. High Energ. Phys.

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∆(54) can serve as a flavor symmetry in particle physics, but remains almost unexplored. We show that in a classification of semi-realistic Z 3 × Z 3 heterotic string orbifolds, ∆(54) turns out to be the most natural flavor symmetry, providing additional motivation for its study. We revisit its phenomenological potential from a low-energy perspective and subject to the constraints of string models. We find a model with ∆(54) arising from heterotic orbifolds that leads to the Gatto-Sartori-Tonin relation for quarks and charged-leptons. Additionally, in the neutrino sector, it leads to a normal hierarchy for neutrino masses and a correlation between the reactor and the atmospheric mixing angles, the latter taking values in the second octant and being compatible at three sigmas with experimental data.

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“…However, only three of the total 19 Kähler moduli are realized explicitly. A different realization of the Schoen manifold that describes all Kähler parameters explicitly, is given in terms of a resolution of a particular Z 2 × Z 2 orbifold, the (0-2) orbifold in the DonagiWendland classification [53,54]. This description has the advantage that all h 11 = 19 divisors are described explicitly.…”

Section: The Schoen Manifoldmentioning

confidence: 99%

(MS)SM‐like models on smooth Calabi‐Yau manifolds from all three heterotic string theories

Nibbelink

Loukas

Ruehle

2015

Fortschritte der Physik

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We perform model searches on smooth Calabi-Yau compactifications for both the supersymmetric E 8 ×E 8 and SO(32) as well as for the non-supersymmetric SO(16)×SO(16) heterotic strings simultaneously. We consider line bundle backgrounds on both favorable CICYs with relatively small h 11 and the Schoen manifold. Using Gram matrices we systematically analyze the combined consequences of the Bianchi identities and the tree-level Donaldson-Uhlenbeck-Yau equations inside the Kähler cone. In order to evaluate the model building potential of the three heterotic theories on the various geometries, we perform computer-aided scans. We have generated a large number of GUT-like models (up to over a few hundred thousand on the various geometries for the three heterotic theories) which become (MS)SM-like upon using a freely acting Wilson line. For all three heterotic theories we present tables and figures summarizing the potentially phenomenologically interesting models which were obtained during our model scans.

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Classification of symmetric toroidal orbifolds

Cited by 59 publications

References 68 publications

On flavor symmetries of phenomenologically viable string compactifications

On flavor symmetries of phenomenologically viable string compactifications

Δ(54) flavor phenomenology and strings

(MS)SM‐like models on smooth Calabi‐Yau manifolds from all three heterotic string theories

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