Orbifold | EPFL Graph Search

En mathématiques, un orbifold (parfois appelé aussi orbivariété) est une généralisation de la notion de variété contenant de possibles singularités. Ces espaces ont été introduits explicitement pour la première fois par Ichirō Satake en 1956 sous le nom de V-manifolds. Pour passer de la notion de variété (différentiable) à celle d'orbifold, on ajoute comme modèles locaux tous les quotients d'ouverts de par l'action de groupes finis. L'intérêt pour ces objets a été ravivé considérablement à la fin des années 70 par William Thurston en relation avec sa conjecture de géométrisation. En physique, ces espaces ont été considérés initialement comme espaces de compactification en théorie des cordes car malgré la présence de singularités la théorie y est bien définie. Lorsqu'ils sont utilisés dans le cadre plus particulier de la théorie des supercordes, les orbifolds autorisés doivent avoir la propriété supplémentaire d'être des variétés de Calabi-Yau afin de préserver une quantité minimale de supersymétrie. Mais dans le cas où des singularités sont présentes, il s'agit là d'une extension de la définition originale des espaces de Calabi-Yau car ceux-ci sont en principe des espaces sans singularité. De même qu'une variété, un orbifold est spécifié par des données de recollement entre des modèles locaux ; cependant, au lieu que ces modèles locaux soient des ouverts de Rn, ce sont des quotients de tels ouverts par des actions de groupes finis. Les données de recollement décrivent non seulement la structure de l'espace quotient, qui n'est pas nécessairement une variété, mais aussi celle des sous-groupes d'isotropie. Un atlas d'orbifold de dimension n est la donnée simultanée : d'un espace de Hausdorff , appelé l'espace sous-jacent, d'un recouvrement ouvert (Ui) de , clos par intersections finies pour chaque indice , d'une carte constituée (outre Ui) d'un ouvert de d'une action fidèle linéaire d'un groupe fini sur d'un homéomorphisme (on notera l'application composée) tels que pour toute inclusion Ui Uj il existe un morphisme de groupes injectif fij : Γi Γj et un homéomorphisme ψij de dans un ouvert de , appelé application de recollement, Γi-équivariante (relativement à fij) compatible avec les cartes (i.

Tackling the Supersymmetric Flavour Problem in String Models

Christopher John Andrey

In this work we address one of the phenomenological issues of beyond the Standard Model scenarios which embed Supersymmetry, namely the Supersymmetric Flavour Problem, in the context of String Theory. Indeed, the addition of new interactions to the Standard Model generically spoils its flavour structure which is one of its major achievements since it for example leads to a very elegant understanding of the absence of flavour changing neutral currents in the leptonic sector and of the stability of the proton, thanks to accidental symmetries. We focus on a subset of the phenomenologically dangerous operators, namely the soft scalar masses. One way out of the Supersymmetric Flavour Problem is to geographically separate the observable and hidden sectors along a fifth dimension, gravity being the only interaction propagating in the bulk. In such scenarios, the soft scalar masses are vanishing at the classical level since there is no direct contact term between the observable and hidden multiplets and tend to be universal at the loop-level. However such setups hardly ever come about in String Theory, which is one of the most promising candidates of quantum gravity. In order to make contact with the five-dimensional picture, we focus on the prototypical case of the E8 × E8 Heterotic M-Theory which, in a certain regime, effectively looks five-dimensional and embeds matter fields on two end-of-the-world branes. In these scenarios, not only gravity but also vector multiplets propagate in the five-dimensional bulk, effectively spoiling the sequestered picture. However, since the contact terms responsible for the appearance of soft scalar masses arise due to the exchange of heavy vectors, they do enjoy a current-current structure which can be exploited to inhibit the emergence of soft scalar masses by postulating a global symmetry in the hidden sector. In order to assess the possibility of realising such a mechanism, we first study the full dependence of the Kähler potential on both the moduli and the matter fields in the case of orbifold and Calabi-Yau compactifications. We then determine whether an effective sequestering may be achieved thanks to a global symmetry and argue that whereas for orbifold models our strategy can naturally be put at work, it can only be implemented in a subset of Calabi-Yau models.

EPFL2011

Sequestering by global symmetries in Calabi–Yau string models

Claudio Scrucca, Christopher John Andrey

We study the possibility of realizing an effective sequestering between visible and hidden sectors in generic heterotic string models, generalizing previous work on orbifold constructions to smooth Calabi-Yau compactifications. In these theories, genuine sequestering is spoiled by interactions mixing chiral multiplets of the two sectors in the effective Kahler potential. These effective interactions however have a specific current-current-like structure and can be interpreted from an M-theory viewpoint as coming from the exchange of heavy vector multiplets. One may then attempt to inhibit the emergence of generic soft scalar masses in the visible sector by postulating a suitable global symmetry in the dynamics of the hidden sector. This mechanism is however not straightforward to implement, because the structure of the effective contact terms and the possible global symmetries is a priori model dependent. To assess whether there is any robust and generic option, we study the full dependence of the Kahler potential on the moduli and the matter fields. This is well known for orbifold models, where it always leads to a symmetric scalar manifold, but much less understood for Calabi-Yau models, where it generically leads to a non-symmetric scalar manifold. We then examine the possibility of an effective sequestering by global symmetries, and argue that whereas for orbifold models this can be put at work rather naturally, for Calabi-Yau models it can only be implemented in rather peculiar circumstances.

Elsevier2011

Soft masses in superstring models with anomalous U(1) symmetries

Claudio Scrucca

We analyze the general structure of soft scalar masses emerging in superstring models involving anomalous U(1) symmetries, with the aim of characterizing more systematically the circumstances under which they can happen to be flavor universal. We consider both heterotic orbifold and intersecting brane models, possibly with several anomalous and non-anomalous spontaneously broken U(1) symmetries. The hidden sector is assumed to consist of the universal dilaton, Kahler class and complex structure moduli, which are supposed to break supersymmetry, and a minimal set of Higgs fields which compensate the Fayet-Iliopoulos terms. We leave the superpotential that is supposed to stabilize the hidden sector fields unspecified, but we carefully take into account the relations implied by gauge invariance and the constraints required for the existence of a metastable vacuum with vanishing cosmological constant. The results are parametrized in terms of a constrained Goldstino direction, suitably defined effective modular weights, and the U(1) charges and shifts. We show that the effect induced by vector multiplets strongly depends on the functional form of the Kahler potential for the Higgs fields. We find in particular that whenever these are charged matter fields, like in heterotic models, the effect is non-trivial, whereas when they are shifting moduli fields, like in certain intersecting brane models, the effect may vanish.

2007

Tackling the Supersymmetric Flavour Problem in String Models

Christopher John Andrey

EPFL2011