Darmstadt, Techn. University, Diss., 2000.

Dans le premier chapitre de la thèse, nous résumons d’abord les définitions des algèbres Hom-Nambu n-aires (resp. Hom-Nambu- Lie) et algèbres Hom-Nambu n-aires multiplicatives (resp. Hom-Nambu-Lie multiplicatives). Ensuite, on donne,quelques exemples d'algèbres Hom-Nambu de dimension finie. Dans la troisième section du chapitre on rappellela classication des algèbres Hom-Nambu-Lie ternaires de dimension 3 correspondant auxhomomorphismes diagonaux donnée par Ataguema, Makhlouf et Silvestrov dans [12]. Laquatrième section est consacrée aux différentes manières de construire des algèbres n-airesde type Hom-Nambu. On rappelle la construction par twist initiée par Yau. Ensuite on la généralise en une construction d'algèbre n-aire de Hom-Nambu à partir d'une algèbre n-aire de Hom-Nambu et d'un morphisme faible. On s'intéresse aussi à des constructions d'arité plus grande ou plus petite et par produit tensoriel. On montre par ailleurs comment obtenir de nouvelles algèbres n-aires de Hom-Nambu en utilisant les éléments du centroide. La cinquième section est consacrée aux notions de dérivations et de représentationspour les algèbres n-aires. On étudie les αk-dérivations, les dérivations centrales et dansle cas général, la théorie des représentations des algèbres Hom-Nambu n-aires. Nousdiscutons en particulier les cas des représentations adjointes et coadjointes. Les résultatsobtenus dans cette section généralisent ceux donnés pour le cas binaire dans [16, 57]. / The aim of this thesis is to study representation theory and cohomology of n-ary Hom-Nambu-Lie algebras, as well as quadratic structures on these algebras. It is organized as follows.• Chapter 1. n-ary Hom-Nambu algebras : in the first section we recall the definitions of n-ary Hom-Nambu algebras and n-ary Hom-Nambu-Lie algebras, introduced by Ataguema, Makhlouf and Silvestrov and provide some key constructions. These algebras correspond to a generalized version by twisting of n-ary Nambu algebras and Nambu-Lie algebras which are called Filippov algebras. We deal in this chapter with a subclass of n-ary Hom-Nambu algebras called multiplicative n-ary Hom-Nambu algebras. In Section 1.2, we recall the list of 3-dimensional ternary Hom-Nambu-Lie algebras of special type corresponding to diagonal homomorphisms. In Section 1.4 we show different construction procedures. We recall the construction procedures by twisting principles and provide some new constructions using for example the centroid. The first twisting principle, introduced for binary case, was extend to n-ary case. The second twisting principle was introduced for binary algebras. We will extend it to n-ary case in the sequel. Also we recall a construction by tensor product of symmetric totally n-ary Hom-associative algebra by an n-ary Hom-Nambu algebra. In Section 1.5, we extend representation theory of Hom-Lie algebras to the n-ary case and discuss the derivations, αk-derivations and central derivations. The last section of chapter 1 is dedicated to ternary q-Virasoro-Witt algebras. We recall constructions of infinite dimensional ternary Hom-Nambu algebras.• Chapter 2. Cohomology of n-ary multiplicative Hom-Nambu algebras : InSection 2.1. We define a central extension. In the second Section we show that for an n-ary Hom-Nambu-Lie algebra N, the space ∧n−1 N carries a structure of Hom-Leibniz algebra and we dene a cohomology which is suitable for the study of one parameter formal deformations of n-ary Hom-Nambu-Lie algebras. In Section 2.4, we extend to n-ary multiplicative Hom-Nambu-Lie algebras the Takhtajan's construction of a cohomology of ternary Nambu-Lie algebras starting from Chevalley-Eilenberg cohomology of binary Lie algebras. The cohomology of multiplicative Hom-Lie algebras. The cohomology complex for Leibniz algebras was defined by Loday and Pirashvili.• Chapter 3. Quadratic n-ary Hom-Nambu algebras : In the first section we introduce a class of Hom-Nambu-Lie algebras which possess an inner product. In Section 3.3, we provide some constructions of Hom-quadratic Hom-Nambu-Lie algebras starting from an ordinary Nambu-Lie algebra and from tensor product of Hom-quadratic commutative Hom-associative algebra and Hom-quadratic Hom-Nambu-Lie algebra. In Section 3.5, we provide a construction of n-ary Hom-Nambu algebra L which is a generalization of the trivial T∗-extension. In Section 3.6, we give a construction of ternary algebra arising from quadratic Lie algebra. In Section 3.7, we construct quadratic n-ary Hom-Nambu algebras involving elements of the centroid of n-ary Nambu algebras.

O presente trabalho consiste na expansão1/N de uma versão estendida do modelo de Nambu-Jona-Lasinio SU(3) no contexto de integrais funcionais. A equação de gap propagadores mesônicos, decaimentos e espalhamentos, aparecem naturalmente como ordens diferentes na expansão. A característica nova nesta abordagem é a inclusão de correções de ordem superior à ordem dominante, que nunca foram consideradas anteriormente. O método também permite a construção de uma densidade de Lagrangeana quiral mésons interagentes baseada no modelo Nambu-JonaLasinio SU(3) aqui obtida pela primeira vez. / The present work consists in 1/N expansion extended version of the SU(3) Nambu-Jona-Lasinio model in the context of the Functional Integral. The gap equations, meson propagators, triangle diagram, etc, appear quite naturally as different orders in the expansion. The new features of this approach in the inclusion of high order corrections in the I/N leading orders, which have never been included in the previous one. The method also allows for the construction of a chical Lagrangean of interacting mesons based on the SU(3) NJL model, here obtained for the first time.

O presente trabalho consiste na expansão1/N de uma versão estendida do modelo de Nambu-Jona-Lasinio SU(3) no contexto de integrais funcionais. A equação de gap propagadores mesônicos, decaimentos e espalhamentos, aparecem naturalmente como ordens diferentes na expansão. A característica nova nesta abordagem é a inclusão de correções de ordem superior à ordem dominante, que nunca foram consideradas anteriormente. O método também permite a construção de uma densidade de Lagrangeana quiral mésons interagentes baseada no modelo Nambu-JonaLasinio SU(3) aqui obtida pela primeira vez. / The present work consists in 1/N expansion extended version of the SU(3) Nambu-Jona-Lasinio model in the context of the Functional Integral. The gap equations, meson propagators, triangle diagram, etc, appear quite naturally as different orders in the expansion. The new features of this approach in the inclusion of high order corrections in the I/N leading orders, which have never been included in the previous one. The method also allows for the construction of a chical Lagrangean of interacting mesons based on the SU(3) NJL model, here obtained for the first time.

The Standard model of particle physics provides a successful theory to understand the experimental results of the electroweak and strong interactions. However, it does not have a satisfactory explanation for the hierarchy problem. Many extensions of the Standard Model that solve the hierarchy problem result in new particles. We will study the phenomenology of vector-like fermions resulting in theories where the Higgs boson is typically a pseudo-Nambu-Goldstone boson. In these theories we study the case where a heavy fermion will be heavier than a heavy gluon, and then the channel of a heavy fermion decaying into a color octet is considered. We study this phenomenology at high energy colliders, both the LHC as well as future machines. / O modelo padrão de física de partículas fornece uma teoria bem-sucedida para entender os resultados experimentais das interações eletrofracas e fortes. No entanto, não tem uma explicação satisfatória para o problema de hierarquia. Muitas extensões do Modelo Padrão que resolvem o problema hierarquia resultam em novas partículas. Estudaremos a fenomenologia de férmions vetoriais resultando em teorias onde o bóson de Higgs é tipicamente um bóson pseudo-Nambu-Goldstone. Nessas teorias, estudaremos o caso em que um férmion pesado será mais pesado do que um glúon pesado, e então o canal de um férmion pesado decaindo em um octeto de cor é considerado. Estudamos esta fenomenologia em colisores de alta energia, tanto para o LHC quanto as futuras máquinas.

The Standard model of particle physics provides a successful theory to understand the experimental results of the electroweak and strong interactions. However, it does not have a satisfactory explanation for the hierarchy problem. Many extensions of the Standard Model that solve the hierarchy problem result in new particles. We will study the phenomenology of vector-like fermions resulting in theories where the Higgs boson is typically a pseudo-Nambu-Goldstone boson. In these theories we study the case where a heavy fermion will be heavier than a heavy gluon, and then the channel of a heavy fermion decaying into a color octet is considered. We study this phenomenology at high energy colliders, both the LHC as well as future machines. / O modelo padrão de física de partículas fornece uma teoria bem-sucedida para entender os resultados experimentais das interações eletrofracas e fortes. No entanto, não tem uma explicação satisfatória para o problema de hierarquia. Muitas extensões do Modelo Padrão que resolvem o problema hierarquia resultam em novas partículas. Estudaremos a fenomenologia de férmions vetoriais resultando em teorias onde o bóson de Higgs é tipicamente um bóson pseudo-Nambu-Goldstone. Nessas teorias, estudaremos o caso em que um férmion pesado será mais pesado do que um glúon pesado, e então o canal de um férmion pesado decaindo em um octeto de cor é considerado. Estudamos esta fenomenologia em colisores de alta energia, tanto para o LHC quanto as futuras máquinas.

Made available in DSpace on 2016-12-23T14:34:49Z (GMT). No. of bitstreams: 1 Carla Rodrigues Almeida.pdf: 592195 bytes, checksum: 070fca888db010e772db2fafedfd378d (MD5) Previous issue date: 2012-08-13 / O objetivo deste trabalho é estudar as folheações que surgem a partir de estruturas de Nambu e apresentar a relação entre formas diferenciais e algumas destas estruturas. Mais precisamente, fazer um estudo da geometria de Poisson e de folheações singulares, enfatizando o caso da folheação simplética que surge da estrutura de Poisson e, em seguida, apresentar a geometria de Nambu, estudando o caso das folheações que surgem destas estruturas de ordem maiores ou iguais a três. Neste caso particular, vamos mostrar como tais estruturas de Nambu se relacionam com formas diferenciais e, por esta relação, classificar as estruturas de Nambu lineares através de um resultado de classificação de p-formas integráveis / The aim of this work is to study the foliations that arise from Nambu structures and present the relationship between differential forms and some of this structures. More specifically, to make a study of the Poisson geometry and of singular foliations, emphasiz-ing the case of the simplectic foliation that arises from the Poisson structure and then, to present the Nambu geometry, studying the case of the foliations that arise from the this structures of order grater than or equal to three. In this particular case, we shall show how this Nambu structures are related with differential formas and, by this relationship, classify linear Nambu structure through a result of classification of integrable differential p-forms

Les modèles effectifs de type Nambu—Jona-Lasinio (NJL) peuvent être utilisés pour étudier les phases à densité et température finies de la chromodynamique quantique (QCD). Alors que les prédictions de ces modèles effectifs peuvent être comparées avec les résultats sur réseaux aux faibles densités, un tel garde-fou n'existe pas à plus haute densité où la discrétisation fait face à un problème de signe sévère. Dans cette thèse nous proposons une méthode systématique permettant de calculer la stabilité d'une prédiction par rapport aux données d'entrée du modèle. De cette manière un critère quantitatif est fabriqué permettant d'évaluer le pouvoir prédictif d'un modèle. La discussion est principalement orientée sur le point critique chiral.Enfin les phases très hautes densités, telles que pouvant exister à l'intérieur des étoiles compactes, sont abordées et la superconductivité de couleur est discutée dans le cadre des modèles NJL / Nambu--Jona-Lasinio models can be used to study finite density and finite temperature quantum chromodynamics phases. Finite temperature and low density predictions of these models can be compared to lattice results. Such a comparison is not possible at larger density because of the so called sign problem. In this thesis the proposed systematic method allows to compute the stability of a prediction with respect to the inputs of the model. In this way a quantitative criterium is constructed which can be used to evaluate the predictive power of the studied model. Finally the high density phases which can exist in the interior of compact stellar objects are discussed along with color superconductivity in NJL type models

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23000号 / 理博第4677号 / 新制||理||1671(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川合 光, 教授 田中 貴浩, 准教授 吉岡 興一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Nesta tese exploramos uma classe de modelos de N-sítios que foram desenvolvidos para produzir grandes hierarquias de escalas. Usando a abordagem de desconstrução dimensional e correspondências apropriadas, esses modelos puramente quadridimensionais coincidem com modelos AdS5 no limite do contínuo, que corresponde ao limite com um grande núumero de grupos de gauge. Por outro lado, no limite em que há poucos grupos de gauge, tais teorias possuem os acoplamentos entre estados excitados e modos zero dos campos muito distintos dos acoplamentos em construções AdS5, resultando em uma rica fenomenologia a ser explorada no Large Hadron Collider (LHC). O problema da hierarquia do Modelo Padrão (MP) é resolvido se o campo de Higgs estão localizado no infravermelho, assim como nas teorias Randall-Sundrum. A hierarquia de massa dos férmions do MP e misturas são obtidas pelas diferentes localizações dos modos zero dos férmions no espaço dos sítios. Essa estrutura é empregada para abordar o problema da hierarquia sob uma nova perspectiva. Nós mostramos que uma descrição efetiva com poucos sítios de uma dimensão extra curva pode implementar os recentemente introduzidos modelos de relaxion, que são uma nova alternativa para explicar a estabilidade radiativa do setor escalar do MP através do mecanismo de relaxação cosmológico. Esses modelos requerem que o campo experimente grandes variações, que s~ao difíceis de serem geradas em um modelo ultravioleta consistente e de serem compatíveis com o espaço compacto do relaxion. Nós propomos um modelo de N-sítios que gera naturalmente essa grande constante de decaimento necessária para abordar esses problemas. No nosso modelo, a matriz de massa dos pseudo Bósons de Nambu-Goldstone (pBNGs), cujo modo zero faz o papel do relaxion, é idêntica à matriz obtida para uma linha de Wilson pBNG na desconstrução de AdS5. / this thesis we explore a class of N-site models that were developed to generate large-scale hierarchies. Using the dimensional deconstruction approach and appropriate matchings, these purely four-dimensional theories coincide with AdS5 models in the continuum limit, which corresponds to the limit with a large number of gauge groups. On the other hand, in the coarse lattice limit such theories have very distinct couplings of the excited states to zero mode fields compared with AdS5 constructions, resulting in a rich phenomenology to be explored at the Large Hadron Collider (LHC). The Standard Model (SM) hierarchy problem is solved if the Higgs field is infrared-localized as in Randall-Sundrum scenarios. The SM fermion mass hierarchy and mixings are obtained by different localizations of zero mode fermions in the theory space. This framework is employed to tackle the electroweak hierarchy problem from a new perspective. We show that an effective few site description of a warped extra dimension can implement the recently introduced relaxion models, which are a new alternative to explain the radiative stability of the SM scalar sector through the cosmological relaxation mechanism. These models require very large field excursions, which are difficult to generate in a consistent ultraviolet completion and to reconcile with the compact field space of the relaxion. We propose an N-site model that naturally generates the large decay constant needed to address these problems. In our model, the mass matrix of the pseudo-Nambu-Goldstone Bosons (pNGBs), whose zero mode plays the role of the relaxion field, is identical to the one obtained for a pNGBWilson line in the deconstruction of AdS5.