Há duas brechas quânticas nos Teoremas da Singularidade em Relatividade Geral: violações das condições clássicas de energia e flutuações quânticas da geometria do espaço-tempo. Nesta dissertação, estudamos a primeira brecha e abordamos os Teoremas da Singularidade através da condição de energia. Revisamos a abordagem algébrica de Teoria Quântica de Campos para o campo de Klein-Gordon e, neste formalismo, revisamos a derivação de uma desigualdade quântica de energia para os estados de Hadamard em espaços-tempos globalmente hiperbólicos. Apesar das desigualdades quânticas de energia não poderem ser aplicadas diretamente nos Teoremas de Singularidade, mostramos que generalizações dos Teoremas de Hawking e Penrose são provadas considerando condições de energia enfraquecidas inspiradas por elas. Assim sendo, os Teoremas de Singularidade continuam valendo se considerarmos efeitos quânticos sutis. A questão de se efeitos de interação ou efeitos de ``backreaction\'\' poderiam quebrá-los ainda está em aberto; há razões para se esperar ambas as respostas. / There are two quantum loopholes in the Singularity Theorems of General Relativity: violations of the classical energy conditions and quantum fluctuations of the spacetime geometry. In this dissertation, we study the first loophole and approach Singularity Theorems through the energy condition. We review the algebraic approach of Quantum Field Theory for the Klein-Gordon field and, within it, we review the derivation of a quantum energy inequality for Hadamard states on globally hyperbolic spacetimes. However quantum energy inequalities cannot be directly applied to Singularity Theorems, we show that generalized Hawking and Penrose Theorems are proven considering weakened energy conditions inspired by them. Hence, Singularity Theorems do hold under subtle quantum effects. The question of whether interaction or backreaction effects could break them is still open; there are reasons to expect both answers.

Esta tese apresenta estudos sobre uma possível extensão do Modelo Padrão, suas características teóricas e fenomenológicas. São estudados aspectos do Modelo Padrão relevantes para a análise do setor eletrofraco. Motivado pela solução do problema da hierarquia, é introduzido um espaço de cinco dimensões, com a quinta dimensão curva e compactificada em orbifold. Neste espaço são analisados campos escalares, espinoriais e vetoriais, exibindo modos excitados, os chamados modos de Kaluza-Klein. É incluída uma quarta geração de férmions, sendo então possível obter um setor eletrofraco fortemente acoplado na escala TeV, com a condensação de quarks. Este mecanismo é consequência de acoplamentos não universais com o primeiro modo de Kaluza-Klein do glúon, acoplamentos mais intensos com a quarta geração de quarks. É feita a determinação dos parâmetros dos quarks no espaço de cinco dimensões, resultando no setor de quarks do Modelo Padrão como limite da teoria a baixas energias. A análise teórica termina com a determinação dos acoplamentos dos quarks com o primeiro modo de Kaluza-Klein do glúon. Valendo-se da propriedade de o primeiro modo excitado do glúon trocar sabor, mesmo sendo uma partícula neutra, um estudo fenomenológico é realizado, mostrando que é possível observar eventos no LHC que indicam haver o setor fortemente acoplado, mediante a aplicação dos cortes descritos neste trabalho. / This thesis presents studies concerning a possible extension of the Standard Model, its theoretical and phenomenological characteristics. Aspects of the Standard Model that are relevant for the analysis of the electroweak sector are studied. In order to solve the hierarchy problem, a space with ve dimensions is introduced, with the fth dimension curved and compactied in orbifold. Within this space scalar, spinorial and vectorial elds are analysed, showing excited modes, the so-called Kaluza-Klein modes. A fourth generation of fermions is included, which makes it possible to obtain a strongly coupled electroweak sector at the TeV scale, with quarks condensation. This mechanism is possible due to non-universal couplings with the rst Kaluza-Klein mode of the gluon, couplings which are stronger with the fourth generation quarks. The quarks parameters in the ve-dimensional space are determined, leading to the quark sector of the Standard Model as a low energy limit of the theory. The theoretical analysis is nished by the determination of the quarks couplings with the rst Kaluza-Klein mode of the gluon. Using the property of avor exchange by the gluon, even this being a neutral particle, a phenomenological study is carried out, showing that is possible to observe events at the LHC that indicate the existence of the strongly coupled sector, by means of the use of the cuts described in this work.

O Modelo Padrão (MP) da física de partículas fornece uma descrição extremamente bem sucedida de todos os dados experimentais atuais. No entanto, temos razões para esperar que ele não seja válido até escalas de energia arbitrariamente altas. No MP a massa do bóson de Higgs é quadraticamente sensível a correções radiativas, sofrendo de grandes problemas de ajuste fino. Isso gera o chamado problema da hierarquia de gauge, cuja solução natural requer nova física na escala TeV. O MP também não fornece nenhuma explicação para a grande hierarquia de massas e ângulos de mistura dos férmions. Os problemas de hierarquia podem ser resolvidos naturalmente em teorias com uma dimensão extra curva. No entanto, a sua versão mais simples viola sabor a nível árvore, em conflito com os dados. Nesta tese investigaremos modelos quadridimensionais que descrevem a física na escala TeV obtidos da discretização de teorias em cinco dimensões no espaço AdS5, segundo o procedimento de desconstrução dimensional. As hierarquias de gauge e das massas dos férmions são geradas naturalmente como no modelo extra-dimensional, satisfazendo ainda os vínculos de sabor e de precisão eletrofraca. Estudaremos também um modelo desconstruído em que o Higgs é um pseudo bóson de Nambu-Goldstone, a fim de obter um Higgs naturalmente leve e dinamicamente localizado / The Standard Model (SM) of particle physics provides an extremely successful description of all current experimental data. However, we have reasons to expect that it cannot be valid up to arbitrarily high energy scales. In the SM the Higgs boson mass is quadratically sensitive to radiative corrections and, hence, suffers from a severe fine-tunning problem. This creates the so-called gauge hierarchy problem, the natural solution of which requires new physics at the TeV scale. The SM also doesnt provide any explanation for the large hierarchy of fermion masses and mixing angles. The hierarchy problems can be naturally solved in theories with a warped extra dimension. However, their simplest version violates flavor at tree level, conflicting with experimental data. In this thesis we investigate four dimensional models that describe physics at the TeV scale obtained from a coarse discretization of five dimensional theories in AdS5 space, by the dimensional deconstruction procedure. The gauge as well as the fermion mass hierarchies are naturally generated in the same manner as in the extra-dimensional model, while also satisfying bonds from flavor physics and precision electroweak data. We also study a deconstructed model in which the Higgs is a pseudo Nambu-Goldstone boson, with the motivation of obtaining a naturally light and localized Higgs.

No âmbito da teoria quântica de campos (TQC) foram estudados modelos de quench exatamente solúveis. Nestes modelos, obteve-se uma generalização do ansatz de Kadanoff-Baym que se mantém em todos intervalos de tempo. Algumas hipóteses sobre fenômenos de não-equilíbrio em TQC em temperaturas finitas foram analisadas e estendidas neste contexto. Para tanto, examinamos as funções de Green nesses modelos e os comparamos com os resultados aproximados que são frequentemente usados na literatura. Um dos modelos descreve sistemas de não-equilíbrio do tipo vítreo. Esses sistemas exibem um comportamento que é compatível com o esperado do teorema de flutuação-dissipação. As propriedades básicas foram consistentemente deduzidas e resultados explícitos para a temperatura efetiva e frequências características foram obtidas. / We have studied exactly quenched models in the context of Quantum Field Theory(QFT). In these models, a generalization of the Kadanoff-Baym ansatz was obtained which holds at all times. Some assumptions concerning non-equilibrium phenomena in QFT at finite temperatures were analysed and extended in this framework. To this end, we have examined the Green\'s functions in these models and compared them with the approximated results which are often used in the literature. One of the models describes non-equilibrium systems of the glassy-kind. Such systems exhibit a behaviour which is compatible with that expected from the fluctuation-dissipation theorem. The basic properties were consistently deduced and explicit results for the effective temperature and characteristic frequencies were obtained.

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The imaginary part of the retarded self energy is of particular interest as it contains a lot of physical information about particle interactions. In higher order loop diagrams the calculation become extremely tedious and if we have to do the same at finite temperature, it includes an extra dimension to the difficulty. In such a condition we require to switch between bases and select the best basis for a particular diagram. We have shown in our calculation that in higher order loop diagrams, at #12;finite temperature, the R/A basis is most convenient on summing over the internal vertices and very efficient on calculating some particular diagrams while the result is most easily interpretable in the Keldysh basis for most other complex diagrams.

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

Η παρούσα διπλωματική εργασία πραγματοποιήθηκε στο τμήμα Σωματιδιακής Φυσικής του Πανεπιστημίου Santiago de Compostela της Ισπανίας και αποτελεί τη μελέτη της υπερσυμμετρίας στις τρεις χωροχρονικές διαστάσεις. Έμφαση δίνεται σε θεωρίες που περιέχουν τον όρο Chern-Simons που παιζεί συμαντικό ρόλο στους τομείς έρευνας της θεωρητικής φυσικής. Αρχικά, εισάγουμε τις εισαγωγικές ένοιες της υπερσυμμετρίας στις τρεις διαστάσεις και ακολούθως μελέτουμε την Ν=1 ελάχιστη θεωρία με διάφορες φυσικές ποσότες που περιέχουν τον όρο Chern-Simons. Στην συνέχεια, μελετάμε τις ABJM θεωρίες και αποδεικνύουμε ότι είναι αναλλοίωτες κάτω από μετασχηματισμούς βαθμίδας. Τέλος υπολογίζουμε τις κβαντικές διορθώσεις στην διαταρακτική θεωρία Chern-Simons. / The present thesis took part in Department of Particle Physics of University of Santiago de Compostela, Spain, and is the study of supersymmetry in three spacetime dimensions. Emphasis is given to theories containing the Chern-Simons term that plays an important role in the research areas of theoretical physics. First, we introduce the notion of supersymmetry in three dimensions and then we study the N = 1 minimal theory with various physical quantitative containing the term Chern-Simons. Then, we study the ABJM theories and prove that they are invariant under gauge transformations. Finally we calculate the quantum corrections to the perturbative Chern-Simons theory.

La notion d’entropie d’intrication a eu un profond impact sur la physique théorique, particulièrement depuis ces dix dernières années. D’abord introduite afin expliquer l’entropie des trous noirs, son champ d’application s’est par la suite ouvert à une grande variété de domaines de recherche, de la matière condensée à la gravitation quantique, de l’information quantique à la théorie quantique des champs. Dans ce contexte scientifique effervescent, l’entropie d’intrication apparait comme un outil central et doit donc intensivement être étudiée. A l’origine de cette thèse se trouve le désir de mieux comprendre cette entropie. D’intéressants développements concernant les effets de bord sur l’entropie d’intrication ont vu le jour récemment. Nous proposons donc d’explorer comment le bord d’un espace affecte l’entropie, en particulier dans la situation où la surface d’intrication intersecte ce bord. Nous présentons des calculs explicites de l’entropie d’intrication en espace plat avec bords. Nous montrons que des termes induits par ces bords apparaissent dans l’entropie et nous soulignons le rôle prépondérant que jouent les conditions aux bords. Nous étudions ensuite la contribution de bord dans le terme logarithmique de l’entropie d’intrication en dimensions trois et quatre. Nous calculons en premier lieu ce terme en théorie des champs pour la théorie N = 4 de Yang-Mills, puis nous répétons ce calcul de manière holographique. Nous montrons que ces deux méthodes de calcul donnent le même résultat, si du côté théorie des champs les conditions aux bords préservent la moitié de la supersymétrie et que du côté gravité l’extension du bord dans le bulk est une surface minimale. / The entanglement entropy has had a tremendous and profound impact on theoretical physics, particularly since the last decade. First introduced in an attempt to explain black holes entropy, it has then found applications in a wide range of research areas, from condensed matter physics to quantum gravity, from quantum information to quantum field theory. In this exciting scientific context, the entanglement entropy has thus emerged as a useful and pivotal tool, and as such justifies the need to be intensively studied. At the heart of this thesis therefore lies the desire to better understand the entanglement entropy. Interesting developments during the recent years concern the boundary effects on the entanglement entropy. This dissertation proposes to explore the question of how the presence of spacetime boundaries affects the entropy, specifically in situations where the entangling surface intersects these boundaries. We present explicit calculations of entanglement entropy in flat spacetime with plane boundaries. We show that boundary induced terms appear in the entropy and we emphasize the prominent role of the boundary conditions. We then study the boundary contribution to the logarithmic term in the entanglement entropy in three and four dimensions. We perform the field theoretic computation of this boundary term for the free N = 4 super-gauge multiplet and then repeat the same calculation holographically. We show that these two calculations are in agreement provided that on the field theory side one chooses the boundary conditions which preserve half of the full supersymmetry and that on the gravity side the extension of the boundary in the bulk is minimal.