In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with $SU(3)$ structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions. Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions. It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation. It turns out that the most interesting solutions are obtained from SU(3)/U(1)². This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families.

The purpose of this thesis is to study a symmetry of string theory known as T-duality. We focus on a particular example establishing the equivalence between a quantized string moving in a circular space of radius R and a dual string moving in a similar space of radius 1/R . We will show that this duality implies that the momentum of the string in one picture becomes the number of times the string is wound around the circle in the dual picture. We present two proofs of T-duality. The first reflects the standard interpretation of T-duality as an isomorphism of quantum theories. The second approach is based on Hull's Double Field Theory.

In this Thesis I explore aspects of dark radiation and its role in String Phenomenology. Dark radiation is any additional hidden type of relativistic matter present in the Universe today, conventionally labelled as an "excess effective number of neutrino species", Δ N_eff. It provides a powerful test of hitherto untested theoretical models based on fundamental theories such as String Theory. I begin by considering dark radiation in the LARGE Volume Scenario, a phenomenologically viable class of string compactifications. First I review how the minimal setup slightly overproduces axionic dark radiation via modulus decay. I then demonstrate that loop corrections to the main competing visible-sector decay process have a negligible effect and are unable to alleviate the tension with observations. In the following chapter I explore fibred extensions of the LARGE Volume Scenario. The predictions for Δ N_eff are qualitatively different: in particular, models with a sequestered visible sector on D3 branes at a singularity are swamped by massless axions and decisively ruled out. I then consider TeV-scale supersymmetry in a model with anisotropic modulus stabilisation. If the Standard Model is realised on D7 branes wrapping the small volume cycle a hierarchy of soft terms is generated, which may have applications to natural supersymmetry. The final chapter takes a different approach and investigates the proposition that dark radiation, in the form of a Cosmic Axion Background, could explain the long-standing soft X-ray excess from galaxy clusters. I show for the Coma cluster that the morphology of the excess can be reproduced by axion-photon conversion in the intracluster magnetic field, provided the field is allowed to have more structure on smaller scales than typically assumed based on Faraday rotation data. This explanation requires an inverse axion-photon coupling M ∼ 10¹¹ - 10¹² GeV and a mean axion energy (E_CAB) ∼ 50 - 250 eV.

L'objet de cette thèse est l'étude de certaines propriétés de théories des champs à fort couplage via la dualité avec la théorie des cordes, dans la limite de supergravité. L'analyse expérimentale du plasma de quarks et de gluons produit au RHIC et au LHC tend en effet à indiquer que cet état de la matière se comporte comme un fluide quasiment parfait. Les méthodes perturbatives de la QCD sont impuissantes à décrire ses propriétés et la chromodynamique quantique sur réseau fait face à des problèmes tant techniques que conceptuels pour calculer les observables dynamiques d'un tel système. La correspondance AdS/CFT offre par conséquent un outil unique permettant d'étudier en première approximation cette phase de la QCD. L'un des aspects de cette thèse consiste en la description par une équation stochastique de Langevin d'un parton massif se propageant dans un plasma de Yang--Mills maximalement supersymétrique. Bien que cette théorie semble décrire de manière satisfaisante la phase déconfinée de la QCD, il est toutefois désirable de chercher un dual en théorie des cordes rendant compte des aspects de la QCD à basse énergie. L'autre axe directeur de cette thèse propose ainsi de rendre compte de solutions de moindre supersymétrie, sans invariance conforme, et avec confinement. On obtient le dual gravitationnel d'états metastables de telles théories. En particulier, on dérive une contribution au potentiel inflationnaire dans le cadre d'un modèle cosmologique générique de la théorie des cordes. / In this thesis, we apply the gauge/string duality in its supergravity limit to infer some properties of field theories at strong coupling. Experiments at RHIC and at the LHC indeed suggest that the quark--gluon plasma behaves as one of the most perfect fluid ever achieved in any controlled experimental setup. Perturbative approaches fail at accounting for its properties, whereas lattice QCD methods face technical as well as conceptual difficulties in computing dynamical aspects of this new state of matter. As a result, the AdS/CFT correspondence currently is the best tool at our disposal for analytically modelling this phase of QCD. One of the contributions of this thesis amounts to deriving a stochastic Langevin equation for a heavy quark moving across a maximally supersymmetric Yang--Mills plasma at strong coupling. Even though this theory seems to describe in a surprisingly satisfactory way the high--energy, deconfined phase of QCD, it is also of much interest to try and search for a string theory dual making closer contact with QCD at lower energies. As such, the other main focus of this thesis deals with supergravity solutions of lesser supersymmetry, without conformal invariance and exhibiting confinement. We build for the first time the gravity dual to metastable states of such theories. In particular, we find the contribution from anti--branes to the inflation potential in some general scenario of string cosmology.

Este trabalho tem o objetivo de rever a obtenção das soluções do tipo brana em supergravidade e contém uma dedução detalhada das soluções extrema e negra. A fim de motivar algumas escolhas feitas ao longo do cálculo, o trabalho inclui uma breve revisão dos conceitos advindos da teoria de cordas e supersimetria. Esta revisão nos permitirá ainda relacionar as soluções da supergravidade com as branas da teoria de cordas e tecer considerações sobre o papel desta relação na dualidade entre teoria de calibre e gravitação. / This work intends to review the brane solutions of supergravity and contains a datailed deduction of the extremal and black solutions. In order to provide some motivations to the choices through the calculation, this work includes a brief review of some concepts from string theory and supersymmetry. This review will enable us to relate the supergravity solutions to string theory\'s branes and to make considerations about the role of this relationship in the duality between gauge and gravity theories.

O principal objetivo deste trabalho é estudar a quantização covariante da corda bosônica e da supercorda RNS, explorando as simetrias envolvidas, ou seja, as simetrias BRST e conforme no caso da corda bosônica e as generalizações correspondentes para a corda fermiônica. Em particular, discutimos alguns aspectos perturbativos da teoria bosônica e a construção de operadores de vértice da corda fermiônica. / The main goal of this work is to study the covariant quantization of the bosonic and RNS string theories by exploiting the involved symmetries, namely, the BRST and conformal invariance for the bosonic string and the corresponding supersymmetric generalizations for the fermionic case. In particular, we discuss some perturbative aspects of the bosonic theory and the construction of vertex operators for the fermionic string.

In the present thesis, we offer an introduction to type IIB string compactifications on $\mathbb{T}^{d}/\Gamma$ toroidal orbifolds. We first describe the technical method to construct these spaces and reduce the string background on it. We will have (non)-geometrical fluxes arising from these spaces which decorate with discrete deformations our four $\mathcal{N}=1$ dimensional supergravity theory. Solving its equations of motion, we find several families of supersymmetric AdS vacua with fixed moduli, which can be related through a set of  $SL(2,\mathbb{Z})$ symmetries.

Apresentamos uma revisão dos elementos básicos do estudo da teoria clássica das supercordas em backgrounds planos e curvos, dando ênfase ao caso importante em que o background e a variedade AdS5 S5. Nós inclumos um estudo da corda bosonica para revisarmos alguns conceitos básicos da teoria de campos conforme em duas dimensões. Em seguida estudamos a teoria das supercordas em um espaço plano onde apresentamos uma introdução pedagógica ao formalismo de espinores puros. A ultima parte e dedicada a generalização da ação de Green-Schwarz para o caso de AdS5 S5 e uma apresentação do modelo sigma do formalismo de espinores puros no mesmo background. / We present a review of the basic elements of the study of classical superstring theory in at and curved backgrounds, giving emphasis to the very important case of the AdS5S5 background. We include a study of the bosonic string to review some basic concepts of two dimensional conformal eld theory. We then move on to the superstring in at space where we present a pedagogical introduction to the pure spinor formalism of superstrings. The last part is devoted to the generalization of the Green-Schwarz action to AdS5 S5 and a presentation of the pure spinor sigma model in the same background.

Cette thèse intitulée « Studies of fractional D-branes in the gauge/gravity correspondence & Flavored Chern-Simons quivers for M2-branes » se place dans le cadre de la théorie des cordes, en physique théorique. Elle consiste en une introduction suivie de deux parties. Dans l'introduction sont résumés les différents outils de théorie des cordes qui seront utilisés. La première partie étudie des théories de type quiver en 3+1 dimensions et leur dual gravitationnel, qui découlent de la considération de D-branes fractionnaires vivant sur des espaces possédant des singularités en codimension complexe un. La thèse principale de cette partie est que la solution de supergravité de Bertolini et al. 2001 and Polchinski 2001 pour des branes de type N=2 a une interprétation dans la théorie des champs de type quiver duale comme un groupe de renormalisation de type cascade qui résulte d'un choix particulier sur la branche de Coulomb de la théorie. Cette compréhension nouvelle permet d'étudier des solutions de supergravité plus générales. Elle donne aussi une plus grande compréhension des branes N=2 dans des contextes avec seulement une supersymmétrie N=1. La second partie de la thèse étudie les quivers de type Chern-Simons, récemment apparus dans la littérature, décrivant des théories en dimension 2+1, qui sont conjecturé dual à des solutions de M-théorie. Il est montré que des théories plus générales que des quivers, possédant également des champs dans la représentation fondamentale des groupes de jauges, permettent la description de M2-branes sur des espaces possédant des singularités de dimension complexe deux, du moins du point de vue de la structure complexe, dans le cas où seules 4 supercharges sont préservées. La thèse principale est que la considération des operateurs monopoles diagonaux dans la théorie de champs N=2 supersymmétrique en 2+1 dimensions, plus une relation entre ces opérateurs proposée comme conjecture, permettent de reproduire l'espace des modules d'une M2-brane sur n'importe quelle géométrie torique ayant des singularités en codimension complexe deux.

In this Ph.D. thesis, we construct and study a number of new type IIB supergravity backgrounds that realize various flavored, finite temperature, and non-supersymmetric deformations of the resolved and deformed conifold geometries. We make heavy use of a U-duality solution generating procedure that allows us to begin with a modification of a family of solutions describing the backreaction of D5 branes wrapped on the S^2 of the resolved conifold, and generate new backgrounds related to the Klebanov-Strassler background. We first construct finite temperature backgrounds which describe a configuration of N_c D5 branes wrapped on the S^2 of the resolved conifold, in the presence of N_f flavor brane sources and their backreaction i.e. N_f/N_c ~ 1. In these solutions the dilaton does not blow up at infinity but stabilizes to a finite value. The U-duality procedure is then applied to these solutions to generate new ones with D5 and D3 charge. The resulting backgrounds are a non-extremal deformation of the resolved deformed conifold with D3 and D5 sources. It is tempting to interpret these solutions as gravity duals of finite temperature field theories exhibiting phenomena such as Seiberg dualities, Higgsing and confinement. However, a first necessary step in this direction is to investigate their stability. We study the specific heat of these new flavored backgrounds and find that they are thermodynamically unstable. Our results on the stability also apply to other non-extremal backgrounds with Klebanov-Strassler asymptotics found in the literature. In the second half of this thesis, we apply the U-duality procedure to generate another class of solutions which are zero temperature, non-supersymmetric deformations of the baryonic branch of Klebanov-Strassler. We interpret these in the dual field theory by the addition of a small gaugino mass. Using a combination of numerical and analytical methods, we construct the backgrounds explicitly, and calculate various observables of the field theory. / text