O objetivo desta dissertação é revisar os operadores laços de Wilson no contexto da correspondência AdS/CFT. Estes operadores, presentes em qualquer teoria de calibre, são importantes por nos fornecer um parâmetro de ordem para a transição de fase confinante/desconfinante. Além disso, eles são particularmente importantes no estudo da correspondência AdS/ CFT pois: i) Eles nos dão, em alguns casos, resultados exatos graças ao fato de poderem ser localizados em um modelo de matrizes, desta forma nos permitindo fazer testes altamente não triviais da correspondência; ii) Eles são os objetos da teoria de calibre que são duais as cordas propagando no interior do espaço, nos dando um rico dicionário entre quantidades no interior (AdS) e na borda do espaço (CFT). Depois de revisarmos os laços de Wilson em teorias de calibre e a correspondência Ads/CFT, introduziremos a definição dos laços de Wilson supersimétricos 1/2 BPS. Calcularemos eles para o caso de um acoplamento fraco e para qualquer outro valor da constante de acoplamento usando técnicas de modelos de matrizes. Finalmente, compararemos nossos resultados com computações de superfícies minimais no interior do espaço, encontrando uma concordância perfeita. / The aim of this thesis is to review Wilson loop operators in the contexto f the AdS/CFT correspondence. These operators, wich are present in any gauge theory, are important because they furnish an order parameter for confinement/deconfinement phase transitions. Besides this, they are particularly relevant in the study of the AdS/CFT correspondence because: i) they allow, in some cases, for exact results thanks to localization to matrix models and make it possible to perform highly non-trivial tests of the correspondence; ii) they are the gauge theory objects dual to strings propagating in the bulk of the space and give a rich dictionary between bulk (AdS) and boundary (CFT) quantities. After reviews of Wilson loops in gauge theories and of the Ads/CFT correspondence, we will introduce the definition of 1/2 BPS supersymmetric Wilson loops, we will compute them at weak coupling and then at any order in the coupling constant via matrix model techniques, and finally we will compare our results with minimal surface computations in the bulk, finding perfect agreement.

Die vorliegende Arbeit beinhaltet ein einführendes Kapitel über Orbifold-Konstruktionen in dem neben rudimentären Grundlagen bereits speziellere Themen wie Diskrete Torsion und asymmetrische Orbifold-Gruppen behandelt werden. Als Beispiele für Orbifolde werden Kompaktifizierungen auf Tori sowie das asymmetrische T^4/Z(3)^L x Z(3)^R Orbifold behandelt. Danach wird eine allgemein gehaltene Einführung in Orientifolde gegeben, einschließlich des offenen String Sektors samt Chan-Paton Freiheitsgraden. Die darauf folgenden Kapitel 4-7 behandeln von mir durchgeführte Forschungsarbeiten. Kapitel 4 beschäftigt sich mit der Quantisierung des offenen Strings mit linearen Randbedingungen, wie sie bei Strings in elektro-magnetischen Feldern auftreten. Weiterhin wird die Quantisierung der Null- und Impuls-Moden des offenen Strings in Torus-Kompaktifizierungen durchgeführt. Außerdem wird für den Fall allgemeiner konstanter Hintergrund Neveu-Schwarz U(1)-Hintergrundfelder der Kommutator der Stringkoordinaten berechnet. Dieser stützt bisherige Resultate zur Nicht-Kommutativität von offenen Stringtheorien in Neveu-Schwarz Hintergründen. Kapitel 5 gibt, zusammen mit einigen neuen Erkenntnissen, Resultate von [1] über asymmetrische Orientifolde, insbesondere deren D-Branen Inhalt wieder. Kapitel 6 faßt die Veröffentlichung [2] zusammen, in der untersucht wurde, inwieweit sich phänomenolgisch interessante Modelle in Orientifolden von Torus-Kompaktifizierungen finden lassen. Insbesondere tragen die D9-Branen magnetische Flüsse, womit chirale Fermionen im Spektrum auftreten. Die Rechnungen werden größtenteils im gleichwertigen, T-dualen Bild ausgeführt. In diesem ist die Anzahl der chiralen Fermionen durch die topologische Schnittzahl der D-Branen gegeben. Existieren auf Torus-Kompaktifizierungen entweder nur nicht-chirale oder nicht-supersymmetrische Modelle, so lassen sich auf gewissen Orbifolden beide Eigenschaften miteinander vereinbaren. Kapitel 7 behandelt das "sigma Omega"-Orientifold auf einem T^6/Z(4) Orbifold. Als besonders interessantes Beispiel wird ein supersymmetrisches U(4) x U(2)^3_L x U(2)^3_R Modell vorgestellt, daß durch Einschalten geeigneter Hintergrundfelder in der effektiven Niederenergie-Wirkung auf ein Modell gebrochen wird, daß dem MSSM (minimalem supersymmetrischen Standard Modell) sehr ähnlich ist. Dieses Kapitel basiert auf unserer Publikation [3]. Ferner ist der Arbeit ein Anhang beigefügt, der einige der verwendeten Formeln sowie Beweise zu zwei Sätzen enthält, die im Text verwendet wurden. / This thesis contains an introductory chapter on orbifolds. Besides rudimentary basics we discuss more advanced topics like discrete torsion and asymmetric orbifold groups. As examples we investigate torus compactifications and an asymmetric T^4/Z(3)^L x Z(3)^R orbifold. The following chapter explains the foundations of orientifolds, including open strings with Chan-Paton degrees of freedom. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they show up in electro-magnetic fields. We quantize the zero- and momentum-modes for toroidal compactifications, too. As an application we calculate the commutator of the coordinate fields in the case of general constant Neveu-Schwarz U(1)-field strengths. Thereby we confirm previous results on non-commutativity of open string theories in Neveu-Schwarz backgrounds. Chapter 5 reviews the results of a former publication [1] on asymmetric orientifolds, supplemented by some recent insights in connection with the preceeding chapter. Chapter 6 is a summary of [2]. In this publication we investigated to what extend one can build phenomenologically interesting models from toroidal orientifolds. By turning on magnetic fluxes on D9-branes we induce chiral fermions. Most calculations are performed in an (equivalent) T-dual picture. Here the number of chiral fermions is given by the topological intersection number of D-branes. In orientifolds of toroidal compactifications one obtains either non-chiral or non-supersymmetric orientifold solutions. However both properties can be reconciled in orientifolds that are obtained from specific supersymmetric orbifold compactifications. In chapter 7 we present the "sigma Omega"-Orientifold on a T^6/Z(4) orbifold. As a very attractive example we investigate a supersymmetric U(4) x U(2)^3_L x U(2)^3_R model that is broken to an MSSM-like model by switching on suitable background fields in the low energy effective action. This chapter is based on our publication [3]. The thesis is supplemented by an appendix with formulas applied in the text, as well as proofs to two theorems that were used as well.

Des progrès expérimentaux importants sont en cours dans l’étude des désintégrations rares de mésons contenant un quark beau et impliquant un quark étrange et une paire de leptons. Le travail présent mesure la portée indirecte de ces progrés sur des extensions supersymétriques du modèle standard. Même dans des modèles contraints, les limites indirectes ainsi obtenues peuvent dans certains cas être plus fortes que celles provenant de la recherche directe de particules supersymétriques. La précision gagnée par les facteurs de forme et les corrections d’ordre supérieur nouvellement implémentés dans le programme public ”SuperIso” montrent alors leur importance. / There are fast progresses in the experimental study of rare decay sof mesons containing a b-quark, and involving a pair of leptons and an s-quark. The present work measures the indirect implications of these progresses on the supersymmetric extensions of the Standard Model. Even within constrained models, the indirect limits obtained in this way can in some cases be stronger than those coming from direct searches of supersymmetric particles. The accuracy gained by the form factors and higher order corrections newly implemented in the public code ”SuperIso” are then fully relevant.

The work of this Ph.D. thesis in mathematics concerns the problem of determining existence, uniqueness, and structure of zero-energy states in supersymmetric matrix models, which arise from a quantum mechanical description of the physics of relativistic membranes, reduced Yang-Mills gauge theory, and of nonperturbative features of string theory, respectively M-theory. Several new approaches to this problem are introduced and considered in the course of seven scientific papers, including: construction by recursive methods (Papers A and D), deformations and alternative models (Papers B and C), averaging with respect to symmetries (Paper E), and weighted supersymmetry and index theory (Papers F and G). The mathematical tools used and developed for these approaches include Clifford algebras and associated representation theory, structure of supersymmetric quantum mechanics, as well as spectral theory of (matrix-) Schrödinger operators. / QC20100629

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-13T13:01:16Z No. of bitstreams: 1 arquivototal.pdf: 7899614 bytes, checksum: f001983854e55609b8ccfb1ce80578f2 (MD5) / Made available in DSpace on 2017-09-13T13:01:16Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 7899614 bytes, checksum: f001983854e55609b8ccfb1ce80578f2 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / One of the main problems that permeates the Particle Physics and Cosmology is the Dark Matter (DM), which makes up about 26% of the energy content of the Universe. The main evidence pointing to its existence provides us with important features, such as being neutral, stable (with lifetime over the age of the Universe), cold or warm, weakly interacting with Particle Physics Standard Model (SM) particles and sufficiently abundant. The SM does not provide a candidate who meets these characteristics and hence it is necessary to extend it. One of the most sophisticated extensions of the SM is the Supersymmetry, that in addition to solving the problem of DM, explains other unsolved puzzles that are present in SM, among them, the hierarchy and the unification of the gauge couplings. This model implies the inclusion of a new symmetry that puts bosons and fermions in equal footing. The minimal supersymmetric version of the SM is the Minimal Supersymmetric Standard Model (MSSM), whose viable candidate is the neutralino, which is a fermion composed of superpartners of neutral Higgs and gauge bosons. In this work, we performed the neutralino analysis as DM candidate in CMSSM or mSUGRA scenario, which contains 5 free parameters, M0, M1/2, tan , sign(μ) and A0, for two different analyzes. In the first one we varied the M0 and M1/2 parameters for three different values of tan while in the second and third one we varied all parameters except the sign(μ). In this study, we use some computational tools, including, SARAH, SPheno, SSP and Micromegas, in order to obtain DM Relic Abundance and DM scattering cross section in this scenario. We compared our results with the most recent experimental data, namely, we have used Planck satellite data for the relic abundance, LUX and XENON1T (prospect) for the spin-independent scattering cross section and XENON100 for the spin dependent one. We finally analyzed the implications concerning the viability of the MSSM under the light of the DM problem. / Um dos principais problemas que permeia a Física de Partículas e Cosmologia é a Matéria Escura (ME), que compõe cerca de 26% do conteúdo energético do Universo. As principais evidências que apontam para a sua existência nos fornecem importantes características, tais como, ser neutra, estável (com tempo de vida maior que a idade do Universo), fria ou morna, pouco interagente com partículas do Modelo Padrão de Física de Partículas (MP)e suficientemente abundante. O MP não fornece um candidato que supre estas características, sendo necessário estendê-lo. Uma das mais sofisticadas extensões do MP é a Supersimetria, que além de resolver o problema da ME, soluciona outros que estão presentes no MP, dentre eles, a hierarquia e a unificação dos acoplamentos de gauge. Tal modelo implica na inclusão de uma nova simetria que coloca bósons e férmions em pé de igualdade. A versão mínima supersimétrica do MP é o Modelo Padrão Supersimétrico Mínimo (MSSM), cujo candidato viável à ME é o neutralino, que se trata de um férmion composto pelos superparceiros dos bósons de gauge e Higgs neutros. Neste trabalho, fizemos uma análise do neutralino como candidato à ME no cenário CMSSM ou mSUGRA, que contém 5 parâmetros livres, M0, M1/2, tan , sinal(μ) e A0, para três análises distintas. Na primeira variamos apenas os parâmetros M0 e M1/2 para três valores distintos da tan e na segunda e terceira variamos todos os parâmetros com exceção do sinal(μ). Neste estudo, utilizamos algumas ferramentas computacionais, entre as quais, SARAH, SPheno, SSP e micrOMEGAs, no intuito de obter abundância e seção de choque de espalhamento de ME neste cenário. Obtidos os gráficos, comparamos com os resultados experimentais mais recentes, para a abundância utilizamos dados do satélite Planck, para a seção de choque de espalhamento independente de spin, o LUX e XENON1T (2017) e para dependente de spin, XENON100 e verificamos suas implicações na viabilidade do modelo.

O objetivo desta dissertação é revisar os operadores laços de Wilson no contexto da correspondência AdS/CFT. Estes operadores, presentes em qualquer teoria de calibre, são importantes por nos fornecer um parâmetro de ordem para a transição de fase confinante/desconfinante. Além disso, eles são particularmente importantes no estudo da correspondência AdS/ CFT pois: i) Eles nos dão, em alguns casos, resultados exatos graças ao fato de poderem ser localizados em um modelo de matrizes, desta forma nos permitindo fazer testes altamente não triviais da correspondência; ii) Eles são os objetos da teoria de calibre que são duais as cordas propagando no interior do espaço, nos dando um rico dicionário entre quantidades no interior (AdS) e na borda do espaço (CFT). Depois de revisarmos os laços de Wilson em teorias de calibre e a correspondência Ads/CFT, introduziremos a definição dos laços de Wilson supersimétricos 1/2 BPS. Calcularemos eles para o caso de um acoplamento fraco e para qualquer outro valor da constante de acoplamento usando técnicas de modelos de matrizes. Finalmente, compararemos nossos resultados com computações de superfícies minimais no interior do espaço, encontrando uma concordância perfeita. / The aim of this thesis is to review Wilson loop operators in the contexto f the AdS/CFT correspondence. These operators, wich are present in any gauge theory, are important because they furnish an order parameter for confinement/deconfinement phase transitions. Besides this, they are particularly relevant in the study of the AdS/CFT correspondence because: i) they allow, in some cases, for exact results thanks to localization to matrix models and make it possible to perform highly non-trivial tests of the correspondence; ii) they are the gauge theory objects dual to strings propagating in the bulk of the space and give a rich dictionary between bulk (AdS) and boundary (CFT) quantities. After reviews of Wilson loops in gauge theories and of the Ads/CFT correspondence, we will introduce the definition of 1/2 BPS supersymmetric Wilson loops, we will compute them at weak coupling and then at any order in the coupling constant via matrix model techniques, and finally we will compare our results with minimal surface computations in the bulk, finding perfect agreement.

The nature of interactions of fundamental particles is governed by symmetries. These interactions are well described by an elegant and simple SU(3)c x SU(2)L x U(1)Y symmetric gauge theory that we call the Standard Model (SM) of particle physics. Very recently the CMS and ATLAS experiments at the Large Hadron Collider (LHC) confirmed the discovery of a boson of mass of about 125 GeV. Already, the data collected from these experiments seem to indicate that this particle is in fact the last missing piece and essential ingredient of the Standard Model : the Higgs boson. The Higgs has the very distinct role of providing a mechanism through which masses for other particles can be generated without destroying gauge invariance and hence the renormalizability of the theory. While this discovery completes the picture we have of the SM, the SM itself does not account for several experimentally observed phenomena , notably, dark matter (DM) and the baryon asymmetry in the universe (BAU). From a theoretical perspective a possibility for gauge coupling unification, an explanation for the quark flavour structure and the stability of the Higgs mass to radiative corrections are features that are absent in the framework of SM. This provides a strong basis to the hypothesis that there must be some intermediate scale (between the Planck scale and electroweak scale) of new physics, i.e. physics beyond the SM (BSM). The renormalizability of SM guarantees that various parameters of SM can be determined from the electroweak scale all the way up to the Planck scale. It is interesting to note that the RG evolution of the Higgs quartic coupling is driven to smaller values and can also become negative as the energy scale increases. Naively, a negative quartic coupling indicates destabilization of the EWSB vacuum. The energy scale at which the quartic coupling becomes negative would signify a break down of the theory and would set a scale for new physics. In principle the potential can be made stable through Planck scale dynamics and other vacua (other than the EWSB vacuum) may crop up. In this scenario the EWSB vacuum may decay to the deeper vacua. It is safe to say that, within experimental uncertainties of the Higgs and top quark masses the EWSB vacuum appears to be metastable. We are now left clueless: neither do we have any hints as to the nature of BSM physics nor the scale at which SM breaks down and new physics is assured. One should also note that although the evidence for BSM is compelling, data analysed from 7 and 8 TeV runs of the LHC have not produced any signals of BSM physics so far. Thus any indications of TeV scale BSM physics have been eluding us. In such a scenario the Higgs boson has assumed the role of a portal to study the possibilities of new physics. This is also motivated by the key role that the Higgs plays in generation of mass in a gauge symmetric theory. It is therefore reasonable to assume that the Higgs boson does in fact couple to particles predicted in BSM physics. Such couplings would play a role in modifying the properties of this boson. It is now essential to determine the properties of the Higgs as precisely as possible to search for signs of BSM. This thesis explores the idea of using the Higgs as a portal to study BSM physics. The properties of the Higgs that have already been measured with data from the first two runs of the LHC are its mass, branching ratios, spin and CP. When placed in the framework of a particular new physics model, these properties impose restrictions on the couplings and masses of BSM particles. A strong candidate for a BSM scenario is a Supersymmetric extension of the SM. Supersymmetry is an extension of the Poincar´e group that describes space time symmetries. Fermionic and bosonic degrees of freedom are mixed through the generators of this extended symmetry. In the minimal supersymmetric extension of the SM (MSSM), each particle of SM has a corresponding superpartner with identical quantum numbers modulo its spin. Since we do not see, for example, a bosonic superpartner of the fermionic top quark of the same mass as that of the top quark, this must mean that the supersymmetry, even if it is realized in nature, is not exact and must be broken. Although the symmetry may be broken the MSSM has some very appealing features: stabilization of the Higgs mass to quantum corrections, gauge coupling unification and possible dark matter candidate if the lightest Supersymmetric particle happens to be both stable and neutral. It is interesting to note that in MSSM, the tree level Higgs mass is bounded from above by the Z boson mass ( ~90 GeV ). The measured value of the Higgs mass (~126 GeV ) is still achievable in the MSSM through quantum corrections, the largest contribution coming from the top quarks and stop squarks. One therefore sees that the mass of the Higgs can already provide information about top superpartners. The presence of additional charged and coloured scalars implies the possibility of existence of charge and colour breaking (CCB) minima which would affect the stability of the Electroweak Symmetry breaking (EWSB) minima generated by the Higgs potential. Stability of EWSB is then dependent on parameters in the scalar sector of MSSM. We explore the nexus between the Higgs mass and vacuum stability in this model and find restrictions on the MSSM parameter space. The lighter Higgs of the MSSM couples differently to SM particles than the SM Higgs boson. More specifically one expects the couplings of the MSSM Higgs to gauge bosons to be smaller than in SM and unlike the SM Higgs, up type quarks have couplings strengths that are different from that of down type quarks. In the decoupling regime these differences become negligible and the lighter MSSM Higgs behaves identically to the SM Higgs. The measured Higgs rates do not show any large deviations from the expectations of a SM Higgs. It is therefore reasonable to assume that MSSM, if realized, resides in the decoupling regime. While tree level processes are not altered significantly in this regime, the same cannot be said about loop induced processes such as (h→ γγ) or (gg → h). Such processes may be affected significantly by sparticles running in the loops. Higgs decays to two photons can be strongly affected by the stau sector of MSSM and we study this in connection with EWSB vacuum stability. In several models of dark matter, the dark matter candidate particle couples to the Higgs boson. It may well be that this candidate particle may be light enough so that the decay of the Higgs boson to these particles may be possible. For example, in the framework of the MSSM, the LSP (˜χ01) is the dark matter candidate and a decay of the form hχ˜→01χ˜01is possible depending on the mass and strength of coupling of such a particle. At the LHC this would show up as an branching ratio to particles that are invisible to the detectors. The dominant production mode of the Higgs at LHC proceeds through gluon fusion. In this channel a signal for an “invisibly” decaying Higgs would show up as missing energy plus jets at LHC. This has already been studied in quite some detail. We focus on other production modes, namely Vector Boson Fusion (VBF) and associated production (VH), in determining an invisible branching fraction at LHC. These two production channels are much less sensitive to any other BSM signals that may mimic an invisibly decaying Higgs and thus provide clean signals for the latter. A determination of the nature of interactions between the Higgs and gauge bosons is of paramount importance. An understanding of these interactions is closely tied to an understanding of the nature of EWSB. There are two aspects to probing these interactions. One is a determination of the Lorentz structure of the Higgs and gauge boson vertices and the second is to determine the strength of its couplings. The Higgs coupling to two gauge bosons (the hVV vertex) in SM is of the form ~ agµν . Under the assumption that BSM physics does not alter this Lorentz structure, information about possible new physics can be simply extracted through a determination of the strength of the coupling aV . However, the most general structure of this vertex is of the form (aV gµν + bV pµq ν + cV ɛ µνρσpρqσ) . Here p and q are the sum and difference of the two gauge boson momenta respectively and ɛµνρσ the completely antisymmetric Levi-Civita tensor. The term cV parametrizes CP-odd couplings while the rest are CP-even. The terms proportional to b V and cV may be generated by new physics. But which new physics model do we look at? There are a plethora of such models. Rather than shooting in the dark at random BSM directions one could adopt the following approach. In the absence of BSM signals at the LHC so far, one could assume that the scale of physics is relatively high and BSM particles are more massive than SM particles and can therefore be integrated out of the Lagrangian. It is also prudent to assume that new physics respects the SU(3)c x SU(2)L x U(1)Y gauge symmetry of SM. With these two assumptions in hand, one could supplement the SM Lagrangian with additional operators. These operators which generally have mass dimensions greater than four would destroy the renormalizability of the theory, though an interpretation as an effective theory up to a scale Λ is still valid. The idea is to now study the consequences that this effective theory would have on measurable properties of the Higgs. The effective theory could affect both the Lorentz structure as well as the strength of the couplings of the Higgs to the gauge bosons. This thesis deals with the determination of the Lorentz structure of the Higgs coupling to two gauge bosons , i.e the trilinear vertex. An analysis of this for the hZZ vertex has already been performed by ATLAS and CMS using h → ZZ *decays. A pure pseudoscalar Higgs (cZ ≠0, aZ = bZ = 0) coupling has been ruled out at about 2 ~ 3 σ level. Bounds have also been placed on a mixed scalar-pseudoscalar coupling (a Z =0,cZ =0,bZ = 0). This however, is not the end of the story. There are two important points to note here. Firstly it is important to be able to verify these findings in other production modes. To this end, we investigate the ability of VBF production to probe such anomalous couplings and find strong effects on the pseudo-rapidity distributions of the tagging jets in VBF. Secondly it is important to also look for such anomalous couplings in the hWW vertex. At this point, one might argue that the hZZ vertex and hWW vertex are connected by Custodial symmetry. However this symmetry is violated in SM by gauging of the hypercharge. It follows that violations of this symmetry should arise naturally in BSM physics. A study of the anomalous vertex is not easily achieved in h→ WW ∗ decays due to backgrounds and difficulties in reconstructing momenta. The VBF channel can be quite effective here although there is significant contamination from VBF production through the Z boson. We find that a cleaner production mode to use would be associated production. Until recently the low cross-section of Vh made it difficult to analyse this channel at LHC. An analysis of Vh has been made possible by the use of modern jet substructure techniques using (h→ bb) decays. We use these techniques and study how one can probe anomalous couplings in the Vh production mode at LHC. One of the most important couplings of the Higgs is that to the top, the heaviest SM particle. Not only is this coupling responsible for the main production channel of the SM Higgs at the LHC but the interaction with the top also has important consequences on spontaneous symmetry breaking within the SM – notably, vacuum stability arguments – as well as beyond the SM – supersymmetry, for instance, where the top drives electroweak symmetry breaking in some scenarios. The strength as well as the CP property of the Higgs top coupling is therefore an important aspect of to study. more specifically we investigate terms of the form ψ¯t(at + ibtγ5)ψth. here ψt and h corresponds to the top quark and Higgs fields respectively. at and bt parametrize scalar and pseudoscalar couplings respectively. Since the dominant production mode of the Higgs at the LHC (gluon fusion) proceeds through a top quark loop as do decays of the Higgs to two photons, some information about these couplings may be extracted just by looking at Higgs production and decay rates. However, an unambiguous determination of these couplings is possible only through Higgs production with a top and anti-top pair. Although the production rates are very small at the LHC, such a study is of prime importance. We investigate t¯th production at the LHC and list some useful observable that can probe the couplings described above. The outline of the thesis is as follows. We start with brief introduction to SM and Electroweak Symmetry breaking (EWSB) also briefly reviewing SM Higgs production and decay at the LHC. We then investigate the information that the Higgs mass in conjunction with stability of the EWSB vacuum provides about the stop sector of the MSSM. We further investigate the information that Higgs decay rates in conjunction with the stability of the EWSB vacuum could provide about the stau sector in the MSSM. We move on to examining the extent to which an invisible branching ratio of the Higgs could be measured or excluded directly at the LHC. Coming to the second part of the thesis we examine in a model independent way the nature of the Higgs-gauge boson couplings. We first give a brief description of the Higgs gauge boson vertex and the effective theory approach following it up with a description of how this could be probed using Higgs decays. We then follow it up with a study on how the Lorentz structure could affect Higgs production in Vector Boson fusion and Higgs production in association with W or Z boson. Finally, we show how the CP properties of the Higgs coupling to the top quark can be investigated using tth production along with Higgs rates.

Le présent mémoire est dédié à l’étude du rôle de la mécanique quantique supersymétrique dans la construction d’opérateurs d’échelle et de leurs applications pour le système quantique de Rosen-Morse. L’aboutissement de ces travaux est contenu dans un article qui constitue le dernier chapitre du mémoire. Précisément, on motive l’échec de la réalisation des opérateurs d’échelle comme opérateurs différentiels pour le potentiel de Rosen-Morse avec les méthodes traditionnelles. On exploite la propriété d’invariance de forme dans le contexte de la mécanique quantique supersymétrique comme un outil alternatif pour offrir une première approche quantique à la réalisation des opérateurs d’échelle pour la version hyperbolique de ce potentiel. On utilise cette réalisation pour obtenir celle d’opérateurs d’échelle pour une classe particulière d’extensions rationnelles du potentiel de Rosen-Morse hyperbolique avec des techniques issues de la supersymétrie. Des états cohérents sont construits à partir des réalisations obtenues pour les différents systèmes. Certaines de leurs propriétés sont analysées et mises en comparaison. En parallèle, on utilise une transformation canonique ponctuelle pour déduire une première réalisation des opérateurs d’échelle comme opérateurs différentiels pour le système de Rosen-Morse trigonométrique. De cette réalisation sont construits des états cohérents pour lesquels des propriétés sont similairement analysées. / This master thesis is dedicated to the study of the role of supersymmetric quantum mechanics in the construction of ladder operators and of their applications for the quantum Rosen-Morse system. The results of this work are presented in an article that constitutes the last chapter of the thesis. Precisely, we motivate the failure of traditional methods in providing a realization for the Rosen-Morse ladder operators as differential operators. We provide a first quantum-based solution to this problem by using the shape invariance property in supersymmetric quantum mechanics as a tool in the construction of the ladder operators for the hyperbolic version of this potential. We use the latter realization to obtain that of a specific class of rational extensions of the hyperbolic Rosen-Morse system by means of supersymmetric techniques. Coherent states are constructed from the ladder operators obtained for the different systems. Some properties are analyzed and compared. In addition, we make use of a point canonical transformation in the derivation of the first realization of the ladder operators of the trigonometric Rosen-Morse system as differential operators. From this realization, we construct coherent states for which some properties are similarly analyzed.

No description available.

Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected "Adinkraic network". Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 - > 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories.