We investigate semiclassical contributions to correlation functions in N = 1 supersymmetric gauge theories. Our principal example is the gluino condensate, which signals the breaking of chiral symmetry, and should be exactly calculable, according to a persymmetric non-renormalisation theorem. However, the two calculational approaches previously employed, SCI and WCI methods, yield different values of the gluino condensate. We describe work undertaken to resolve this discrepancy, involving a new type of calculation in which the space is changed from R(^4) to the cylinder R(3) x S(1) This brings control over the coupling, and supersymmetry ensures that we are able to continue to large radii and extract answers relevant to R(^4). The dominant semiclassical configurations on the cylinder are all possible combinations of various types of fundamental monopoles. One specific combination is a periodic instanton, so monopoles are the analogue of the instanton partons that have been conjectured to be important at strong coupling. Other combinations provide significant contributions that are neglected in the SCI approach. Monopoles are shown to generate a superpotential that determines the quantum vacuum, where the theory is confining. The gluino condensate is calculated by summing the direct contributions from all fundamental monopoles. It is found to be in agreement with the WCI result for any classical gauge group, whereas the values for the exceptional groups have not been calculated before. The ADS superpotential, which describes the low energy dynamics of matter in a supersymmetric gauge theory, is derived using monopoles for all cases where instantons do not contribute. We report on progress made towards a two monopole calculation, in an attempt to quantify the missed contributions of the SCI method. Unfortunately, this eventually proved too complicated to be feasible.

Despite its indisputable successes, the Standard Model of particle physics (SM) is widely considered to be an effective low-energy approximation to an underlying theory that describes physics at higher energy scales. While there are many candidates for such a theory, nearly all of them predict the existence of additional particles beyond those of the Standard Model. In this work, we present three analyses aimed at discovering new particles at current and future particle colliders. The first two analyses are designed to probe extended scalar sectors, which often arise in theories beyond the Standard Model (BSM). The structure of these extended scalar sectors can be described by a physically well-motivated class of models, known collectively as Two- Higgs Doublet Models (2HDMs). The scalar mass spectrum of 2HDMs is comprised of two CP-even states h and H, a CP-odd state A, and a pair of charged states H± . Traditional searches for these states at particle colliders focus on finding them via their decays to SM particles. However, there are compelling scenarios in which these heavy scalars decay through exotic modes to non-SM final states. In certain regions of parameter space, these exotic modes can even dominate the conven- tional decay modes to SM final states, and thus provide a complementary avenue for discovering new Higgs bosons. The first analysis presented aims to discover charged Higgs bosons H± via top decay at the LHC. We find that the exotic decay modes outperform the conventional decay modes for regions of parameter space with low values of the 2HDM parameter tan β. The second analysis aims to systematically cover all the exotic decay scenarios that are consistent with theoretical and experimental con- straints, at both the 14 TeV LHC and a future 100 TeV hadron collider. We find that the preliminary results are promising - we are able to ex- clude a large swathe of 2HDM parameter space, up to scalar masses of 3.5 TeV, for a wide range of values of tan β, at a 100 TeV collider. In addition to these two analyses, we also present a third, aimed at discovering pair produced higgsinos that decay to binos at a 100 TeV collider. Higgsinos and binos are new fermion states that arise in the Minimal Supersymmetric Standard Model (MSSM). This heavily- studied model is the minimal phenomenologically viable incorporation of supersymmetry - a symmetry that connects fermions and bosons - into the Standard Model. In the scenario we consider, the bino is the lightest supersymmetric partner, which makes it a good candidate for dark matter. Using razor variables and boosted decision trees, we are able to exclude Higgsinos up to 1.8 TeV for binos up to 1.3 TeV.

Recently it has been shown that N = 4 super Yang-Mills theory is integrable in the planar limit. Past arguments suggest the integrability is only present in the planar limit. However, this conclusion was shown to be incorrect. Two speci c classes of operators were studied in the O(N) sector. The rst were labelled by Young diagrams having two long columns. The second were labelled by Young diagrams having two long rows. This result was then generalized to p long rows or columns with p xed to be O(1) as N ! 1. For this case, the non-planar limit was found to be integrable. In this dissertation, we extend this work by considering p to be O(N). We have calculated the dilation operator for the case with two impurities.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. March 2013. / In the past decade, the gauge/gravity duality has been extensively explored in the large N limit. In particular, the spectrum of anomalous dimensions have been compared with the energy spectrum of the dual string theory showing remarkable agreement. In this limit, for operators with a bare dimension of order 1, planar diagrams give the leading contribution to the anomalous dimension. To obtain the anomalous dimensions, one needs to diagonalize the dilatation operator. One of the methods used to accomplish this is integrability. This allows an exact computation of the spectrum of the anomalous dimensions. There is by now a great deal of evidence that N = 4 supersymmetric Yang-Mills (SYM) theory and N = 6 superconformal Chern Simons (ABJ(M)) theory are integrable in the planar limit. In this thesis we probe the gauge gravity duality at finite N using novel tools developed from the representation theory of symmetric and unitary groups. We start by studying the action of the nonplanar dilatation operator of N = 4 SYM theory and ABJ(M) theory. The gauge invariant operators we consider are the restricted Schur polynomials. In the case of N = 4 SYM theory, we obtain the spectrum of the anomalous dimension beyond the SU(2) sector at one loop, and in the SU(2) sector at two loops. In both cases, we obtain the spectrum at arbitrary (finite) N. We then obtain the spectrum of anomalous dimensions in the SU(2) sector of ABJ(M) theory at two loops. The class of gauge invariant operators we consider have classical dimension of order O(N). In both theories, the spectrum of the anomalous dimensions reduces to a set of decoupled harmonic oscillators at large N. This indicates, for the first time, that N = 4 SYM theory and ABJ(M) theory exhibit nonplanar integrability. We expect to recover non-perturbative quantum gravity effects, from the gauge/gravity duality, when N is finite. The non-planar integrability we discover here may play an important role in finite N studies of the gauge/gravity duality, and hence may play an important role in understanding non-perturbative string stringy physics. In addition, we study various classes of correlators in ABJ(M) theory. In this context, we derive extremal n-point correlators in ABJ(M) theory and we probe the giant graviton dynamics in these theories.

Neste trabalho são apresentados alguns conceitos básicos da Teoria de Liouville e N=1 Super Liouville, enfatizando o cálculo das funções de três pontos dessas teorias.Uma introdução a Teoria de Campos Conformes (CFT) e a Supersimetria também sao incluídas, as quais constituem ferramentas básicas da presente pesquisa. / In this dissertation we present some basic features about Liouville and N=1 Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field Theories (CFT) and Supersymmetry, which are the basic tools of the present research.

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.

Nesta tese, apresentamos os resultados do estudo realizado para os modelos -não lineares com simetria O(N) bosônico ou supersimétrico assim como a adição do termo topológico de Wess-Zumino (teoria WZNW). Obtivemos as suas cargas conservadas não locais e a estrutura das álgebras clássicas de parênteses de Dirac correspondentes, utilizando um método gráfico que criamos para realizar estes cálculos nos modelos estudados. / In this thesis, we exhibit the results of the study made for the non linear models with O(N) symmetry, bosonic or supersymmetric as well as with the addition the topological Wess-Zumino term (WZNW theory). We found their non-local conserved charges and the structure of the corresponding c1assical algebras of Dirac brackets, using a graphical method that we created to make these calculations.

Warm inflation is an implementation of exponential early-universe expansion that incorporates interactions between the inflaton field and its environment. These interactions allow the inflaton to dissipate some of its energy into other fields, which may then thermalise and form a radiation bath. A radiation bath present throughout inflation changes the inflaton dynamics and introduces thermal fluctuations that enhance the spectrum of primordial density perturbations. In the models we consider, the inflaton decays into the light particles of the radiation bath via heavy mediator particles. Warm inflation is subject to a complicated set of constraints which typically requires a large number of such mediator fields to be included in the model. The motivation for this work was to use the parametric dependence of the full low-temperature dissipation coefficient to uncover regimes where this number can be reduced. Previous studies have examined primarily the low-momentum regime of the dissipation coefficient, where inflaton dissipation occurs via off-shell mediator particles. In the low-temperature regime, the production of on-shell mediators in the so-called pole regime suffers from Boltzmann suppression and was therefore thought to be negligible. It has been found, however, that the exponential suppression can be compensated by a sufficiently small effective coupling between the mediator fields and the light fields. In this thesis, we present a numerical code that scans the parameter space of warm-inflation models including both the low-momentum and the pole contribution to the dissipation coefficient. We generate random values for the parameters of the model and the initial conditions of the field and the radiation density; we then solve the full equations of motion for the radiation density and the inflaton field using the general low-temperature dissipation coefficient. Our search includes chaotic, hybrid, and hilltop models, each of which inhabits different regions of warm-inflation parameter space. Our main finding is that the pole contribution to inflaton dissipation significantly extends the parameter ranges accessible to warm inflation. Specifically, we can achieve 50 e-folds of inflation and a spectral index compatible with Planck data with fewer mediator fields and smaller coupling constants. For instance, while low-momentum-dominated dissipation typically requires O(10⁶) mediator fields, we find pole-dominated solutions with as few as O(10⁴) for the quadratic hilltop potential. It is clear that the inclusion of the pole contribution opens up interesting model-building possibilities and that the parametric dependence of the full dissipation coefficient holds promise for achieving even greater reductions of the field content.

Neste trabalho são apresentados alguns conceitos básicos da Teoria de Liouville e N=1 Super Liouville, enfatizando o cálculo das funções de três pontos dessas teorias.Uma introdução a Teoria de Campos Conformes (CFT) e a Supersimetria também sao incluídas, as quais constituem ferramentas básicas da presente pesquisa. / In this dissertation we present some basic features about Liouville and N=1 Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field Theories (CFT) and Supersymmetry, which are the basic tools of the present research.

Orientador: Abraham Hirsz Zimerman / Banca: Waldyr Alves Rodrigues Junior / Banca: Cesar Augusto Linhares / Banca: Juan Alberto Mignaco / Banca: Ruben Aldrovandi / Doutor