When calculating scattering processes in theories involving massless gauge bosons, such as gluons in Quantum Chromodynamics (QCD), one encounters infrared (IR), or soft, divergences. To obtain precise predictions, it is important to have exact expressions for these IR divergences, which are present in any on-shell scattering amplitude. Due to their long wavelength, soft gluons factorise with respect to short-distance, or hard, interactions and can be captured by correlators of semi-infinite Wilson lines. The latter obey a renormalisation group equation, which gives rise to exponentiation. The exponent can be represented diagrammatically in terms of weighted sums of Feynman diagrams, called webs. A web with L external legs, each with ni gluon attachments, is denoted (n1; n2; : : : ; nL). In this way all soft gluon interactions can be described by a soft anomalous dimension. It is currently known at three loops with lightlike kinematics, and at two loops with general kinematics. Our work is a step towards a three-loop result in general kinematics. In recent years, much progress has been made in understanding the general physical properties of scattering amplitudes and in exploiting these properties to calculate specific amplitudes. At the same time, we have discovered a lot of structure underpinning the space of multiple polylogarithms, the functions in terms of which most known amplitudes can be written. General properties include analyticity, implying that scattering amplitudes are analytic functions except on certain branch cuts, and unitarity, or conservation of probability. These two properties are both exploited by unitarity cuts. Unitarity cuts provide a diagrammatic way of calculating the discontinuities of a Feynman diagram across its branch cuts, which is often simpler than calculating the diagram itself. From this discontinuity, the original function can be reconstructed by performing a dispersive integral. In this work, we extend the formalism of unitarity cuts to incorporate diagrams involving Wilson-line propagators, where the inverse propagator is linear in the loop momenta, rather than the quadratic case which has been studied before. To exploit this for the calculation of the soft anomalous dimension, we first found a suitable momentum-space IR regulator and corresponding prescription, and then derived the appropriate largest time equation (LTE). We find that, as in the case of the scalar diagrams, most terms contributing to the LTE turn out to be zero, albeit for different reasons. This simplifies calculations considerably. This formalism is then applied to the calculation of webs with non-lightlike Wilson lines. As a test, we first looked at webs that have been previously studied using other methods. It emerges that, when using the correct variables, the dispersive integrals one encounters here are trivial, illustrating why unitarity cuts are a particularly useful tool for the calculation of webs. We observe that our technique is especially efficient when looking at diagrams involving three-gluon vertices, such as the (1; 1; 1) web and the Y diagram between two lines. We then focus on three-loop diagrams connecting three or four external non-lightlike lines and involving a three-gluon vertex. We calculate the previously unknown three-loop three-leg (1; 1; 3) web in general kinematics. We obtain a result which agrees with the recently calculated lightlike limit. We also develop a technique to test our results numerically using the computer program SecDec, and we find agreement with our analytical result. The result for the (1; 1; 3) web can then be exploited to gain insight into the more complicated three-loop four-leg (1; 1; 1; 2) web. Indeed, the (1; 1; 1; 2) web reduces to the (1; 1; 3) web in a certain collinear limit. We propose an ansatz for the (1; 1; 1; 2) web in general kinematics, based on a conjectured basis of multiple polylogarithms. The result for the (1; 1; 3) web, together with the known result for the lightlike limit of the (1; 1; 1; 2) web, imposes strong constraints on the ansatz. Using these constraints, we manage to fix all but four coefficients in the ansatz. We fit the remaining coefficients numerically, but find that the quality of the fit is not good. We find possible explanations for this poor quality. This calculation is still a work in progress. Our results provide a major step towards the full calculation of the three-loop soft anomalous dimension for non-lightlike Wilson lines. We calculated new results for three-loop webs, and also deepened the understanding of webs in general. We confirm a conjecture about the functional dependence of the soft anomalous dimension on the cusp angles. We also confirm earlier findings about the symbol alphabet of the relevant functions. This confirms the remarkable simplicity found earlier in the expressions for the soft anomalous dimension.

Numerical Stochastic Perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice quantum field theory. The standard algorithm based on the Langevin equation, however, suffers from several limitations which in practice restrict the potential of this technique: first of all it is not exact, a sequence of simulations with finer and finer discretization of the relevant equations have to be performed in order to extrapolate away the systematic errors in the results; and, secondly, the numerical simulations suffer from critical slowing down as the continuum limit of the theory is approached. In this thesis I investigate some alternative methods which improve upon the standard approach. In particular, I present a formulation of Numerical Stochastic Perturbation theory based on the Generalised Hybrid Molecular Dynamics algorithm and a study of the recently proposed Instantaneous Stochastic Perturbation Theory. The viability of these methods is investigated in φ4 theory.

This thesis is divided into two parts. The first part concerns the study of the ambitwistor string and the scattering equations, while the second concerns the interplay of the symmetries of the asymptotic null boundary of Minkowski space, called [scri], and scattering amplitudes. The first part begins with a review of the CHY formulas for scattering amplitudes, the scattering equations and the ambitwistor string including its pure spinor version. Next are the results of this thesis concerning these topics, they are: generalizing the ambitwistor model to higher genus surfaces; calculating the one-loop NS-NS scattering amplitudes and studying their modular and factorization properties; deriving the one-loop scattering equations and analyzing their factorization; showing that, in the case of the four graviton amplitude, the ambitwistor amplitude gives the expected kinematical prefactor; matching this amplitude to the field theory expectation in a particular kinematical regime; solving the one loop scattering equations in this kinematical regime; a conjecture for the IR behaviour of the one-loop ambitwistor integrand; computing the four graviton, two-loop amplitude using pure spinors; showing that this two-loop amplitude has the correct kinematical prefactor and factorizes as expected for a field theory amplitude; generalizing the ambitwistor string to curved backgrounds; obtaining the field equations for type II supergravity as anomaly cancellation on the worldsheet; generalizing the scattering equations for curved backgrounds. The second part begins with a review of the definition of the null asymptotic boundary of four dimensional Minkowski space, its symmetry algebra, and their relation to soft particles in the S-matrix. Next are the results of this thesis concerning these topics, they are: constructing two models consisting of maps from a worldsheet to [scri], one containing the spectrum of N=8 supergravity, and the other the spectrum of N=4 super Yang-Mills; showing how certain correlators in these theories calculate the tree-level S-matrix of N=8 sugra and N=4 sYM respectively; defining worldsheet charges which encode the action of the appropriate asymptotic symmetry algebra and showing that their Ward-identities recover the soft graviton, and soft gluon factors; defining worldsheet charges for proposed extensions of these symmetry algebras and showing that their Ward-identities give the subleading soft graviton and subleading soft gluon factors.

MENDES, Wendel Macedo. Localização de Férmions em D dimensões. 2013. 55 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2013. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-23T19:20:31Z No. of bitstreams: 1 2013_dis_wmmendes.pdf: 369040 bytes, checksum: cd60b4ab7c07a63351d2b9dd5a277139 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-23T19:38:03Z (GMT) No. of bitstreams: 1 2013_dis_wmmendes.pdf: 369040 bytes, checksum: cd60b4ab7c07a63351d2b9dd5a277139 (MD5) / Made available in DSpace on 2015-10-23T19:38:03Z (GMT). No. of bitstreams: 1 2013_dis_wmmendes.pdf: 369040 bytes, checksum: cd60b4ab7c07a63351d2b9dd5a277139 (MD5) Previous issue date: 2013 / In this work we analyzed the localization of fermions of spin-1/2 in a D-dimensional bulk in a (D-2)-branes scenario. The model used for this is a dimensional extension of models Randall-Sundrum (RS) and thick branes. It is known as co-dimension 1 model. The obtained results are based in no-factorizable geometry type Anti-de Sitter. During the zero mode localization process, it is uses both the Randall-Sundrum metric as a metric with smooth warped factor that depends on the coordinate of extra dimension, frequently used in thick brane models. As the spin-1/2 representations change with dimension of spacetime, the localization process, somehow, must take into account the dimensionality of bulk. Based on these models, one finds that the localization fermions in (D-2)-branes changes when the spacetime is par or odd. They are not located when the dimensionality of bulk is par an only one of chiralities can be located when D is odd. / Nesse trabalho é analizado a localização de férmions de spin 1/2 em um bulk D-dimensional em um cenário de (D-2)-branas. O modelo usado para tal é uma extensão para mais dimesões dos modelos Randall-Sundrum (RS) e de brana espessa. Ele é conhecido como modelo de codimensão 1. Os resultados obtidos são fundamentados em uma geometria não-fatorizável do tipo Anti-de Sitter. Durante o processo de localização do modo zero, usa-se tanto a métrica de Randall-Sundrum como uma métrica com fator de dobra suave que depende da coordenada da dimensão extra, frequentemente usada nos modelos de brana espessa. As representações de spin 1/2 variam com a dimensão do espaço-tempo, então o processo de localização deve levar em conta a dimensionalidade do bulk. Baseados nesses modelos, descobre-se que a localização de férmions em (D-2)-branas muda quando o espaço-tempo é par ou ímpar. Eles não são localizados quando a dimensionalidadedo bulk é par e somente uma das quiralidades pode ser localizada quando D é ímpar.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / O objetivo desta dissertação é apresentar uma conexão entre a condição de Gribov-Zwanziger para o gap de massa e o mecanismo de quebra espontânea de simetria, através do estudo de um operador composto introduzido numa maneira localizada. Para tornar esta relação mais clara, um modelo é apresentado e alguns aspectos quânticos são discutidos. / The aim of this work is to present a connection between the Gribov-Zwanziger condition for the mass gap and the spontaneous symmetry breaking mechanism, by studying a composite operator introduced in a localized form. In order to clarify these relationship a toy model is presented and some quantum aspects are discussed.

Nós estudamos a competição entre a instabilidade de Pomeranchuk no canal de spin com momento angular l=1 e uma interação atrativa, favorecendo a formação de um par de Cooper. Achamos, numa aproximação de campo médio, uma forte supressão da instabilidade de Pomeranchuk via supercondutividade. Além disso, identificamos uma fase supercondutora metaestável com características semelhantes ao estado FFLO. Um líquido de Fermi é, com exceção de uma dimensão, um estado muito estável da matéria. Por outro lado dois tipos de instabilidades, relacionadas com interações atrativas, são conhecidas: Instabilidades Pomeranchuk e supercondutora. As instabilidades Pomeranchuk ocorrem na presença da interação de dois corpos contendo uma forte componente atrativa no canal de espalhamento para frente com momento angular definido. No contexto da teoria de Landau, a instabilidade ocorre quando um ou mais parâmetros admensionais de Landau nos canais de spin ou carga, adquirem altos valores negativos. As instabilidades Pomeranchuk no setor de carga quebram a simetria de rotação. Em particular, uma instabilidade em alguns canais produz uma deformação elipsoidal na superfície de Fermi. / We study the competition between a Pomeranchuk instability in the spin channel with angular momentum l = 1 and an attractive interaction, favoring Cooper pair formation. We find, at mean-field approximation, that superconductivity strongly suppress the Pomeranchuk instability. Moreover, we have found a metastable modulated superconducting phase with similar characteristics of the FFLO state. A Fermi liquid is, except in one dimension, a very stable state of matter. At least two types of instabilities, related with attractive interactions, are known: Pomeranchuk and superconducting instabilities. Pomeranchuk instabilities occur in the presence of two-body interactions containing a strong attractive component in the forward scattering channel with a definite angular momentum. In the context of Landau theory, the instability sets in when one or more dimensionless Landau parameters in the charge or spin channel, acquire large negative values. Pomeranchuk instabilities in a charge sector spontaneously break rotational symmetry. In particular, an instability in the some channels produces an ellipsoidal deformation of the Fermi surface.

Made available in DSpace on 2014-06-11T19:25:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-11-10Bitstream added on 2014-06-13T18:28:53Z : No. of bitstreams: 1 ried_k_me_ift.pdf: 945643 bytes, checksum: 96fe05a885b68fc97682e8238f4ecf2c (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / When seeking inspiration for a future theory of quantum gravity, studying black holes is a promising ansatz, since they present us with several puzzles at the intersection of quantum theory and gravity. Among these is their entropy: although there are compelling arguments for its existence, its origin and statistical meaning remain a mystery. Previous work showed that at least some aspects of this phenomenon can be accounted for by the entanglement of quantum fields across the horizon: if a field is globally in a pure state, yet part of it is hidden behind the event horizon, then the reduced state of the remainder possesses non-zero entropy. This is the possibility we explore in the present work, in the simplest of settings: a ground-state escalar field, defined in three-dimensional, flat or unifromily curved space, and derive an expression for the entropy, which is evauated numerically. the results show that the entropy scales with the boundary area of the inaccessible region, a key feature of black hole entropy known as the area law. Furthermore. we conclude that the dominant contribution to the entropy is due to short-range interactions, and discuss some physical implications of this insight for the puzzle of black hole entropy

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-03Bitstream added on 2014-06-13T20:33:11Z : No. of bitstreams: 1 maia_cas_me_ift.pdf: 968895 bytes, checksum: 0a94d217b227cfdce0aee0d507acf35f (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Sabe-se já há algum tempo que a Teoria Quântica de Campos permite violações das Condições Clássicas de Energia na forma de densidades e fluxos de energia negativa. Um exemplo contundente é o efeito Casimir, onde o estado de vácuo do campo eletromagnético entre duas placas metálicas possui densidade de energia negativa. Porém, se as leis da física não colocassem restrições sobre tais violações das Condições de Energia, aparentemente seria possível usar energias negativas para, por exemplo, produzir violações macroscópicas da segunda lei da termodinâmica, da conjectura de cosmic censorship, além de se proporcionar a criação de wormholes e possíveis máquinas do tempo. Uma linha de pesquisa desenvolvida para abordar essa questão envolve as chamadas Desigualdades Quânticas, estudadas primeiramente por L.H. Ford, que são desigualdades sobre fluxos e densidades de energia negativa que impõem restrições capazes de tornar as violações acima não observáveis macroscopicamente. Nesta dissertação apresentaremos alguns exemplos de sistemas que possuem densidades ou fluxos de energia negativa, revisaremos os teoremas de Desigualdades Quânticas e discutiremos algumas de suas aplicações. Discutiremos também algumas limitações destes teoremas apresentando sistemas que não estão sujeitos a desigualdades quânticas, dos quais um exemplo é o próprio efeito Casimir. Iremos enfim propor um modelo que introduz flutuações quânticas nas condições de contorno (e.g., nas placas metálicas) do efeito Casimir, e iremos mostrar que a introdução destes efeitos de flutuação no cálculo da energia de Casimir tem por resultado impedir que violações de leis físicas macroscópicas manifeste-se nesse sistema. / Abstracts: It has been known for some time that Quantum Field Theory allows the violation of Classical Energy Conditions in the form of negative energy densities and fluxes. A remarkable exemple is the Casimir effect, where the vacuum state of the electromagnetic field between two perfectly conducting parallel plates presents negative energy density. However, if he laws of physics did not place constraints on such a violation of the Energy Conditions, it appears that it would be possible to use negative energies for producing, for example, macroscopic violation of the second law of thermodynamics, of the cosmic censorship conjecture, and also provide the creation of woemholes and time machines. A line of research wich was developed to approach this question is the so called Quantum Inequalities, first studied by L.H. Ford, which are constraints over negative energy densities and fluxes with capacity to render the above violations macroscopically unobservable. We present here some examples of systems with negative energy densities or fluxes, review the Quantum Inequalities theorems and discuss some of its applications. We also discuss some limitations of these theorems showing systems where there are no quantum inequalities, being the Casimir effect one example. At last we propose a model which introduces quantum fluctuations in the description of the boundaries conditions (e.g., the conducting plates) of Casimir effect and we'll show that the introduction of these fluctuations in the calculation of Casimir energy results in the impossibility of violation of macroscopic physical laws using Casimir configuration.

Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-06-13Bitstream added on 2014-06-13T19:53:28Z : No. of bitstreams: 1 leme_rr_me_ift.pdf: 924435 bytes, checksum: 92fdbfbe29ac1970f3d28a01d822ca6c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho apresentamos resultados de simulações de Monte Carlo de uma teoria quântica de campos escalar com autointeração ´fi POT. 4' em uma rede (1+1) empregando o recentemente proposto algoritmo worm. Em simulações de Monte Carlo, a eficiência de um algoritmo é medida em termos de um expoente dinâmico 'zeta', que se relaciona com o tempo de autocorrelação 'tau' entre as medidas de acordo com a relação 'tau' 'alfa' 'L POT. zeta', onde L é o comprimento da rede. O tempo de autocorrelação fornece uma medida para a “memória” do processo de atualização de uma simulação de Monte Carlo. O algoritmo worm possui um 'zeta' comparável aos obtidos com os eficientes algoritmos do tipo cluster, entretanto utiliza apenas processos de atualização locais. Apresentamos resultados para observáveis em função dos parâmetros não renormalizados do modelo 'lâmbda' e 'mü POT. 2'. Particular atenção é dedicada ao valor esperado no vácuo < 'fi'('qui')> e a função de correlação de dois pontos <'fi'('qui')'fi'('qui' POT. 1')>. Determinamos a linha crítica ( ´lâmbda IND. C', 'mu IND C POT. 2') que separa a fase simétrica e com quebra espontânea de simetria e comparamos os resultados com a literatura / In this work we will present results of Monte Carlo simulations of the ´fi POT. 4'quantum field theory on a (1 + 1) lattice employing the recently-proposed worm algorithm. In Monte Carlo simulations, the efficiency of an algorithm is measured in terms of a dynamical critical exponent 'zeta', that is related with the autocorrelation time 'tau' of measurements as 'tau' 'alfa' 'L POT. zeta', where L is the lattice length. The autocorrelation time provides a measure of the “memory” of the Monte Carlo updating process. The worm algorithm has a 'zeta' comparable with the ones obtained with the efficient cluster algorithms, but uses local updates only. We present results for observables as functions of the unrenormalized parameters of the theory 'lâmbda and 'mü POT. 2'. Particular attention is devoted to the vacuum expectation value < 'fi'('qui')> and the two-point correlation function <'fi'('qui')fi(qui pot. 1')>. We determine the critical line( ´lâmbda IND. C', 'mu IND C POT. 2') that separates the symmetric and spontaneously-broken phases and compare with results of the literature

Made available in DSpace on 2014-06-11T19:32:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-07-26Bitstream added on 2014-06-13T19:21:25Z : No. of bitstreams: 1 chumbes_aer_dr_guara.pdf: 1041702 bytes, checksum: 47a1578e891ec7863ecc69ecabd574b7 (MD5) / Nesta tese analisamos a localização de campo de matéria em bramas duplas. Estudamos a localização de férmions não-massivos em paredes de domnio (3-brana) imersa no espaço de 4+1 dimensões em cenários Randall-Sundrum (espaço warped), e Rubakov-Shaposhnikov (espaço plano), respectivamente. Abordamos a localização do campo fermiônico, acoplando os férmions com uma função de campo escalar, cuja solução tipo kink simples é deformada a uma solução tipo kink duplo. No contexto de nosso estudo, este tipo de configuração kink duplo permite ilustrar o fenômeno da separação das branas. Construímos novos modelos não-lineares em teoria de campos que forneçam configurações do tipo kink duplo. Estes modelos são construídos a partir da deformação do modo-zero associado `a equação de estabilidade de outros modelos bem estabelecidos. Por sua vez, estes modelos são aplicáveis na descrição de fenômenos críticos e em cenários de mundos-brana. Além disso, temos conhecimento de que não ´e possível a localiza¸c˜ao de campo de gauge por meio unicamente da curvatura (warped). Propomos um mecanismo que leve à localização do modo-zero do campo de gauge abeliano em branas espessas por meio de uma função suave e contínua que torna a ação normalizável. Esta função suave funcionaria como uma função dielétrica. Neste mesmo contexto, aplicamos este mecanismo para a localização do modo-zero do campo de Kalb-Ramond em branas espessas / In this thesis we analyze the localization of matter field in double branes. We study the localization of massless fermions in domain wall (3-branes) immerse in a space 4+1 dimensions in Randall-Sundrum (warped space), and Rubakov-Shaposhnikov (flat space) scenarios, respectively. We approach the fermions localization, coupling the fermions to a scalar field functional, whose kink-like solutions are deformed to double kink solutions. In the context of our study, this double kink (two-kink) allows to illustrate the brane splitting phenomenon. We construct new non-linear models in field theory which provides double kink configurations. These models are constructed from the deformation of the zero mode associated to the stability equations of well-established models. In turn, these models are applicable in the description of critical phenomena and brane-worlds scenarios. Moreover, we know that it is not possible to achieve gauge fields localization on brane by means of only the warped curvature. We propose a mechanism that leads to the localization of zero mode of Abelian gauge field in thick branes by means of a smooth and continuous function which turns out the action normalizable. This smooth function would work as a dielectric function. In this same context we apply this mechanism for the localization of zero mode of Kalb-Ramond field in thick branes