Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste tese, estudamos os efeitos não perturbativos associados à presença do horizonte de Gribov e à condensação de operadores locais de dimensão dois, numa teoria de Yang-Mills euclidiana em SU(2), quantizada no calibre abeliano maximal. Estes efeitos são introduzidos de modo a preservar as propriedades de renormalizabilidade e localidade da teoria, e refletem-se diretamente no comportamento dos propagadores. A comparação com os dados da rede indicam um bom acordo qualitativo. / In this, we study the nonperturbative effects associated to the presence of the horizon and to the condensation of local dimension two operators in an Eucledean SU(2)Yang-Mills theory quantized in the maximal Abelian gauge. Such effects are introduced in a way to preserve the properties of renormalizability and locality of the theory. The comparison with the lattice data indicates a good qualitative agreement.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste tese, estudamos os efeitos não perturbativos associados à presença do horizonte de Gribov e à condensação de operadores locais de dimensão dois, numa teoria de Yang-Mills euclidiana em SU(2), quantizada no calibre abeliano maximal. Estes efeitos são introduzidos de modo a preservar as propriedades de renormalizabilidade e localidade da teoria, e refletem-se diretamente no comportamento dos propagadores. A comparação com os dados da rede indicam um bom acordo qualitativo. / In this, we study the nonperturbative effects associated to the presence of the horizon and to the condensation of local dimension two operators in an Eucledean SU(2)Yang-Mills theory quantized in the maximal Abelian gauge. Such effects are introduced in a way to preserve the properties of renormalizability and locality of the theory. The comparison with the lattice data indicates a good qualitative agreement.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese estudamos uma extensão supersimétrica do mecanismo de Gribov no caso N = 1 em supercampos. Abordamos as teorias de super Yang-Mills em D = 4 e super Yang-Mills-Chern-Simons em D = 3. E verificamos como nestes casos o princípio de calibre leva ao cenário de confinamento de Gribov. / In this thesis we study a supersymmetric extension of the Gribov mechanism in the case of N = 1 with superfields. We approached the theories of super Yang-Mills in D = 4 and super Yang-Mills-Chern-Simons in D = 3. And we verify how in these cases the gauge principle leads to Gribov confinement scenario.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese estudamos uma extensão supersimétrica do mecanismo de Gribov no caso N = 1 em supercampos. Abordamos as teorias de super Yang-Mills em D = 4 e super Yang-Mills-Chern-Simons em D = 3. E verificamos como nestes casos o princípio de calibre leva ao cenário de confinamento de Gribov. / In this thesis we study a supersymmetric extension of the Gribov mechanism in the case of N = 1 with superfields. We approached the theories of super Yang-Mills in D = 4 and super Yang-Mills-Chern-Simons in D = 3. And we verify how in these cases the gauge principle leads to Gribov confinement scenario.

Le but de cette thèse est l'étude des fonctions de corrélation des théries Yang-Mills dans le régime infrarouge. Il est connu que, à cause de l'invariance jauge, il est nécessaire de fixer la jauge pour calculer des valeurs moyennes analytiquement. La procedure de fixation gauge standard est la procedure de Faddeev-Popov (FP). Le Lagrangien de FP permet de faire des calculs perturbatifs pour la Chromodynamique Quantique dans le régime de hautes énergies dont les résultats sont comparés avec succès avec des expériences. Cependant, dans le régime de basses énergies, il se trouve que la constante de couplage, calculée avec la procedure antérieure, diverge. En conséquence, la théorie des perturbations standard n'est plus valide. D'autre part, les simulations du réseau trouvent que la constante de couplage est finie avec une valeur modérée même dans le régime infrarouge. Ceci suggère qu'il devrait exister une manière de faire des calculs perturbatifs également dans le régime infrarouge. Cette différence dans la constante de couplage peut être due au fait que la procedure de FP n'est pas bien justifiée dans ce régime. Nous proposons de modifier le Lagrangien de FP avec un terme massif pour les gluons. Cette modification est également justifiée par le fait que le réseau trouve un propagateur du gluon qui paraît massive aux basses énergies. Nous utilisons cette version massive pour calculer à une boucle les fonctions de corrélations à deux et trois points pour une configuration cinématique générale et en dimension quelconque dans la jauge de Landau. On trouve que les comparaisons de notre calcul à une boucle avec les résultat du réseau donnent, en géneral, un très bon accord. / The aim of this thesis is to investigate the infrared behaviour of Yang-Mills correlation functions. It is known that the gauge invariance of the theory brings as a consequence the necessity of a gauge fixing procedure in order to compute expectation values analytically. The standard procedure for fixing the gauge is the Faddeev-Popov (FP) procedure which allows one to do perturbation theory in the ultraviolet regime. Perturbative calculations using the FP gauge fixed action successfully reproduce Quantum Chromodynamics observables measured by experiments in the ultraviolet regime. In the infrared regime the coupling constant of the theory computed with the above procedure diverges, and standard perturbation theory does not seem to be valid. However, lattice simulations show that the coupling constant takes finite and not very large value. This suggests that some kind of perturbative calculations should be valid even in the infrared regime. The theoretical justification for the FP procedure depends on the absence of Gribov copies and hence is not valid in the infrared regime (where such copies exist). To correct this we propose to add a mass term for the gluons in the gauge-fixed Lagrangian. The gluon mass term is also motivated by lattice simulations which observe that the gluon propagator behaves as it was massive in the infrared regime. We use this massive extension of the FP gauge fixed action to compute the one loop correction of the two- and three-point correlation functions in the Landau gauge for arbitrary kinematics and dimension. Our one-loop calculations are enough, in general, to reproduce with good accuracy the lattice data available in the literature.

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-04-19T21:37:57Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) phd_thesis_tomaz_final.pdf: 1515583 bytes, checksum: 3c2ee0e8efb867d63bf091191192405d (MD5) / Made available in DSpace on 2017-04-19T21:37:57Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) phd_thesis_tomaz_final.pdf: 1515583 bytes, checksum: 3c2ee0e8efb867d63bf091191192405d (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Construímos teorias de gravidade induzidas a partir de teorias de Yang-Mills para os grupos [fórmula]. No cerne destas construções empregamos um mecanismo que envolve a quebra dinâmica de simetria e a contração do grupo inicial. Através das equações de gap de massa a 1 e 2-laços, estimamos valores para o parâmetro de massa, o qual está envolvido no mecanismo. Este parâmetro, juntamente com parâmetro de acoplamento de Yang-Mills, determinam a constante gravitacional de Newton na teoria de gravidade induzida. Estimativas também foram realizadas para a constante cosmológica renormalizada da teoria, assim como para o corte na escala de energia, o qual consiste em um marcador para a transição entre os regimes ultravioleta e infravermelho da teoria. Estudamos também os aspectos clássicos da teoria de gravidade induzida, onde realizamos um estudo cosmológico preliminar e analisamos soluções esfericamente simétricas estáticas. Para o estudo cosmológico mostramos que uma fase de expansão acelerada pode ser obtida usando as equações de campo da teoria de gravidade induzida para o grupo SO(5). Mostramos também ser possível conectar as equações cosmológicas da presente teoria com as do modelo CDM. No caso das soluções esfericamente simétricas estáticas, demonstramos soluções para o grupo SO(5) perante dois regimes: (i) com alta in uência do termo quadrático de curvatura; (ii) tratando o termo quadrático de curvatura como uma perturbação. Usando tais soluções, perturbativa e exata, determinamos os horizontes de eventos e realizamos um breve estudo da temperatura e da entropia destes horizontes. / we built induced gravity theories from pure Yang-Mills theories for [formule]. In the kernel of these constructions, we have employed a mechanism that encodes the dynamical symmetry breaking and the contraction of the initial group. Through the mass gap equation at 1 and 2-loops, we have estimated numerical values for mass parameter related with the mechanism. This parameter, together with the Yang-Mills coupling parameter, determines the Newton's gravitational constant in the induced gravity theory. We also have provided estimates for the renormalized cosmological constant of the theory even as the cut-o in the energy scale, which consists in a landmark for the transition between the ultraviolet and infrared sectors of the theory. Furthermore, we have studied the classical aspects of the induced gravity, namely, a preliminary cosmological study and spherically symmetric static solutions. For the cosmological study, we have demonstrated that an accelerated phase of expansion can be obtained from the eld equations of the induced gravity theory for the SO(5) group. We also showed to be possible to connect the cosmological equations of the present theory of gravity with those from CDM model. In the case of spherically symmetric static solutions, we have found solutions for the induced gravity originated from the Yang-Mills theory for the SO(5) group under two regimes: (i) with high in uence of the quadratic term of curvature; (ii) dealing with the quadratic term of curvature as a perturbation. Using such solutions, perturbative and exact, we have calculated the event horizons and we briefly analyzed the thermodynamics associated with these horizons.

The present thesis is divided into two parts. Part I is devoted to the study of Gribov ambiguity in gauge systems and its relation with the appearance of degeneracies in the symplectic structure of the corresponding reduced phase space after gauge fixation. Part II is concerned with classical dual field theories for three-dimensional Einstein gravity and the symplectic structure on coadjoint orbits of the corresponding asymptotic symmetry group.In Part I, the Gribov problem is studied in the context of finite temperature QCD and the structure of the gluon propagator is analyzed. The standard confined scenario is found for low temperatures, while for high enough temperatures deconfinement takes place and a free gluon propagator is obtained. Subsequently, the relation between Gribov ambiguity and degeneracies in the symplectic structure of gauge systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems always leads to a degenerate symplectic form upon Dirac reduction. The implications for the Gribov-Zwanziger approach to QCD and the symplectic structure of the theory are discussed. In Part II, geometrical actions for three-dimensional Einstein gravity are constructed by studying the symplectic structure on coadjoint orbits of the asymptotic symmetry group. The geometrical action coming from the Kirillov-Kostant symplectic form on coadjoint orbits is analyzed thought Dirac's algorithm for constrained systems. By studying the case of centrally extended groups and semi-direct products, the symplectic structure on coadjoint orbits of the Virasoro and the BMS3 group are analyzed. This allows one to associate separate geometric actions to each coadjoint orbit of the solution space, leading to two-dimensional dual fiel theories for asymptotically AdS and asymptotically flat three-dimensional gravity respectively. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18789号 / 理博第4047号 / 新制||理||1582(附属図書館) / 31740 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 菅沼 秀夫, 教授 國廣 悌二, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

On étudie les théories de Yang-Mills. Pour ce faire, nous appliquons une nouvelle procédure de fixation de jauge qui vise à prendre en compte la présence des copies de Gribov. Ces copies correspondent à des solutions supplémentaires de la condition de jauge et ne sont pas prises en compte dans la procédure standard de Faddeev-Popov. Cette nouvelle procédure de fixation de jauge a d'abord été implémenté dans la jauge de Landau, où le régime de basse énergie a pu être étudié simplement par la théorie de perturbation et les propagateurs des gluons et des ghosts ont été trouvé en bon accord avec les résultats du réseau. Dans une première partie, nous appliquons cette procédure à une classe de jauges covariantes et non-linéaires (les jauges de Curci-Ferrari-Delbourgo-Jarvis). Nous montrons que ces jauges sont renormalisables en dimension quatre et donnons explicitement les expressions des constantes de renormalisation à une boucle. Nous calculons en théorie de perturbation les propagateurs de la théorie à l'ordre d'une boucle et implémentons le groupe de renormalisation. La seconde partie concerne l'étude du cas à température finie et de la transition de phase confinement-déconfinement. Nous travaillons dans une extention massive de la jauge de Landau-DeWitt. Nous calculons les propagateurs à une boucle et montrons qu'ils présentent de clairs signaux de la transition de phase à la différence de la jauge de Landau. / We investigate Yang-Mills theories. In particular, we follow a recently proposed new gauge-fixing procedure that aims at dealing with the presence of the so-called Gribov copies. These copies correspond to additional solutions to the gauge equation that are disregarded in the standard Faddeev-Popov procedure. This novel gauge-fixing approach was first implemented in the Landau gauge, where the low momentum regime was investigable by means of simple perturbation theory and the one-loop gluon and ghost propagators were found in good agreement with lattice results. In a first part, we extend this proposal to a class of nonlinear covariant (the Curci-Ferrari-Delbourgo-Jarvis) gauges . We prove that these gauges are renormalizable in four dimensions. We provide explicit expression of the renormalization constants at one-loop order. Then we compute the various propagators of the theory at one-loop order with and without renormalization group improvement. The second part of the thesis concerns the finite temperature case and in particular the study of the confinement-deconfinement phase transition. We work in the Landau-DeWitt gauge (a background extention of the Landau gauge) which allows for an explicit presence of an order parameter of the phase transition. This gauge is implemented following the previous gauge-fixing procedure. In particular it has been shown that the phase transition can be studied in perturbation theory. Here, we compute at one-loop order the gluon and ghost propagators (for SU(2) gauge group) and show that they display strong signals of the phase transition. This is to be put in regards with the results obtained for the Landau gauge propagators.