Orientador: Marcos Benevenuto Jardim / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T09:35:57Z (GMT). No. of bitstreams: 1 GonzalesGargate_MichaelSantos_D.pdf: 3866863 bytes, checksum: 1c42833ca2903ade2f3da9409a389b93 (MD5) Previous issue date: 2014 / Resumo: Nesta tese estudamos o conjunto singular de feixes instanton sobre o espaco projetivo P^3. Um dos resultados principais mostra que o conjunto singular de um feixe instanton não localmente livre de posto 2 tem dimensão pura 1, e que o duplo dual E** e um feixe instanton localmente livre (Teorema 3.1.5). Ambos enunciados são falsos quando o posto de E e maior que 2. Também consideramos os feixes S_E = Ext^1(E;O_P^3) e Q_E = E**/E. Se E e feixe instanton não localmente livre de posto 2 em P3, mostramos que S_E e Q_E sâo feixes instanton de posto 0, conforme de nicão introduzida por Hauzer e Langer em [10]. Alem disso, mostramos que S_E e Q_E são suportados no conjunto singular Sing(E) e possuem o mesmo polinômio de Hilbert (Seções 3.1.2 e 3.1.3). Finalmente, apresentamos algumas propriedades do conjunto singular. Garantimos que o conjunto singular esta contido em uma curva de interseção completa de grau c^2, onde c = c_2(E) e chamada a carga de E (Proposição 3.2.1). Por outro lado, baseado na noção de transformações elementares para instantons dada por Jardim, Markushevich e Tikhomirov em [16], constuímos um exemplo de feixe instanton de posto 2 cujo conjunto conjunto singular não e conexo (Seção 3.2.3). Fornecemos tambem exemplos de feixes instantons de posto 3 cujo conjunto singular consiste de um ponto, e um ponto e uma reta / Abstract: In this thesis we study the singular locus of instanton sheaves on the projective space P^3. We prove that the singular locus Sing(E) of a non-locally free instanton sheaf E of rank 2 has pure dimension 1, and that the double dual E** is a locally free instanton sheaf (Theorem 3.1.5). Both statements are false if the rank of E is larger than 2. We also consider the sheaves S_E = Ext^1(E;OP3) and Q_E = E**/E. When E is a non-locally free instanton sheaf of rank 2, we show that S_E and Q_E are rank 0 instantons, according to a de nition of Hauzer and Langer in [10]. In addition, we show that both are supported the singular locus Sing(E) and have the same Hilbert polynomial (Sections 3.1.2 and 3.1.3). Finally, we present some properties of the singular locus. We guarantee that the singular locus is contained in a complete intersection curve of degree c_2, where c=c_2(E) is called the charge of E (Proposition 3.2.1). Moreover, based on the notion of elementary transformations for instantons given by Jardim, Markushevich and Tikhomirov in [16], we construct an example of a rank 2 instanton sheaf whose singular locus is not connected (Section 3.2.3). We also provide examples of rank 3 instanton sheaves whose singular loci are a single point, and a straight line plus a point / Doutorado / Matematica / Doutor em Matemática

Like other field theories of physical interest, the moduli-space integrals of the non-linear two-dimensional 0(3) sigma model diverge. We show that in the one-instanton sector the imposition of a cut-off in the moduli-space leads to an unacceptable dependence of the Green’s function on the way that the field is split into the quantum piece and the classical background. This dependence may be isolated in a term which may be interpreted as an anomaly to the Ward Identity of the theory. The moduli-space divergence is associated with degeneration of the field configurations to those of another topological sector. Hence it is possible that by modifying the Green’s function in, say, the zero-instanton sector will be able to cancel the divergence in the one- instanton sector. We show that the Ward Identity anomaly in the one-instanton sector may be written in the zero-instanton sector at next to leading order in powers of h, and hence we explicitly calculate the Green's function modification. We have called the process of applying this modification "Topological Renormalisation". A central piece of the modification term is the instanton contribution to the Green's function of the model. This is obtained by using two new methods of calculating the determinant of the fluctuation operator. The application of Topological Renormalisation to other theories is also investigated.

No description available.

Thèse doctorat : Mathématiques et applications : Nantes : 2007. / Bibliographie pp.143-145.

This thesis is concerned with so-called higher derivative terms which arise in low energy approximations to certain physical models. In particular, the aim is to investigate the role that such terms play in low energy N=2 supersymmetric gauge theories in 4 dimensions, with gauge group SU(2).Chapter one serves as an introduction to the notions of supersymmetry and superfields. The problem of constructing an effective action which describes the low energy dynamics is introduced, and the construction of the Wilsonian action in terms of light and heavy modes is developed. The concept on a derivative expansion is also described. Chapter two introduces N=2 supersymmetric gauge theories with spontaneous symmetry breaking. It is observed that such systems always have a Bogomolnyi bound, and the consequences are discussed. We then develop a derivative expansion of this system in terms of N=2 superfields, drawing particular attention to the next-to- leading order derivative term (that is, those with 4 derivatives/8 fermions). The duality properties of such a term are reviewed, and their impact on the mass formula discussed. Conclusions are drawn as to their influence on the results of Seiberg and Witten. Chapter three deals with a non-renormalisation theorem for the next-to-leading order higher derivative term proposed by Dine and Seiberg. This states that instanton contributions to such a term in massless N=2 SU(N(_c)) gauge theories vanish when the number of flavours N(_f) = 2N(_c). We prove this result using the ADHM formalism for multi-instantons in the case N(_c) = 2.

Orientador: Marcio Antonio de Faria Rosa / Dissertação (mestrado) - Universidade estadual de Campinas, Instituto de Fisica "Gleb Wataghin" / Made available in DSpace on 2018-09-24T17:49:07Z (GMT). No. of bitstreams: 1 Terra-Cunha_MarcelodeOliveira_M.pdf: 1190931 bytes, checksum: 3a5888d43c5ea59564f037a1cd77a9ed (MD5) Previous issue date: 1997 / Resumo: Introduzimos a Teoria de Yang & Mills clássica com um enfoque geométrico. Vários argumentos são apresentados em favor da "realidade física" dos potenciais, mesmo no nível clássico. Especializamos para o caso do grupo SU(2) sobre espaço-tempo euclideano. Definimos os Instantons desta teoria e apresentamos um método para sua obtenção. Como subsídio ao leitor, apresentamos o conceito de Homotopia, incluindo as sequências exatas de fibração e alguns resultados da homotopia das esferas. Apresentamos a construção de [Rigas] de representantes de S3-fibrados sobre S4, que mostramos ser o ambiente matemático natural das soluções instantônicas desta teoria. Finalmente, adaptamos tal construção e apresentamos um novo método de construção do instanton e do anti-instanton fundamentais e apresentamos caminhos que podem levar à generalização deste método / Abstract: Classical Yang & Mills Theory is presented from a geometrical viewpoint. Many arguments leading to the "physical reality" of Yang & Mills potentials are given. Further, we specialize to SU(2) Lie group theory over Euclidean space-time. Instantons of this theory are defined and a way to compute them is shown. It is also given an introduction to Homotopy theory, starting from the very basic concepts and leading to exact sequences of fiber spaces and to some important results about the homotopy of spheres. The construction of S3-bundles over S4 representants given in [Rigas] is presented. Such mathematical objects are shown to be the natural place of instanton solutions of this theory. We adapt this construction and show how to find the fundamental instanton and anti-instanton solutions and also we give some possible ways to obtain the generalizations of this result to find multi-instantons / Mestrado / Física / Mestre em Física

Résumé anglais: This thesis consists of an introductory text followed by two separate parts which may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of spacelike singularities (the BKL-limit). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be mapped to an auxiliary problem given in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of gravity. We investigate the modification of the billiard dynamics when the original gravitational theory is formulated on a compact spatial manifold of arbitrary topology, revealing fascinating mathematical structures known as galleries. We further use the conjectured hyperbolic symmetry E10 to generate and classify certain cosmological (S-brane) solutions in eleven-dimensional supergravity. Finally, we show in detail that eleven-dimensional supergravity and massive type IIA supergravity are dynamically unified within the framework of a geodesic sigma model for a particle moving on the infinite-dimensional coset space E10/K(E10). Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are typically given by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by moduli-dependent functions which are manifestly invariant under G(Z), known as automorphic forms. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on a special class of functions known as (non-holomorphic) Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also discuss the possibility that certain generalized Eisenstein series, which are covariant under the maximal compact subgroup K(G), could play a role in determining the exact effective action for toroidally compactified higher derivative corrections. Finally, we propose that in the case of rigid Calabi-Yau compactifications in type IIA string theory, the exact universal hypermultiplet moduli space exhibits a quantum duality group given by the emph{Picard modular group} SU(2,1;Z[i]). To verify this proposal we construct an SU(2,1;Z[i])-invariant Eisenstein series, and we present preliminary results for its Fourier expansion which reveals the expected contributions from D2-brane and NS5-brane instantons. / Résumé francais: Cette thèse est composée d'une introduction suivie de deux parties qui peuvent être lues indépendemment. Dans la première partie, nous analysons des structures hyperboliques apparaissant dans l'étude de la gravité au voisinage d'une singularité de type espace (la limite BKL). Dans cette limite, les points spatiaux se découplent et la dynamique suit un comportement ultralocal qui peut être reformulé en termes d'un billiard hyperbolique (qui peut être chaotique). Dans toutes les supergravités qui sont des limites de basse énergie de théories de cordes ou de la théorie M, la dynamique du billiard prend place à l'intérieur des chambres de Weyl fondamentales de certaines algèbres de Kac-Moody hyperboliques, ce qui suggère que ces algèbres correspondent à des symétries cachées de dimension infinie de la gravité. Nous examinons comment la dynamique du billard est modifiée quand la théorie de gravité originale est formulée sur une variété spatiale compacte de topologie arbitraire, révélant ainsi de fascinantes structures mathématiques appelées galleries. De plus, dans le cadre de la supergravité à onze dimensions, nous utilisons la symétrie hyperbolique conjecturée E10 pour engendrer et classifier certaines solutions cosmologiques (S-branes). Finalement, nous montrons en détail que la supergravité à onze dimensions et la supergravité de type IIA massive sont dynamiquement unifiées dans le contexte d'un modèle sigma géodesique pour une particule se déplaçant sur l'espace quotient de dimension infinie E10/K(E10). La deuxième partie de cette thèse est consacrée à étudier comment les dualités U en théorie des cordes fournissent des contraintes puissantes sur les corrections quantiques perturbatives et non perturbatives. Ces dualités sont typiquement données par des groupes arithmétiques G(Z) dont il est conjecturé qu'ils préservent l'action effective. Les couplages exacts sont donnés par des fonctions des moduli qui sont manifestement invariantes sous G(Z), et qu'on appelle des formes automorphiques. Nous discutons en détail différentes méthodes de construction de ces formes automorphiques, en insistant particulièrement sur une classe spéciale de fonctions appelées séries d'Eisenstein (non holomorphiques). Nous présentons comme exemples les cas de SL(2,Z) et SL(3,Z), qui sont physiquement pertinents. Nous construisons les séries d'Eisenstein correspondantes et leurs expansions de Fourier (non abéliennes). Nous discutons également la possibilité que certaines séries d'Eisenstein généralisées, qui sont covariantes sous le sous-groupe compact maximal, pourraient jouer un rôle dans la détermination des actions effectives exactes pour les théories incluant des corrections de dérivées supérieures compactifiées sur des tores.

Orientador: Marcio Antonio de Faria Rosa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-23T09:34:22Z (GMT). No. of bitstreams: 1 Motter_AdilsonEnio_M.pdf: 1951510 bytes, checksum: a577fce684e8889e9bd14309b99f844c (MD5) Previous issue date: 1998 / Resumo: A dissertação consiste essencialmente do estudo de casos particulares de Análise de Clifford. Inicialmente revisamos a Análise Quaterniônica de Fueter comparando com abordagens alternativas e, neste contexto, pesquisamos uma aplicação das correspondentes relações de dispersão em fenomenologia de partículas elementares. Empregando a mesma sistemática investigamos a teoria de funções resultante no caso da álgebra não divisora dos biquatérnios, onde os principais resultados dizem respeito à formulação rigorosa da Fórmula Integral e a relações com o eletromagnetismo. Situamos estes e outros casos no escopo das Análises de Clifford, chamando a atenção para aspectos de caráter geral. Tendo em vista os vínculos algébricos entre quatérnios e Instantons da Teoria de YangMills SU(2), chamamos a atenção, também, para relações analíticas entre os Instantons e a teoria de Fueter. / Abstract: This thesis reíers essentially to the study oí particular cases oí Clifford analysis. First we review Fueter's quaternionic analysis and compare it with alternative theories. In this context we have inquired a possible application oí the corresponding dispersion relations in íenomenology oí elementary particles. Making use oí the the same approach, we have investigated the íunction theory resulting in the case oí the non-division biquaternion algebra. Concerning that. the most important results are the rigorous íormulation oí the Integral Formula and the relations with eletromagnetism. We have situated these and others cases in the picture oí the Clifford analysis, paying attention to general íeatures. Mindíul oí the algebraic links between quaternions and Instantons oí the SU(2) YangMills Theory, we call attention again to analytical relations between Instantons and the Fueter's theory. / Mestrado / Mestre em Matemática Aplicada

Orientador: Ricardo Antonio Mosna / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-24T14:09:39Z (GMT). No. of bitstreams: 1 Tavares_GustavoMarques_M.pdf: 695474 bytes, checksum: c437bafa3afb0c0768437e1a139eea12 (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estudamos os instantons da teoria de Yang-Mills nos espaços de Schwarzs-child e de Reissner-Nordstrom com grupo de gauge SU(2).Instantons são soluções clássicas da teoria de Yang-Mills definida em um espaço com métrica riemanniana (positiva-definida) e com ação finita. Primeiramente revisamos a formulação geométrica da teoria de Yang-Mills em uma variedade 4-dimensional,identificando os campos de gauge com conexões em um fibrado principal. Em seguida apresentamos os principais resultados clássicos relacionados aos instantons no espaço plano. Na segunda parte da dissertação realizamos um estudo sistemático das soluções da teoria de Yang-Mills nos espaços de Schwarzschild e de Reissner-Nordstrom euclidianos. Esta abordagem nos permitiu descobrir novas famílias de instantons neste contexto.Ainda,os resultados obtidos mostram que o número de famílias de instantons no espaço de Reissner- Nordstrom depende diretamente da carga elétrica que caracteriza esta geometria / Abstract: In this work we study instanton solutions of the Yang-Mills theory in Schwarzschild and Reissner-Nordstrom spaces with gauge group SU(2).Instantons are solutions to the classical field equations of Yang-Mills theory defined in a space with Riemannian (positive de finite)metric with finite action. We begin with a review of the geometric setting of Yang-Mills theory on a four dimensional manifold,which relates the gauge fields to connections on a fiber bundle.We proceed by presenting the main results related to instantons in flat space. In the second part of this thesis we perform a systematic study of the solutions of Yang-Mills theory in Euclidian Schwarzschild and Reissner-Nordstrom spaces.This approach led us to discover a new family of instantons de fined in those backgrounds. Moreover, our results show that the number of instanton families in the Reissner-Nordstrom space depends directly on the eletric charge which caracterizes this geometry / Mestrado / Física das Particulas Elementares e Campos / Mestre em Física

On étude les effets non-perturbatifs généré par des branes instantoniques Euclidiens en compactifications de la théorie des cordes de type I/II avec orientifolds et D-branes magnétisées. Le focus est sur les instantons qui peuvent générer des corrections au superpotentiel. Une condition nécessaire est que les instantons doivent enrouler des cycles rigides. On considère la compactification de la théorie de Type I (IIB) sur l'orientifold T^6/Z_2xZ_2 avec torsion discrète et D-branes magnétisées. Les instantons enroulant le même cycle que l'O-plane exotique (requis par la torsion discrète) ont la structure désiré de modes zéro pour générer des corrections au superpotentiel. On construit des modèles globales basée sur cet orientifold ou les instantons génère des termes linaires et de termes de masse dans le superpotentiel. En théorie des cordes on calcule un couplage physique duquel on doit extraire la partie olomorphique pour obtenir le superpotentiel non-perturbatif. Les facteurs non-olomorphiques sont absorbés dans le potentiel de Kähler et dans redéfinitions des champs chiraux et modules des cordes fermées. On a dérivé ces redéfinitions pour les compactifications toroïdales (avec orientifolds) de la théorie de Type I avec branes magnétisées et lignes Wilson. Finalement, on a considéré des modèles globales avec des termes linéaires. On a calculé explicitement le superpotentiel non-perturbatif pour les orientifolds toroïdales. On a montré comment faire la somme sur les contributions a un instanton. Les modèles analysées possédaient des vides non-perturbatifs supersymétriques ou le group de jauge était brisé et certains modules des cordes ouvertes étaient stabilisés.