No description available.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 72-77).

University, Diss., 2003--Bonn.

Submitted by LUIS MAX GUILLEN QUIROZ null (luismax@ift.unesp.br) on 2016-05-10T15:29:35Z No. of bitstreams: 1 Pure-Spinor-Superfield-Formalism-MasterDissertation.pdf: 748046 bytes, checksum: dc1994a99330048c6f153d322a0863ee (MD5) / Rejected by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: O arquivo submetido está sem a ficha catalográfica e folha de aprovação. Lembramos que a versão submetida por você é considerada a versão final da dissertação/tese, portanto não poderá ocorrer qualquer alteração em seu conteúdo após a aprovação. Corrija estas informações e realize uma nova submissão contendo o arquivo correto. Agradecemos a compreensão. on 2016-05-13T12:10:28Z (GMT) / Submitted by LUIS MAX GUILLEN QUIROZ null (luismax@ift.unesp.br) on 2016-09-22T03:10:43Z No. of bitstreams: 1 Pure-Spinor-Superfield-Formalism-MasterDissertation.pdf: 748046 bytes, checksum: dc1994a99330048c6f153d322a0863ee (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-09-27T14:13:13Z (GMT) No. of bitstreams: 1 quiroz_lmg_me_ift.pdf: 748046 bytes, checksum: dc1994a99330048c6f153d322a0863ee (MD5) / Made available in DSpace on 2016-09-27T14:13:13Z (GMT). No. of bitstreams: 1 quiroz_lmg_me_ift.pdf: 748046 bytes, checksum: dc1994a99330048c6f153d322a0863ee (MD5) Previous issue date: 2016-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / E bem conhecido como descrever as teor´ıas de Super Yang-Mills (SYM) ´ em D = 10 dimens˜oes e Supergravidade (SG) em D = 11 dimens˜oes no superespa¸co e via seus campos componentes. No entanto, uma nova vers˜ao desses modelos foi formulada nos finais da d´ecada de 2000, quando Martin Cederwall usando o formalismo de supercampo de espinor puro conseguiu construir uma pure spinor a¸c˜ao, que a diferen¸ca das anteriores abordagens, esta n˜ao precisa de impor constraints a m˜ao, proporciona uma descri¸c˜ao completa de cada modelo (no sentido do formalismo BV) e as equa¸c˜oes do movimento obtidas a partir do respectivo principio de a¸c˜ao s˜ao supersim´etricas. Neste trabalho iremos explicar toda a base necess´aria para entender a constru¸c˜ao de tal formalismo. Para esse prop´osito, come¸caremos estudando a teoria SYM (abeliana) em D = 10 em suas formula¸c˜oes em componentes e no superespa¸co. Usaremos a a¸c˜ao da formula¸c˜ao on-shell para quantizar a teoria via o formalismo de Batalin-Vilkovisky (BV). Seguiremos para SG em D = 11 e estudaremos suas formula¸c˜oes em componentes e no superespa¸co. Ent˜ao iremos mostrar que podemos obter o mesmo espectro f´ısico de SYM em D = 10 (SG em D = 11) estudando a superpart´ıcula em D = 10 (D = 11) na calibre do cone de luz. De forma a ter uma quantiza¸c˜ao covariante desses modelos, introduziremos a superpart´ıcula de espinor puro em D = 10 (D = 11), a qual possui o operador BRST usual de espinor puro (Q = λD). Verificar-se-´a que a cohomologia desse operador coincidir´a com a teoria SYM em D=10 (SG em D=11) linearizada depois de ser quantizada via o formalismo BV. Esse resultado introduzir´a naturalmente a ideia de construir a¸c˜oes usando um supercampo de espinor puro. Finalmente, explicaremos como o formalismo de supercampo de espinor puro surge nesse contexto e como podemos us´a-lo para construir a¸c˜oes manifestamente supersim´etricas para SYM em D=10 e SG em D=11. / It is well known how to describe the D = 10 (SYM) Super Yang-Mills and D = 11 (SG) Supergravity theories on superspace and by component fields. However, a new version of these models was formulated in the late 2000, when Martin Cederwall using the pure spinor superfield formalism achieved to construct a pure spinor action for these theories, which unlike the previously mentioned approaches, this does not require to impose any constraint by hand, provides a full description of each model (in the BV sense) and the equations of motion coming from the corresponding action principle are supersymmetric. In this work we will explain all the background required to understand the construction of this action. For this purpose, we will start with the D=10 (abelian) SYM theory in its component and superspace formulations. We will use the action of the on-shell formulation to quantize the theory via the Batalin-Vilkovisky framework. We will move to D=11 supergravity and study its component and superspace formulations. Then we will show that we can obtain the same physical spectrum of D = 10 SYM (D = 11 SG) by studying the D = 10 (D = 11) superparticle in the light-cone gauge. In order to have a covariant quantization of these models, we will introduce the D = 10 (D = 11) pure spinor superparticle, which possesses the usual pure spinor BRST operator (Q = λD). It will turn out that the cohomology of this operator will coincide with the linearized D = 10 SYM (D = 11 SG) theory after being quantized via BV-formalism. This result will introduce naturally the idea of constructing pure spinor actions. Finally, we will explain how the pure spinor superfield framework arises in this context and how we can use it to construct manifestly supersymmetric actions for D = 10 SYM and D = 11 SG.

Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are related to those of N = 4 super-Yang-Mills (SYM) theory. This makes all-plus amplitudes a useful testing ground for new methods of simplifing more general classes of amplitudes. In this thesis we consider three new approaches, focusing on the structure before integration. We begin with the planar (leading-colour) sector. A D-dimensional local-integrand presentation, based on four-dimensional local integrands developed for N = 4 SYM, is developed. This allows us to compute the planar six-gluon, two-loop all-plus amplitude. Its soft structure is understood before integration, and we also perform checks on collinear limits. We then proceed to consider subleading-colour structures. A multi-peripheral colour decomposition is used to find colour factors based on underlying tree-level amplitudes via generalised unitarity cuts. This allows us to find the integrand of the full-colour, two-loop, five-gluon all-plus amplitude. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. Finally, we consider representations satisfying colour-kinematics duality. We discuss obstacles to finding such numerators in the context of the same five-gluon amplitude at two loops. The obstacles are overcome by adding loop momentum to our numerators to accommodate tension between the values of certain cuts and the symmetries of certain diagrams. Control over the size of our ansatz is maintained by identifying a highly constraining, but desirable, symmetry property of our master numerator.

Made available in DSpace on 2018-07-27T18:26:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-09-04. Added 1 bitstream(s) on 2018-07-27T18:30:19Z : No. of bitstreams: 1 000866848.pdf: 631406 bytes, checksum: 951f24cae0a92bf26987f68a9faaef16 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta dissertação apresentamos uma descrição da dualidade elétrica-magnética e seus aspectos clássicos e quânticos. Nosso análise se inicia com os monopolos magéticos sugeridos por Dirac em 1931[1] e vai até o trabalho do Seiberg e Witten em 1994 [27]. Na descrição clássica, precisamos introduzir os monopolos magnéticos a fim de obter a dualidade elétrica-magnética manifesta. Mais tarde, a origem dos monopolos se mais torna mais clara quando começamos com uma teoria de Yang-Mills. Os aspectos clássicos da teoria foram explicados pela conjetura de Montonen e Olive 1977 [7]. Explorando os aspectos quânticos da teoria, notamos a importância de introduzir supersimetria, principalmente supersimetria estendida, onde tiramos vantagem da propiedade de holomorficidade, a qual nos leva aos teoremas não renormalizáveis, onde o cálculo é mais simples. Focamos na teoria de gauge supersimétrica N = 2 SU(2). A teoria é completamente resolvível para baixas energias. A maior parte do conteúdo deste trabalho é baseada nas várias revisões da dualidade de Seiberg-Witten [30],[31],[32] / In this dissertation we present a description of the electric-magnetic duality and their classical and quantum aspects. Our analysis starts from the suggested magnetic monopoles by Dirac in 1931 [1] and goes until the work of Seiberg and Witten in 1994 [27]. In the classical description, we need to introduce the magnetic monopoles in order to make manifest the electricmagnetic duality. Later, the origin of monopoles becomes clear when we start from a Yang-Mills theory. The classical aspects of the E-M duality are covered in the Montonen-Olive conjecture 1977[7]. Working on the quantum aspects of the theory, we note the importance of introducing supersymmetry. Specially for extended supersymmetry, where we take advantage of the holomorphicity property, which leads us to the non-renormalizable theorems, where the computation is easier. We focus on theN = 2SU(2) supersymmetric gauge theories. It turns out that the theory is fully solvable at the low energies regime[27]. Most of this work is based on reviews about the Seiberg and Witten duality [30],[31],[32]

Orientador: Nathan Jacob Berkovits / Banca: Horatiu Stefan Nastase / Banca: Diego Trancanelli / Resumo: Nesta dissertação apresentamos uma descrição da dualidade elétrica-magnética e seus aspectos clássicos e quânticos. Nosso análise se inicia com os monopolos magéticos sugeridos por Dirac em 1931[1] e vai até o trabalho do Seiberg e Witten em 1994 [27]. Na descrição clássica, precisamos introduzir os monopolos magnéticos a fim de obter a dualidade elétrica-magnética manifesta. Mais tarde, a origem dos monopolos se mais torna mais clara quando começamos com uma teoria de Yang-Mills. Os aspectos clássicos da teoria foram explicados pela conjetura de Montonen e Olive 1977 [7]. Explorando os aspectos quânticos da teoria, notamos a importância de introduzir supersimetria, principalmente supersimetria estendida, onde tiramos vantagem da propiedade de holomorficidade, a qual nos leva aos teoremas não renormalizáveis, onde o cálculo é mais simples. Focamos na teoria de gauge supersimétrica N = 2 SU(2). A teoria é completamente resolvível para baixas energias. A maior parte do conteúdo deste trabalho é baseada nas várias revisões da dualidade de Seiberg-Witten [30],[31],[32] / Abstract: In this dissertation we present a description of the electric-magnetic duality and their classical and quantum aspects. Our analysis starts from the suggested magnetic monopoles by Dirac in 1931 [1] and goes until the work of Seiberg and Witten in 1994 [27]. In the classical description, we need to introduce the magnetic monopoles in order to make manifest the electricmagnetic duality. Later, the origin of monopoles becomes clear when we start from a Yang-Mills theory. The classical aspects of the E-M duality are covered in the Montonen-Olive conjecture 1977[7]. Working on the quantum aspects of the theory, we note the importance of introducing supersymmetry. Specially for extended supersymmetry, where we take advantage of the holomorphicity property, which leads us to the non-renormalizable theorems, where the computation is easier. We focus on theN = 2SU(2) supersymmetric gauge theories. It turns out that the theory is fully solvable at the low energies regime[27]. Most of this work is based on reviews about the Seiberg and Witten duality [30],[31],[32] / Mestre

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20173号 / 理博第4258号 / 新制||理||1612(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 大西 明, 教授 國廣 悌二, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

On s'intéresse dans cette thèse à l'étude de variables aléatoires sur les groupes de Lie compacts classiques. On donne une déformation du calcul de Weingarten tel qu'il a été introduit par B. Collins et P. Sniady. On fait une étude asymptotique du mouvement brownien sur les groupes de Lie compacts de grande dimension en obtenant des nouveaux résultats de fluctuations. Deux nouveaux objets, que l'on appelle champ maître gaussien planaire et champ maître orienté planaire, sont introduits pour décrire le comportement asymptotique des mesures de Yang-Mills pour des groupes de structure de grande dimension.

On s'intéresse dans cette thèse à l'étude de variables aléatoires sur les groupes de Lie compacts classiques. On donne une déformation du calcul de Weingarten tel qu'il a été introduit par B. Collins et P. Sniady. On fait une étude asymptotique du mouvement brownien sur les groupes de Lie compacts de grande dimension en obtenant des nouveaux résultats de fluctuations. Deux nouveaux objets, que l'on appelle champ maître gaussien planaire et champ maître orienté planaire, sont introduits pour décrire le comportement asymptotique des mesures de Yang-Mills pour des groupes de structure de grande dimension. / In the following text, we are interested in the study of Lie-groups valued random variables. We give a deformation of the Weingarten calculus introduced by Benoît Collins and Piotr Sniady. We study the asymptotic behavior of Brownian motion on compact Lie groups in high dimensions and obtain new fluctuations results. Two new objects called the planar gaussian master field and the planar oriented master field are introduced here to describe the asymptotic behavior of the Yang-Mills measure as the dimension of the structure group is large.