Submitted by JOGEAN MATHEUS CARVALHO FERREIRA (jogeanmcf@gmail.com) on 2018-04-13T15:33:45Z No. of bitstreams: 1 Dissertação-Jogean.pdf: 463408 bytes, checksum: d2ae1ba2ff2f5b812d60078e1735eff9 (MD5) / Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-04-13T17:16:56Z (GMT) No. of bitstreams: 1 ferreira_jmc_me_ift.pdf: 463408 bytes, checksum: d2ae1ba2ff2f5b812d60078e1735eff9 (MD5) / Made available in DSpace on 2018-04-13T17:16:56Z (GMT). No. of bitstreams: 1 ferreira_jmc_me_ift.pdf: 463408 bytes, checksum: d2ae1ba2ff2f5b812d60078e1735eff9 (MD5) Previous issue date: 2018-02-26 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Supersimetria é um tema de bastante interesse na física, em particular na física de partículas, existem dezenas de modelos supersimétricos e diversos estudos sobre o assunto. Outra área de bastante interesse na física, e na matemática, é a integrabilidade de equações diferenciais, que as vezes é uma propriedade exigida em modelos físicos. Este trabalho é dedicado ao estudo de modelos tanto integráveis quanto supersimétricos para campos clássicos. No primeiro capítulo nós falamos sobre todos os conhecimentos necessários para o entendimento dos capítulos subsequentes; introduzimos conceitos sobre grupos, álgebra de Lie, loop algebra, álgebra de Kac-Moody e propriedades requeridas para construção dos modelos. No capítulo três nós apresentamos dois modelos supersimétricos e integráveis que são obtidos por vias diferentes. No capítulo três nós propomos transformações para eliminar redundâncias e discutimos as principais diferenças entres esses três modelos. / Supersymmetry is a well studied branch of physics having promising physical models applied to theoretical physics and we still are looking forward experimental evidences for such phenomenon. Integrability is another great interesting theme on physics, and mathematics, that is sometimes required for physical models. This works put together supersymmetry and integrability of models based on standard principles. However, we treat of classical point of view, just looking for supersymmetry transformations and integrability of motion equations for fields. In chapter one we speak about groups, Lie algebra, loop algebra, superalgebra and others property needed to constructions of our models, introducing all knowledge for understanding the follows chapters. In chapter two we develop three supersymmetric and integrable models by different ways. In chapter three we discus the correspondence of this three models, proposing transformations with aim of to eliminate redundancies, and discuss the main differences between them. / 131664/2016-6

<p>This thesis deals with different aspects of string and /p/-brane theories. One of the motivations for string theory is to unify the forces in nature and produce a quantum theory of gravity. /p/-branes and related objects arise in string theory and are related to a non-perturbative definition of the theory. The results of this thesis might help in understanding string theory better. The first part of the thesis introduces and discusses relevant topics for the second part of the thesis which consists of five papers.</p><p>In the three first papers we develop and treat a perturbative approach to relativistic /p/-branes around stretched geometries. The unperturbed theory is described by a string- or particle-like theory. The theory is solved, within perturbation theory, by constructing successive canonical transformations which map the theory to the unperturbed one order by order. The result is used to define a quantum theory which requires for consistency d = 25 + p dimensions for the bosonic /p/-branes and d = 11 for the supermembrane. This is one of the first quantum results for extended objects beyond string theory and is a confirmation of the expectation of an eleven-dimensional quantum membrane.</p><p>The two last papers deal with a gauged WZNW-approach to strings moving on non-trivial space-times. The groups used in the formulation of these models are connected to Hermitian symmetric spaces of non-compact type. We have found that the GKO-construction does not yield a unitary spectrum. We will show that there exists, however, a different approach, the BRST approach, which gives unitarity under certain conditions. This is the first example of a difference between the GKO- and BRST construction. This is one of the first proofs of unitarity of a string theory in a non-trivial non-compact space-time. Furthermore, new critical string theories in dimensions less then 26 or 10 is found for the bosonic and supersymmetric string, respectively.</p>

This thesis deals with different aspects of string and /p/-brane theories. One of the motivations for string theory is to unify the forces in nature and produce a quantum theory of gravity. /p/-branes and related objects arise in string theory and are related to a non-perturbative definition of the theory. The results of this thesis might help in understanding string theory better. The first part of the thesis introduces and discusses relevant topics for the second part of the thesis which consists of five papers. In the three first papers we develop and treat a perturbative approach to relativistic /p/-branes around stretched geometries. The unperturbed theory is described by a string- or particle-like theory. The theory is solved, within perturbation theory, by constructing successive canonical transformations which map the theory to the unperturbed one order by order. The result is used to define a quantum theory which requires for consistency d = 25 + p dimensions for the bosonic /p/-branes and d = 11 for the supermembrane. This is one of the first quantum results for extended objects beyond string theory and is a confirmation of the expectation of an eleven-dimensional quantum membrane. The two last papers deal with a gauged WZNW-approach to strings moving on non-trivial space-times. The groups used in the formulation of these models are connected to Hermitian symmetric spaces of non-compact type. We have found that the GKO-construction does not yield a unitary spectrum. We will show that there exists, however, a different approach, the BRST approach, which gives unitarity under certain conditions. This is the first example of a difference between the GKO- and BRST construction. This is one of the first proofs of unitarity of a string theory in a non-trivial non-compact space-time. Furthermore, new critical string theories in dimensions less then 26 or 10 is found for the bosonic and supersymmetric string, respectively.