In this work, 2 + 1 dimensional Chern-Simons theory have been used in an attempt to describe superconductivity. It was examined if the two defining properties of superconductivity, infinite direct current (DC) conductivity and the Meissner effect, as well as the two characteristic length scales of superconductors, the London penetration depth and the coherence length, could be obtained. Three approaches modelling bulk properties of superconductivity were developed for this purpose. It was found that the London penetration depth could be obtained from a Maxwell-Chern-Simons theory, which explains the Meissner effect too, but not the mechanism responsible for the effect. Infinite DC conductivity was achieved by introducing a Proca mass term. The coherence length was not obtained. Although, the coherence length and the mechanism of the Meissner effect is expected to appear from an edge treatment.

Estudamos as teorias não-relativísticas e não-comutativas de campos de spin zero e l/2 acoplado minimamente com o campo ele Chern-Simons em 2+ 1 dimensões. Na situação comutativa o modelo escalar foi usado para simular o efeito Aharonov-Bohrn na abordagem da teoria de campos. Na teoria escalar verificamos que, contrariamente ao resultado comutativo, a inclusão ele urna auto--interação quártica do campo escalar não ó necessária para garantir a renormalização ultravioleta do modelo. Entretanto, para obter um limite comutativo analítico a presença ele uma auto-interação quártica é exigida. Mostramos para o caso ele partículas ele spin 1/2 que a contribuição em um laço para a matriz ele espalhamento contendo o termo de Pauli é puramente não--planar. O termo de Pauli desempenha a mesma função ela auto-interação quártica como no caso escalar. Para valores pequenos do parâmetro da não--comutatividade determinamos as correções para o espalhamento Aharonov-Bohm e provamos que, até ordem de um laço, os modelos são livres de singularidades ultravioleta/infravermelha. / We study noncommutative nonrelativistic theories of spin 0 and 1/2 field coupled to thc Chern-Sirnons field in 2+1 dimensions. In the commutative situation the scalar model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrarily to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalization of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For the case of spin 1/2 particles we show that the one-loop contributions to the that scattering matrix the which contain the Pauli\'s term are purely nonplanar. Thc Pauli\'s term plays the same role of a quartic self-interaction in the scalar case. For small values of the noncommutative parameter we fix the corrections to the Aharonov-Bohm scattering and prove that up to one-loop the models are free from dangerous infrared/ultraviolet divergences.

In this thesis, we considered electrically charged vortex solutions of Born- Infeld Chern-Simons gauge theory in 2+1 dimensions, with a sixth order charged scalar eld potential. For this purpose, rst Nielsen-Olesen vortex solutions are extensively reviewed. Then, Born-Infeld and Chern-Simons theories are summarized. Finally, vortex solutions are obtained for the Born-Infeld-Higgs system with a Chern-Simons term. These solutions are analyzed numerically, comparing their properties with Nielsen-Olesen vortices.

Gauge theories are one of the corner stones of modern theoretical physics. They describe the nature of all fundamental interactions and have been applied in multiple branches of physics. The most challenging problem of gauge theories, which has not been solved yet, is their strong coupling dynamics. A class of gauge theories that admits simplifications allowing to deal with the strong coupling regime are supersymmetric ones. For example, recently proposed method of supersymmetric localization allows to reduce expectation values of supersymmetric observables, expressed through the path integral, to finite-dimensional matrix integral. The last one is usually easier to deal with compared to the original infinite-dimensional integral. This thesis deals with the matrix models obtained from the localization of different 5D gauge theories. The focus of our study is N=1 super Yang-Mills theory with different matter content as well as N=1 Chern-Simons-Matter theory with adjoint hypermultiplets. Both theories are considered on the five-spheres. We make use of the saddle-point approximation of the matrix integrals, obtained from localization, to evaluate expectation values of different observables in these theories. This approximation corresponds to the large-N limit of the localized gauge theory. We derive <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N%5E%7B3%7D" /> behavior for the free energy of 5D N=1* super Yang-Mills theory at strong coupling. This result is important in light of the relation between 5D theory and the world-volume theories of M5-branes, playing a significant role in string theory. We have also explored rich phase structure of 5D SU(N) N=1 super Yang-Mills theory coupled to massive matter in different representations of the gauge group. We have shown that in the case of the massive adjoint hypermultiplet theory undergoes infinite chain of the third order phase transitions while interpolating between weak and strong coupling in the decompactification limit. Finally, we obtain several interesting results for 5D Chern-Simons theory, suggesting existence of the holographic duals to this theory. In particular, we derive <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N%5E%7B5/2%7D" /> behavior of the free energy of this theory, which reproduces the behavior of the free energy for 5D theories with known  holographic duals.

Estudamos as teorias não-relativísticas e não-comutativas de campos de spin zero e l/2 acoplado minimamente com o campo ele Chern-Simons em 2+ 1 dimensões. Na situação comutativa o modelo escalar foi usado para simular o efeito Aharonov-Bohrn na abordagem da teoria de campos. Na teoria escalar verificamos que, contrariamente ao resultado comutativo, a inclusão ele urna auto--interação quártica do campo escalar não ó necessária para garantir a renormalização ultravioleta do modelo. Entretanto, para obter um limite comutativo analítico a presença ele uma auto-interação quártica é exigida. Mostramos para o caso ele partículas ele spin 1/2 que a contribuição em um laço para a matriz ele espalhamento contendo o termo de Pauli é puramente não--planar. O termo de Pauli desempenha a mesma função ela auto-interação quártica como no caso escalar. Para valores pequenos do parâmetro da não--comutatividade determinamos as correções para o espalhamento Aharonov-Bohm e provamos que, até ordem de um laço, os modelos são livres de singularidades ultravioleta/infravermelha. / We study noncommutative nonrelativistic theories of spin 0 and 1/2 field coupled to thc Chern-Sirnons field in 2+1 dimensions. In the commutative situation the scalar model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrarily to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalization of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For the case of spin 1/2 particles we show that the one-loop contributions to the that scattering matrix the which contain the Pauli\'s term are purely nonplanar. Thc Pauli\'s term plays the same role of a quartic self-interaction in the scalar case. For small values of the noncommutative parameter we fix the corrections to the Aharonov-Bohm scattering and prove that up to one-loop the models are free from dangerous infrared/ultraviolet divergences.

In this Thesis, we propose to analyze three different aspects of Fundamental Physics.The first part is devoted to the detailed study of what is called "unconventional supersymmetry" in three and four dimensions for Abelian and non-Abelian internal groups. We show the dynamical content of the odd-dimensional theory, counting at the same time the local degrees of freedom for some particular sectors of the phase space. In the non-Abelian three-dimensional case, some black hole solutions are presented, including their Killing spinors. In four dimensions, the supersymmetry is broken explicitly and a standard Dirac Lagrangian coupled with the electromagnetic field and the background geometry is obtained.In the second part, the dynamical content for the free and gauge coupled massless Rarita-Schwinger theory is presented. We are able to do that through the Dirac's Hamiltonian formalism and the Faddeev-Jackiw method, showing at the same time the symmetries of the theory. It is shown that in the gauge extended theory, which includes extra fermionic fields to restore the fermionic symmetries of the free case, the anticommutator of the Rarita-Schwinger field in the canonical quantization is not positive definite in general.As the graphene has been proposed as an on ``table-top laboratory" for some Quantum Gravity scenarios, in the third part of this Thesis we clarify some subtle features of strained graphene in order to manage properly this material. We show particularly that the pseudo-magnetic field induced by the in-plane strain tensor field cannot emerge from a Quantum Field Theory in curved spacetime approach (bottom-up approach) but from the detailed analysis of the tight-binding Hamiltonian of pi electrons in graphene (top-down approach) instead. / Dans cette Thèse, nous nous proposons d'analyser trois aspects différents de la Physique Fondamentale.La première partie est consacrée à l'éude détaillée de ce qu'on appelle "supersymétrie non conventionnelle" à trois et quatre dimensions pour des groupes internes abéliens et non abéliens. Nous montrons le contenu dynamique de la théorie de la dimension impaire, comptant en même temps les degrés de liberté locaux pour certains secteurs particuliers de l'espace des phases. Dans le cas tridimensionnel non-abélien, certaines solutions de trous noirs sont présentées, y compris leurs spinors de Killing. En quatre dimensions, la supersymétrie est brisée explicitement et un Lagrangien de Dirac standard couplé à l'électromagnétisme et à la géométrie d'arriére-plan est obtenu.Dans la deuxième partie, le contenu dynamique de la théorie de Rarita-Schwinger libre et couplée à un champ de jauge sans masse est présenté. Nous sommes en mesure de le faire par le formalisme Hamiltonien de Dirac et la méthode dite de Faddeev-Jackiw, en montrant en même temps les symétries de la théorie. Il est démontré que dans la théorie étendue de jauge, qui comprend des champs fermioniques supplémentaires pour restaurer les symétries fermioniques du cas libre, l'anticommutator du champ Rarita-Schwinger dans la quantification canonique n'est pas définiti positif en général.Comme le graphène a été proposé comme un "laboratoire de table" pour certains scénarios de gravité quantique, dans la troisième partie de cette Thèse, nous clarifions certaines caractéristiques subtiles du graphène sous tension afin de gérer correctement ce matériel. Nous montrons en particulier que le champ pseudo-magnétique induit par le champ tensoriel de déformation dans le plan ne peut pas émerger d'une théorie de champ quantique dans un espace courbe (approche bottom-up), mais bien à partir de l'analyse détaillée de l'Hamiltonien tight-binding des pi électrons dans le graphène (approche top-down). / En esta Tesis se propone analizar tres aspectos diferentes de la Física Fundamental.La primera parte está dedicada al estudio detallado de lo que ha pasado a llamarse "supersimetría no convencional" en tres y cuatro dimensiones para grupos internos abelianos y no abelianos. Se muestra el contenido dinámico en dimensiones impares de la teoría, contando al mismo tiempo los grados de libertad locales para ciertos sectores del espacio de fases. En el caso tridimensional no abeliano, se presentan algunas soluciones de agujeros negros, incluyendo sus espinores de Killing. En cuatro dimensiones, la supersimetría está rota explícitamente y se obtiene un lagrangiano estándar de Dirac acoplado con el campo electromagnético y la geometría de fondo.En la segunda parte, se presenta el contenido dinámico de la teoría de Rarita-Schwinger libre y con acoplamiento gauge. Esto se puede hacer a través del formalismo hamiltoniano de Dirac y el método de Faddeev-Jackiw, mostrando al mismo tiempo las simetrías de la teoría. Se observa que en la teoría gauge extendida, la cual incluye campos fermiónicos extra para restaurar la simetría fermiónica del caso libre, el anticonmutador del campo de Rarita-Schwinger no es definido positivo en la cuantización canónica.Ya que el grafeno se ha propuesto como una "mesa de laboratorio" para algunos escenarios de gravedad cuántica, en la tercera parte de esta Tesis se clarifican algunas características sutiles del grafeno extendido con el objetivo de manejar debidamente el material. Se muestra particularmente que el campo seudo-magnético inducido por el campo de tensión planar no puede emerger de una teoría cuántica de campos en espacios curvos (abordaje top-down), sino de un análisis detallado del hamiltoniano tight-binding de los electrones pi en el grafeno (abordaje bottom-up). / 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19496号 / 理博第4156号 / 新制||理||1597(附属図書館) / 32532 / 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 笹倉 直樹, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Nesta tese, o limite não re1ativistico em teorias quânticas de campos em 2+1 dimensões é discutido1 perturbativamente, através da introdução de um corte intermediário que permite 0 cálculo de.expansão /P/m das amplitudes quânticas. especificando a origem, no espaço dos estados intermediários, de cada uma. das contribuições. Este procedimento é aplicado à teoria 4 e um esquema de redução a nível das amplitudes, que identifica a contribuição do setor de baixas energias com 0 resultado da teoria não re1ativistica, é proposto. Quando aplicado á teoria de Chern-Simons escalar, este procedimento sugere correlações relativísticas para o espalhamento Aharonov-Bohm. / n this thesis, the nonrelativistic limit of quantum field theories in 2 + 1 dimensions is discussed, perturbatively, through the introduction of an intermediate cutoff which generates the /p/m expansion of the quantum amplitudes and specifies the origin of each contribution in the space of the intermediary states. This scheme is applied to the theory 4 and a reduction procedure for the amplitudes that identify the low energy sector contribution with the results of the nonrelativistic theory is proposed. When applied to the scalar Chern-Simons theory, this procedure gives relativistic corrections to the Aharonov- Bohm scattering.

Nesta tese, o limite não re1ativistico em teorias quânticas de campos em 2+1 dimensões é discutido1 perturbativamente, através da introdução de um corte intermediário que permite 0 cálculo de.expansão /P/m das amplitudes quânticas. especificando a origem, no espaço dos estados intermediários, de cada uma. das contribuições. Este procedimento é aplicado à teoria 4 e um esquema de redução a nível das amplitudes, que identifica a contribuição do setor de baixas energias com 0 resultado da teoria não re1ativistica, é proposto. Quando aplicado á teoria de Chern-Simons escalar, este procedimento sugere correlações relativísticas para o espalhamento Aharonov-Bohm. / n this thesis, the nonrelativistic limit of quantum field theories in 2 + 1 dimensions is discussed, perturbatively, through the introduction of an intermediate cutoff which generates the /p/m expansion of the quantum amplitudes and specifies the origin of each contribution in the space of the intermediary states. This scheme is applied to the theory 4 and a reduction procedure for the amplitudes that identify the low energy sector contribution with the results of the nonrelativistic theory is proposed. When applied to the scalar Chern-Simons theory, this procedure gives relativistic corrections to the Aharonov- Bohm scattering.

This thesis consists of two parts, which can be read separately. In the first part we study aspects of topological field theories. We show how to topologically twist three-dimensional N=2 supersymmetric Chern-Simons theory using a contact structure on the underlying manifold. This gives us a formulation of Chern-Simons theory together with a set of auxiliary fields and an odd symmetry. For Seifert manifolds, we show how to use this odd symmetry to localize the path integral of Chern-Simons theory. The formulation of three-dimensional Chern-Simons theory using a contact structure admits natural generalizations to higher dimensions. We introduce and study these theories. The focus is on the five-dimensional theory, which can be understood as a topologically twisted version of N=1 supersymmetric Yang-Mills theory. When formulated on contact manifolds that are circle fibrations over a symplectic manifold, it localizes to contact instantons. For the theory on the five-sphere, we show that the perturbative part of the partition function is given by a matrix model. In the second part of the thesis, we study supersymmetric sigma models in the Hamiltonian formalism, both in a classical and in a quantum mechanical setup. We argue that the so called Chiral de Rham complex, which is a sheaf of vertex algebras, is a natural framework to understand quantum aspects of supersymmetric sigma models in the Hamiltonian formalism. We show how a class of currents which generate symmetry algebras for the classical sigma model can be defined within the Chiral de Rham complex framework, and for a six-dimensional Calabi-Yau manifold we calculate the equal-time commutators between the currents and show that they generate the Odake algebra.