The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing. This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory. The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2n-1, pertinent to nonabelian statistics, in the presence of 2n quasiholes in the Moore-Read state and generalise this result to 2n-k quasiholes and k quasielectrons. In the third approach, we study the topological nature of the degeneracy 2n-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-Tc superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2n-1 for 2n vortices.

In this thesis, we investigated the generation of the higher derivative Chern-Simons term, as well as the ether-like term, both at finite temperature. We also examined the question of the large gauge invariance, with respect to the Chern-Simons term and the hight derivative one. We observed that the coefficient of the Chern-Simons term vanishes, when we taken into account the limit of high temperature. This happens to occur also for the other high derivative terms. With respects to the Chern-Simons term, we observed that the action of the Chern-Simons term and the high derivative one are invariant under the large gauge transformation. For this, we calculated the exactly effective action, however, for a specific gauge choice. Finally, with respects to the ether-like term, we observed that the calculation at finite temperature is ambiguous, as well as it is observed for the calculation at zero temperature. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese, investigamos a geração do termo de Chern-Simons de derivada superior, assim como o termo tipo éter, ambos à temperatura finita. Também estudamos a questão da invariância de gauge ampla, com o termo de Chern-Simons e Chern-Simons de derivada superior. Constatamos que o coeficiente do termo de Chern-Simons de derivada superior anula-se, quando tomamos o limite de altas temperaturas. Esse resultado parece se repetir para os demais termos de derivada superior. Dentro ainda do contexto de Chern-Simons, observamos que a ação de Chern-Simons e a ação de Chern-Simons de derivada superior são invariantes sob transformação de gauge ampla. Para isso, conseguimos calcular a ação efetiva exata, contudo, para uma escolha de gauge específica. Finalmente, com relação ao termo tipo éter, constatamos que o cálculo à temperatura finita e ambíguo, assim como observado no cálculo à temperatura zero.

The goal of the original research presented in this thesis is to study the strong coupling regime of Quantum Field Theories (QFTs) with different methods, making concrete predictions about the phase structure and the dynamics of these theories, and on their observables. The focus is on (gauge) field theories in three spacetime dimensions, which are an interesting laboratory to understand the properties of strong coupling in setups that are usually simpler than in the more familiar case of gauge theories in four dimensions. Importantly, topological effects play a relevant role in three dimensions, thanks to the presence of the so-called Chern-Simons term.The thesis contains a short introduction to QFTs in 3d, principles and applications of infrared dualities, large N techniques, and holography. Indeed, the web of infrared dualities, the large N expansion, and the holographic correspondence between QFT and gravity are the main tools which we use to investigate the strongly coupled regimes of 3d QFTs.Then, the original material is presented. In a first line of research, we focus on the study of the phase diagram of a 3d gauge theory making use of conjectured infrared dualities, extending such dualities to the case where more than one mass parameter can be dialed. In a second line of research, we study a class of 3d gauge theories by engineering their gravity dual in a string theory setup. We prove the existence of multiple phase transitions between phases characterized by both massless particles and topological sectors. In a third line of research, we use holography as a tool to explore the interplay between the physics of 4d QCD and 3d gauge theories. In particular, we analyze the properties of 3d domain walls, which appear as soliton-like solutions of 4d QCD in specific parametric regimes. Finally, we propose a boundary construction of 3d large N vector models, which appear as critical points of theories obtained by coupling degrees of freedom localized on a 3d boundary to a 4d bulk theory. This construction allows to prove new dualities and uncovers a new computational tool for 3d vector models. / 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18788号 / 理博第4046号 / 新制||理||1582(附属図書館) / 31739 / 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 畑 浩之, 教授 田中 貴浩, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Cette thèse porte sur la théorie BF abélienne sur une variété fermée de dimen-sion 3. Elle est formulée en termes de classes de jauge qui sont en fait des classes de cohomologie de Deligne-Beilinson. Cette formulation offre la possibilité d’extraire les quantités mathématiquement pertinentes d’intégrales fonctionnelles formelles. La fonction de partition et les valeurs moyennes d’observables sont ainsi calculées. Ces calculs complètent ceux effectués pour la théorie de Chern-Simons abélienne et ces résultats sont liés entre eux de même qu’avec les invariants de Reshetikhin-Turaev et de Turaev-Viro abéliens. Deux extensions de ce travail sont discutées. Premièrement, une approche graphique est proposée afin de traiter l’invariant classique SU(N) de Chern-Simons. Deuxièmement, une interprétation géométrique de la procédure de fixation de jauge est présentée pour la théorie de Chern-Simons abélienne dans mathbb{R}^{4l+3}. / In this study, the abelian BF theory is considered on a closed manifold of di-mension 3. It is formulated in terms of gauge classes which appear to be Deligne-Beilinson cohomology classes. Such a formulation offers the possibility to extract the quantities mathematically relevant quantities from formal functional integrals. This way, the partition function and the expectation value of observables are computed. Those computations complete the ones performed with the abelian Chern-Simons theory and the results appear to be connected together and also with abelian Reshetikhin-Turaev and Turaev-Viro topological invariants. Two extensions of this study are also discussed. Firstly, a graphical approach is proposed to deal with the SU(N) classical Chern-Simons invariant. Secondly, a geometric interpretation of the gauge fixing procedure is presented for the abelian Chern-Simons theory in mathbb{R}^{4l+3}.

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This thesis is a study of certain aspects of quantum gravity in two- and three-dimensional de Sitter spaces. The model used in dS2 is the Jackiw- Tetitelboim gravity which involves a scalar coupling. At low-energy limit this model becomes Schwarzian theory for which one can compute one-loop partition function. Along the way, the model is recasted into the first order formalism which helps to find an appropriate measure for the partition function. The layout for quantum gravity in dS3 is practically the same and many results appear to be quite similar. Although, there are as many dissimilarities. Ultimately, the goal is different, namely to determine one-loop correction to the central charge of the theory dual to dS3 . Additionally, a putative genus expansion for Jackiw-Teitelboim gravity is investigated along with some concrete computations being done. / Detta examensarbete ̈ar en studie av vissa aspekter av kvantgravita-tion i två och tredimensionella de Sitter-rummen. Den behandlar Jackiw-Teitelboim gravitation i dS2 , en model med en skalär koppling. Vid lågenergigränns blir modellen till Schwarzian teorin som används för att beräkna första ordningskorrektionen till partitionsfunktion. På vägen dit skrivs om modelen till första ordningens formalism som sedan hjälper att hitta ett lämpligt mått för partitionsfunktionen. Plannen för dS3 ser ut i princip likadant och en stor del av resultater är liknande. Emellertid finns det lika många olikheter. I slut änden, målet är annorludna, nämligen att beräkna första ordningens korrektion till centrala laddningen av teorin som dual till dS3 . Dessutom, en förmodad genus expansion för Jackiw-Teitelboim gravitation är undersökt och vissa konkreta beräkningar är gjorda.