Nesta tese investigamos a integrabilidade quântica do modelo de Alday-Arutyunov-Frolov (AAF) através da diagonalização da Hamiltoniana do modelo transformado de AAF. O modelo transformado de AAF é obtido do modelo original após uma redefinição nos campos que tem o objetivo de transformar os parênteses de Dirac na estrutura canônicos padrão entre dois fêrmions. Para diagonalização da Hamiltoniana do modelo transformado nós usamos um método desenvolvido para o modelo de Landau-Lifshitz. Este método exige regularização do produto de operadores definidos no mesmo ponto bem como a construção de extensões auto-adjuntas. Mostramos que a função de onda e os estados do modelo transformado de AAF apresentam descontinuidades que devem ser tratadas cuidadosamente. Nós também investigamos a equivalência entre as matrizes S das duas formulações do modelo de AAF através do cálculo direto da matriz S em ambas as teorias. Também consideramos o teorema da equivalência para o modelo de AAF, para mostrar que a matriz S é invariante por redefinições dos campos da teoria. / In this thesis we investigate the quantum integrability of the Alday-Arutyunov-Frolov model (AAF) by diagonalization of the Hamiltonian of the AAF transformed model. The AAF transformed model is obtained from original model after fields redefinition whose purpose is to transform the Dirac brackets in the standard canonical structure between two fermions. For the diagonalization of the Hamiltonian of the transformed model we use the method developed for the Landau-Lifshitz model. This method requires regularization of the singular product of operators at the same point as well as construction of the selfadjoint extensions. We show that the wave function and the states of the transformed AAF exhibit discontinuities. We also investigated the equivalence of the matrices S of the two formulations of the AAF model through direct calculation of the S-matrix in both theories. We also consider the equivalence theorem applied to AAF model. To shows that the S matrix is invariant under field redefinitions.

In this work we review the basic principles of the theory of the relativistic bosonic string through the study of the action functionals of Nambu-Goto and Polyakov and the techniques required for their canonical, light-cone, and path-integral quantisation. For this purpose, we briefly review the main properties of the gauge symmetries and conformal field theory involved in the techniques studied. / Neste trabalho fazemos uma revisão dos princípios básicos da teoria da corda bosônica relativística através do estudo dos funcionais ação de Nambu-Goto e de Polyakov e das técnicas necessárias para sua quantização canônica, no cone de luz e usando integrais de trajetória. Para tanto apresentamos uma pequena revisão das principais propriedades das simetrias de calibre a da teoria de campos conforme envolvidas nas técnicas estudadas.

Este é um trabalho de revisão. Os principais formalismos no desenvolvimento da teoria de cordas são introduzidos e discutidos: a corda bosônica e as supercordas no formalismo de Ramond-Neveu-Schwarz e no formalismo de Green-Schwarz. São introduzidas também as açôes efetivas no limite de baixas energias das D-branas (ação DBI) e das teorias de supergravidade (D=10,11). Por fim, são analisados alguns aspectos da correspondência AdS/CFT, enunciando a conjectura e introduzindo algumas das entradas do dicionário. Os apêndices contêm tópicos de grande relevância para o texto e podem ajudar a esclarecer vários raciocínios e passagens ao longo do mesmo. / This is a review work. The main formalisms on the development of string theory are introduced and discussed: the bosonic string and the superstrings formalisms of Ramond-Never-Schwarz and Green-Schwarz. The effective actions in the low energy limit of the D-branes (DBI action) and supergravity theories (D=10,11) are introduced as well. Finally, some aspects of the AdS/CFT correspondence are analised, enunciating the conjecture and introducing some entries of the dictionary. The appendices contains some topics that are highly relevant for the whole text and may help clarify several ideas and arguments through it.

O modelo não linear supersimétrico em l+l dimensões é acoplado à supergravidade. Ao quantizarmos a teoria, os campos de matéria adquirem massa dinamicamente, o que ocasiona a quebra da invariança de Weyl. Este fato implica em que as funções de dois pontos do Gravitino e do Graviton, obtidas a partir da ação efetiva, não sejam triviais. Em particular a função de dois pontos do Gravitino apresenta um polo no infravermelho. Nós conjeturamos que este polo está ligado com o confinamento dos graus de liberdade supersimétricos da teoria. Isto porque, ao restringirmos o domínio de integração de x IND. 1 à uma medida finita L (quebrando as invarianças da teoria), aparece na função de dois pontos do Gravitino um termo de massa, que decresce exponencialmente em função de L. Neste contexto relacionamos este model o como da corda supersimetrica e definimos um critério de estabilidade para a mesma. / The nonlinear o supersymmetric model in l+l dimensions is coupled to supergravity. When we quantize the theory, the matter fields acquire mass dynamically, which leads to the breaking of the Weyl invariance. This fact implies that the two point functions of the Gravitino and the Graviton, obtained from the effective action, become non trivial. Particularly, the two point function of the Gravitino presents a pole in the infrared region. We conjecture that this pole is related to the confinement of all supersymmetric degrees of freedom of the theory. If we restraind the integration domain of x1 to a finite lengh L (breaking all invariances of the theory), there appears a mass term in two point function of the Gravitino, which decreases exponentially with L. In this context we relate this model with that of the supersymmetric string and define a stability criteria for the latter.

A presente pesquisa teve como objetivo principal elaborar um plano de ações com alternativas na preparação e colocação da mão esquerda no violino para estudantes de violino. Desenvolveu-se em um estudo experimental, com seis estudantes do Conservatório e da Graduação da Universidade de Caldas na Colômbia. O processo de investigação foi fundamentado em quatro tópicos: (1) a análise do posicionamento inicial da mão, dedos e braço esquerdo, (2) a introdução de padrões motores e de movimentos alternativos, (3) a comparação da mão esquerda antes e depois do plano de ações alternativas, e (4) a avaliação do plano de ações. Este estudo incluiu a coleta de dados por meio de registro de vídeo antes e depois das ações propostas. Esta proposta procura possíveis soluções para tensões musculoesqueléticas, que estão na origem da colocação inadequada dos dedos, mão e braço. O processo teve a fundamentação bibliográfica em Paul Rolland (1911-1981), Ivan Galamian (1903-1981), Carl Flesch (1873-1944), Yehudi Menuhin (1916-1999) entre outros. / The aim of this investigation was to develop a plan of actions for teaching and/or improving left hand positioning of beginner violin students. The goal was to have a teaching alternative that could help solving musculoskeletal tension, derived from inadequate positioning of fingers, and hand. An experimental study was conducted with six students from the Conservatory of Music and undergraduates of the University of Caldas, Colombia. The investigation was based on four topics: (1) analysis of the initial position of hand, fingers and left arm; (2) teaching of the proposed alternative motor and movement patterns; (3) comparison of the left hand before and after the action plan; and (4) evaluation of the action plan. For data collection during this study, video recording were done before and after the actions. This study was based on the writings of Paul Rolland (1911-1981), Ivan Galamian (1903-1981), Carl Flesch (1873- 1944), Yehudi Menuhin (1916-1999) among others.

Esta tese visa realizar um estudo acerca das freqüências quasinormais das p-branas negras utilizando um campo escalar de teste. No contexto da correspondência AdS/CFT estudamos alguns aspectos da formação de estados supercondutores na teoria de campos definida na borda do espaço-tempo de Gauss-Bonnet AdS d-dimensional. Apresentamos a derivação das soluções das p-branas negras, bem como a análise de sua estrutura causal. Revisamos o regime perturbativo da Relatividade Geral e a interpretação dos modos quasinormais de um buraco negro em termos dos elementos que compõem a correspondência AdS/CFT. Estudamos a evolução de um campo escalar sem massa na geometria das p-branas negras em detalhe, sendo que utilizamos o método semianalítico WKB e a integração característica (Problema de Goursat) para calcular as freqüências quasinormais correspondentes. Por fim, apresentamos uma expressão aproximada de um estado supercondutor na teoria de campos definida na borda do buraco negro de Gauss-Bonnet AdS através do dicionário AdS/CFT. / This thesis aims at studying the quasinormal frequencies of black p-branes using a scalar field in the probe limit. In the context of AdS/CFT correspondence we study some aspects regarding the formation of superconductor states in the field theory set on the AdS boundary of the Gauss-Bonnet AdS spacetime. We present the derivation of black p-brane solutions, as well as the analysis of its causal structure. We review the perturbative regime of General Relativity and the interpretation of the black hole quasinormal modes in terms of the correspondence AdS/CFT. We study the evolution of a massless scalar field in the geometry of black p-branes in detail, and we use the WKB method and the characteristic integration (Goursats problem) in order to calculate the corresponding quasinormal frequencies. Ultimately, we present an approximate expression for a superconductor state in the field theory defined in the AdS boundary of Gauss-Bonnet AdS spacetime.

Dans cette thèse, nous présentons des avancements récents en Théorie des Champs Doubles (TCD) et Théories des Champs Exceptionnels (TCE). Ces théories ont la particularité d’être des reformulations de supergravité dans lesquelles les symétries de dualité sont explicites avant toute réduction dimensionnelle. Ces reformulations se basent sur la définition d’un espace-temps étendu qui géométrise le groupe de T-dualité en TCD et les groupes exceptionnels de U-dualité en TCE. Tous les champs de cet espace sont soumis à une contrainte de section qui restreint leur dépendance en coordonnées. Il existe plusieurs solutions à la contrainte de section, qui correspondent donc à des théories différentes. Dans ce sens, le formalisme des théories des champs étendues amène à une unification de ces théories. De plus, grâce à un outil spécifique aux théories des champs étendues, l’ansatz de Scherk-Schwarz généralisé, il est possible de réécrire les ansatz compliqué de type Kaluza-Klein en supergravité sous une forme élégante et compacte: un produit matriciel en dimensions supérieures. Ici, nous présentons plusieurs exemples de l’efficacité de l’ansatz de Scherk-Schwarz généralisé. En particulier, nous prouvons deux conjectures concernant les troncations cohérentes: la réduction dite “de Pauli” de la corde bosonique ainsi que la supergravité de type IIB sur AdS5 x S5. La dernière application de cet ansatz concerne la théorie de type IIB généralisée, apparue récemment dans l’étude des système intégrables, et son plongement dans la TCE E6(6). Enfin, nous présentons la complétion supersymétrique de la TCE E8(8) bosonique. / In this thesis, recent developments in Double Field Theory (DFT) and Exceptional Field Theory (EFT) are presented. They are reformulation of supergravity in which duality symmetries are made manifest before dimensional reduction. This is achieved through the definition of an extended spacetime that “geometrises” the T-duality group O(d,d) in DFT and exceptional U-duality groups in EFT. All functions on this extended space are subject to a covariant `section constraint', whose solutions then restrict the coordinates dependency of the fields. There exist different solutions to the section constraint that correspond to different theories. In this sense, different theories are unified within the formalism of extended field theories. Moreover, extended field theories possess a powerful tool to study compactifications: the generalised Scherk-Schwarz ansatz.Here, we present several examples of the effectiveness of the generalised Scherk-Schwarz ansatz. In particular, we proved two conjectures regarding consistent truncations: the so-called Pauli reduction of the bosonic string on group manifolds and type IIB supergravity on AdS5 x S5. Another application is presented on the embedding of generalised type IIB within the E6(6) EFT, which recently appeared in the study of integrable systems.Finally, we present the supersymmetric completion of the bosonic E8(8) EFT.

The maintenance and updating of Statistics Austria's business register requires a regularly matching of the register against other data sources; one of them is the register of tax units of the Austrian Federal Ministry of Finance. The matching process is based on string comparison via bigrams of enterprise names and addresses, and a quality class approach assigning pairs of register units into classes of different compliance (i.e., matching quality) based on bigram similarity values and the comparison of other matching variables, like the NACE code or the year of foundation. Based on methodological research concerning matching techniques carried out in the DIECOFIS project, an empirical comparison of the bigram method and other string matching techniques was conducted: the edit distance, the Jaro algorithm and the Jaro-Winkler algorithm, the longest common subsequence and the maximal match were selected as appropriate alternatives and evaluated in the study. This paper briefly introduces Statistics Austria's business register and the corresponding maintenance process and reports on the results of the empirical study.

We present comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon electric and magnetic form factors. The lattice QCD estimates of strange quark magnetic moment GsM (0) = −0.064(14)(09) μN and the mean squared charge radius ⟨r2s⟩E = −0.0043(16)(14) fm2 are more precise than any existing experimental measurements and other lattice calculations. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light-sea and strange quarks contribution to the nucleon magnetic moment is−0.022(11)(09) μN and to the nucleon mean square charge radius is −0.019(05)(05) fm2. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about 1%, a negative 2.5(9)% contribution to the proton charge radius and a relatively larger positive 16.3(6.1)% contribution to the neutron charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light-sea and strange quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of 0 ≤ Q2 ≤ 0.5 GeV2.

This thesis consists of four papers on the topics of free loop spaces, Koszul duality and A∞-algebras.  In Paper I we consider a definition of differential operators for noncommutative algebras. This definition is inspired by the connections between differential operators of commutative algebras, L∞-algebras and BV-algebras. We show that the definition is reasonable by establishing results that are analoguous to results in the commutative case. As a by-product of this definition we also obtain definitions for noncommutative versions of Gerstenhaber and BV-algebras.  In Paper II we calculate the free loop space homology of (n-1)-connected manifolds of dimension of at least 3n-2. The Chas-Sullivan loop product and the loop bracket are calculated. Over a field of characteristic zero the BV-operator is determined as well. Explicit expressions for the Betti numbers are also established, showing that they grow exponentially.  In Paper III we restrict our coefficients to a field of characteristic 2. We study the Dyer-Lashof operations that exist on free loop space homology in this case. Explicit calculations are carried out for manifolds that are connected sums of products of spheres.  In Paper IV we extend the Koszul duality methods used in Paper II by incorporating A∞-algebras and A∞-coalgebras. This extension of Koszul duality enables us to compute free loop space homology of manifolds that are not necessarily formal and coformal. As an example we carry out the computations for a non-formal simply connected 7-manifold. / Denna avhandling består av fyra artiklar inom ämnena fria öglerum, Koszuldualitet och A∞-algebror. I Artikel I behandlar vi en definition av differentialoperatorer för ickekommutativa algebror. Denna definition är inspirerad av kopplingar mellan differentialoperatorer för kommutativa algebror, L∞-algebror och BV-algebror. Vi visar att definitionen är rimlig genom att etablera resultat som är analoga med resultat i det kommutativa fallet. Som en biprodukt får vi också definitioner för ickekommutativa varianter av Gerstenhaber och BV-algebror. I Artikel II beräknar vi den fria öglerumshomologin av (n-1)-sammanhängande mångfalder av dimension minst 3n-2. Chas-Sullivans ögleprodukt och öglehake beräknas. Över en kropp av karakteristik noll beräknas även BV-operatorn. Explicita uttryck för Bettitalen fastställs också, vilka visar att de växer exponentiellt. I Artikel III begränsar vi koefficienterna till en kropp av karakteristik 2. Vi studerar Dyer- Lashofoperationer som existerar på den fria öglerumshomologin i detta fall. Explicita beräkningar görs för mångfalder som är sammanhängande summor av produkter av sfärer. I Artikel IV utvidgar vi Koszuldualitetmetoden som används i Artikel II genom att inkorporera A∞-algebror och A∞-koalgebror. Denna utvidgning av Koszuldualitet gör det möjligt att beräkna fri öglerumshomologi för mångfalder som inte nödvändigtvis är formella och koformella. Som ett exempel utför vi beräkningar för en ickeformell enkelt sammanhängande 7-mångfald. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.</p>