Die maximal supersymmetrische Yang-Mills-Theorie im vierdimensionalen Minkowski-Raum ist ein außergewöhnliches Modell der mathematischen Physik. Dies gilt vor allem im planaren Limes, in dem die Theorie integrabel zu sein scheint. So sind etwa ihre Streuamplituden auf Baumgraphenniveau Invarianten einer Yangschen Algebra, die die superkonforme Algebra psu(2,2|4) beinhaltet. Diese unendlichdimmensionale Symmetrie ist ein Kennzeichen für Integrabilität. In dieser Dissertation untersuchen wir Verbindungen zwischen solchen Amplituden und integrablen Modellen, um Grundlagen für eine effiziente, auf der Integrabilität basierende Berechnung von Amplituden zu legen. Dazu charakterisieren wir Yangsche Invarianten innerhalb der Quanten-Inverse-Streumethode, die Werkzeuge zur Behandlung integrabler Spinketten bereitstellt. In diesem Rahmen entwickeln wir Methoden zur Konstruktion Yangscher Invarianten. Wir zeigen, dass der algebraische Bethe-Ansatz für die Erzeugung von Yangschen Invarianten für u(2) anwendbar ist. Die zugehörigen Bethe-Gleichungen lassen sich leicht lösen. Unser Zugang erlaubt es zudem diese Invarianten als Zustandssummen von Vertexmodellen zu interpretieren. Außerdem führen wir ein unitäres Graßmannsches Matrixmodell zur Berechnung Yangscher Invarianten mit Oszillatordarstellungen von u(p,q|m) ein. In einem Spezialfall reduziert es sich zu dem Brezin-Gross-Witten-Model. Wir wenden eine auf Bargmann zurückgehende Integraltransformation auf unser Matrixmodell an, welche die Oszillatoren in Spinor-Helizitäts-artige Variablen überführt. Dadurch gelangen wir zu einer Weiterentwicklung der Graßmann-Integralformulierung bestimmter Amplituden. Die maßgeblichen Unterschiede sind, dass wir in der Minkowski-Signatur arbeiten und die Integrationskontur auf die unitäre Gruppenmannigfaltigkeit festgelegt ist. Wir vergleichen durch unser Integral gegebene Yangsche Invarianten mit Amplituden und kürzlich eingeführten Deformationen derselben. / The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the tree-level scattering amplitudes were shown to be invariant under the Yangian of the superconformal algebra psu(2,2|4). This infinite-dimensional symmetry is a hallmark of integrability. In this dissertation we explore connections between these amplitudes and integrable models. Our aim is to lay foundations for an efficient integrability-based computation of amplitudes. To this end, we characterize Yangian invariants within the quantum inverse scattering method, which is an extensive toolbox for integrable spin chains. Making use of this setup, we develop methods for the construction of Yangian invariants. We show that the algebraic Bethe ansatz can be specialized to yield Yangian invariants for u(2). Our approach also allows to interpret these Yangian invariants as partition functions of vertex models. What is more, we establish a unitary Graßmannian matrix model for the construction of u(p,q|m) Yangian invariants with oscillator representations. In a special case our formula reduces to the Brezin-Gross-Witten model. We apply an integral transformation due to Bargmann to our unitary Graßmannian matrix model, which turns the oscillators into spinor helicity-like variables. Thereby we are led to a refined version of the Graßmannian integral formula for certain amplitudes. The most decisive differences are that we work in Minkowski signature and that the integration contour is fixed to be a unitary group manifold. We compare Yangian invariants defined by our integral to amplitudes and recently introduced deformations thereof.

Inspiriert von den integrablen Strukturen der schwach gekoppelten planaren N=4 Super-Yang-Mills-Theorie studieren wir Q-Operatoren und Yangsche Invarianten. Wir geben eine Übersicht der Quanten-Inverse-Streumethode zusammen mit der Yang-Baxter Gleichung welche zentral für diesen systematischen Zugang zu integrablen Modellen ist. Den Fokus richten wir auf rationale integrable Spinketten und Vertexmodelle. Wir besprechen einige ihrer bekannten Gemeinsamkeiten und wie sie durch Bethe-Ansatz-Methoden mit Hilfe sogenannter Q-Funktionen gelöst werden können. Der Hauptteil basiert auf den ursprünglichen Publikationen des Autors. Zuerst konstruieren wir Q-Operatoren, deren Eigenwerte zu den Q-Funktionen rationaler homogener Spinketten führen. Die Q-Operatoren werden als Spuren gewisser Monodromien von R-Operatoren eingeführt. Unsere Konstruktion erlaubt es uns die Hierarchie der kommutierenden Q-Operatoren und ihre funktionalen Beziehungen herzuleiten. Wir studieren wie der nächste-Nachbarn Hamiltonoperator, sowie höhere lokale Ladungen direkt aus den Q-Operatoren extrahiert werden können. Danach widmen wir uns der Formulierung der Yangschen Invarianzbedingung, wie sie auch im Zusammenhang mit Baumgraphen die bei der Berechnung von Streuamplituden in der N=4 Super-Yang-Mills-Theorie auftreten, innerhalb der RTT-Realisierung. Dies erlaubt es uns den algebraischen Bethe-Ansatz anzuwenden und die dazugehörigen Bethe Gleichungen herzuleiten, welche für die Konstruktion der Eigenzustände die Yangsche Invarianz aufweisen, relevant sind. Die Komponenten dieser Eigenzustände der von uns betrachteten Spinketten können außerdem als Zustandssummen gewisser zweidimensionaler Vertexmodelle angesehen werden. Zudem analysieren wir die Verbindung zwischen den Eigenzuständen und den oben genannten Baumgraphen. Schlussendlich diskutieren wir die von uns vorgelegten Ergebnisse und deren Folgen im Hinblick auf die Erforschung der planaren N=4 Super-Yang-Mills-Theorie. / Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method QISM along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author''s original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the functional relations among them. We study how the nearest-neighbor Hamiltonian and in principle also higher local charges can be extracted from the Q-operators directly. Secondly, we formulate the Yangian invariance condition, also studied in relation to scattering amplitudes of N=4 super Yang-Mills theory, in the RTT-realization. We find that Yangian invariants can be interpreted as special eigenvectors of certain inhomogeneous spin chains. This allows us to apply the algebraic Bethe ansatz and derive the corresponding Bethe equations that are relevant to construct the invariants. We examine the connection between the Yangian invariant spin chain eigenstates whose components can be understood as partition functions of certain two-dimensional lattice models and tree-level scattering amplitudes of the four-dimensional gauge theory. Finally, we conclude and discuss some future directions and implications of our studies for planar N=4 super Yang-Mills theory.

A study of the usage of ALICEs time of flight (TOF), time projection chamber (TPC), and electromagnetic calorimeter (EMCal), aiming at detecting and separating electrons and positrons (e±) originated from different sources, was carried out. To accomplish the objectives of the research, data gathered from the 2012 proton-proton (pp) collision experiment were used. At a center of mass energy of sqrt(s)=8TeV, the collision of the proton beams liberates heavy quarks, charm and bottom, with approximate lifetimes of approximately 10^13s and 10^12s, respectively. The e± generated through weak semileptonic heavy flavor decays are of interest for studying quarks, therefore it served solely as motivation and incentive for the research carried out and described herein. The introduction of carefully selected cuts, with the purpose of separating partial data collected in the three detectors, permitted the understanding of their effect on the results. Furthermore, due to the fact that the TOFs design was not meant to separate e± from the other heavier particles, only the general effects of introducing a simple cut in the beta=v/c values were analyzed. The more specific cuts were only used for the data generated by the events detected by the TPC and the EMCal. A combination of cuts based on the particles energy loss as a function of traveled distance (dE/dx), with the ratio of energy to momentum (E/p) of the particle, was adopted to enable the separation process, thus allowing for the isolation of e± from the other particles, namely pi±, K±, and p/p. The analysis was performed for values of total particle momentum in the range 0<=p<=6GeV/c. A comparison of the raw data with the results obtained by applying this procedure, indicated a substantial increase in the e± yield and efficiency, reaching average values above 90% over the entire momentum range. / Um estudo do uso dos detetores de tempo de voo (TDV), câmara de projeção de tempo (CPT), e calorímetro eletromagnético (CalEM) do ALICE, visando detectar elétrons e pósitrons (e±) originados por diferentes fontes, foi realizado. Para atingir os objetivos da pesquisa, dados coletados durante o experimento de colisões próton-próton em 2012 foram utilizados. Com um nível de enegia do centro de mass igual a raiz(s)=8TeV, a colisão dos feixes de prótons libera quarks pesados, charm e bottom, com tempo de vida de aproximadamente 10^13s e 10^12s, respectivamente. Os e± gerados pelo decaimento fraco semileptônico de sabores pesados é de interesse para o estudo dos quarks, portanto, o conceito serviu somente como motivação e incentivo para a pesquisa realizada e descrita nesta dissertação. A introdução de cortes específicos, com a finalidade de parcialmente separar dados coletados nos três detectores, permitiu adquirir entendimento sobre os efeitos do cortes nos resultados. Adicionalmente, em virtude do projeto do TDV não ter sido feito visando separar e± oriundos do decaimento dos sabores pesados das demais partículas mais massivas, somente os efeitos gerais de introduzir um corte simples nos valores de beta=v/c, foram analisados. Os cortes mais específicos foram somente nos dados detectados pelo CPT e pelo CalEM. Uma combinação de cortes baseados na perda de energia da partícula em função da distância percorrida (dE/dx), com a razão entre a energia e o momento da partícula (E/p), foi adotada para viabilizar o processo de separação, desta forma permitindo a separação dos e± das demais partículas, ou seja, dos pi±, K±, and p/p. A análise foi realizada para valores de momento total das partículas na faixa 0<=p<=6GeV/c. Uma comparação dos dados originais com os resultados obtidos pela aplicação do procedimento, indicou um aumento substancial do rendimento e eficiência dos e±, atingindo valores médios acima de 90% na faixa inteira de momento.

Das Zusammenspiel von Hadronen und Modifikationen ihrer Eigenschaften auf der einen Seite und spontaner chiraler Symmetriebrechung und Restauration auf der anderen Seite wird untersucht. Es werden die QCD Summenregeln für D und B Mesonen in kalter Materie berechnet. Wir bestimmen die Massenaufspaltung von D - D-bar und B - B-bar Mesonen als Funktion der Kerndichte und untersuchen den Einfluss verschiedener Kondensate in der Näherung linearer Dichteabhängigkeit. Die Analyse beinhaltet ebenfalls D_s und D^*_0 Mesonen. Es werden QCD Summenregeln für chirale Partner mit offenem Charmfreiheitsgrad bei nichtverschwindenden Nettobaryonendichten und Temperaturen vorgestellt. Es wird die Differenz sowohl von pseudoskalaren und skalaren Mesonen, als auch von Axialvektor- und Vektormesonen betrachtet und die entsprechenden Weinberg-Summenregeln hergeleitet. Basierend auf QCD Summenregeln werden die Auswirkungen eines Szenarios auf das rho Meson untersucht, in dem alle chiral ungeraden Kondensate verschwinden wohingegen die chiral symmetrischen Kondensate ihren Vakuumwert behalten. Die komplementären Folgerungen einer Massenverschiebung und Verbreiterung der rho Mesonanregung werden diskutiert. Ein alternativer Zugang basierend auf gekoppelten Dyson-Schwinger- und Bethe-Salpeter-Gleichungen für Quarkbindungszustände wird untersucht. Zu diesem Zwecke wird die analytische Struktur des Quarkpropagators in der komplexen Ebene numerisch untersucht und die Möglichkeit getestet die Anwendbarkeit auf den Sektor der schwer-leicht Quark Systeme im skalaren und pseudoskalaren Kanal, wie dem D Meson, durch Variation des Impulsteilungsparameters zu erweitern. Die Lösungen der Dyson-Schwinger-Gleichung in der Wigner-Weyl-Phase der chiralen Symmetrie bei nichtverschwindenden Stromquarkmassen wird benutzt um den Fall einer expliziten Symmetriebrechung ohne spontane Symmetriebrechung zu untersuchen. / The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D - D-bar and B - B-bar mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D_s and $D^*_0 mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the rho meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.

No description available.

A study of the usage of ALICEs time of flight (TOF), time projection chamber (TPC), and electromagnetic calorimeter (EMCal), aiming at detecting and separating electrons and positrons (e±) originated from different sources, was carried out. To accomplish the objectives of the research, data gathered from the 2012 proton-proton (pp) collision experiment were used. At a center of mass energy of sqrt(s)=8TeV, the collision of the proton beams liberates heavy quarks, charm and bottom, with approximate lifetimes of approximately 10^13s and 10^12s, respectively. The e± generated through weak semileptonic heavy flavor decays are of interest for studying quarks, therefore it served solely as motivation and incentive for the research carried out and described herein. The introduction of carefully selected cuts, with the purpose of separating partial data collected in the three detectors, permitted the understanding of their effect on the results. Furthermore, due to the fact that the TOFs design was not meant to separate e± from the other heavier particles, only the general effects of introducing a simple cut in the beta=v/c values were analyzed. The more specific cuts were only used for the data generated by the events detected by the TPC and the EMCal. A combination of cuts based on the particles energy loss as a function of traveled distance (dE/dx), with the ratio of energy to momentum (E/p) of the particle, was adopted to enable the separation process, thus allowing for the isolation of e± from the other particles, namely pi±, K±, and p/p. The analysis was performed for values of total particle momentum in the range 0<=p<=6GeV/c. A comparison of the raw data with the results obtained by applying this procedure, indicated a substantial increase in the e± yield and efficiency, reaching average values above 90% over the entire momentum range. / Um estudo do uso dos detetores de tempo de voo (TDV), câmara de projeção de tempo (CPT), e calorímetro eletromagnético (CalEM) do ALICE, visando detectar elétrons e pósitrons (e±) originados por diferentes fontes, foi realizado. Para atingir os objetivos da pesquisa, dados coletados durante o experimento de colisões próton-próton em 2012 foram utilizados. Com um nível de enegia do centro de mass igual a raiz(s)=8TeV, a colisão dos feixes de prótons libera quarks pesados, charm e bottom, com tempo de vida de aproximadamente 10^13s e 10^12s, respectivamente. Os e± gerados pelo decaimento fraco semileptônico de sabores pesados é de interesse para o estudo dos quarks, portanto, o conceito serviu somente como motivação e incentivo para a pesquisa realizada e descrita nesta dissertação. A introdução de cortes específicos, com a finalidade de parcialmente separar dados coletados nos três detectores, permitiu adquirir entendimento sobre os efeitos do cortes nos resultados. Adicionalmente, em virtude do projeto do TDV não ter sido feito visando separar e± oriundos do decaimento dos sabores pesados das demais partículas mais massivas, somente os efeitos gerais de introduzir um corte simples nos valores de beta=v/c, foram analisados. Os cortes mais específicos foram somente nos dados detectados pelo CPT e pelo CalEM. Uma combinação de cortes baseados na perda de energia da partícula em função da distância percorrida (dE/dx), com a razão entre a energia e o momento da partícula (E/p), foi adotada para viabilizar o processo de separação, desta forma permitindo a separação dos e± das demais partículas, ou seja, dos pi±, K±, and p/p. A análise foi realizada para valores de momento total das partículas na faixa 0<=p<=6GeV/c. Uma comparação dos dados originais com os resultados obtidos pela aplicação do procedimento, indicou um aumento substancial do rendimento e eficiência dos e±, atingindo valores médios acima de 90% na faixa inteira de momento.

Face au déluge actuel de données principalement non structurées, les graphes ont démontré, dans une variété de domaines scientifiques, leur importance croissante comme language abstrait pour décrire des interactions complexes entre des objets complexes. L’un des principaux défis posés par l’étude de ces réseaux est l’inférence de propriétés macroscopiques à grande échelle, affectant un grand nombre d’objets ou d’agents, sur la seule base des interactions microscopiquesqu’entretiennent leurs constituants élémentaires. La physique statistique, créée précisément dans le but d’obtenir les lois macroscopiques de la thermodynamique à partir d’un modèle idéal de particules en interaction, fournit une intuition décisive dans l’étude des réseaux complexes.Dans cette thèse, nous utilisons des méthodes issues de la physique statistique des systèmes désordonnés pour mettre au point et analyser de nouveaux algorithmes d’inférence sur les graphes. Nous nous concentrons sur les méthodes spectrales, utilisant certains vecteurs propres de matrices bien choisies, et sur les graphes parcimonieux, qui contiennent une faible quantité d’information. Nous développons une théorie originale de l’inférence spectrale, fondée sur une relaxation de l’optimisation de certaines énergies libres en champ moyen. Notre approche est donc entièrement probabiliste, et diffère considérablement des motivations plus classiques fondées sur l’optimisation d’une fonction de coût. Nous illustrons l’efficacité de notre approchesur différents problèmes, dont la détection de communautés, la classification non supervisée à partir de similarités mesurées aléatoirement, et la complétion de matrices. / In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges arising in the study of such networks is the inference of macroscopic, large-scale properties affecting a large number of objects, based solely on he microscopic interactions between their elementary constituents. Statistical physics, precisely created to recover the macroscopic laws of thermodynamics from an idealized model of interacting particles, provides significant insight to tackle such complex networks.In this dissertation, we use methods derived from the statistical physics of disordered systems to design and study new algorithms for inference on graphs. Our focus is on spectral methods, based on certain eigenvectors of carefully chosen matrices, and sparse graphs, containing only a small amount of information. We develop an original theory of spectral inference based on a relaxation of various meanfield free energy optimizations. Our approach is therefore fully probabilistic, and contrasts with more traditional motivations based on the optimization of a cost function. We illustrate the efficiency of our approach on various problems, including community detection, randomized similarity-based clustering, and matrix completion.

Cette thèse a pour objet l'étude de l'interaction laser-matière dans un régime d'éclairement extrême que visent à atteindre plusieurs installations multi-pétawatt en cours de développement (CILEX-Apollon, ELI, IZEST, etc.). Pour un éclairement supérieur à 1022 Wcm-2, la dynamique relativiste des électrons accélérés dans l'onde laser est modiée par un important rayonnement Compton inverse non-linéaire. Au-delà de 1023 Wcm2, les photons ainsi produits peuvent, en interagissant à leur tour avec le champ laser, se désintégrer en paires électron-positron via le mécanisme de Breit-Wheeler non-linéaire. Ces mécanismes d'électrodynamique quantique, dont l'étude expérimentale était jusqu'ici l'apanage des grands accélérateurs de particles, peuvent grandement affecter les mécanismes usuels d'interaction laser-plasma, notamment ceux régissant l'accélération de particules chargées et, par conséquent, le bilan global de l'interaction. Afin de modéliser ce régime inédit d'interaction, qui combine processus collectifs, relativistes et d'électrodynamique quantique, nous avons enrichi des mécanismes précédents le code de simulation particle-in-cell calder développé de longue date au CEA/DIF. L'influence de ces mécanismes est d'abord explorée dans le cas d'une impulsion laser interagissant avec une cible dense de taille micrométrique. Un rendement de conversion de l'énergie laser en photons supérieur à 10% est observée au-dessus de 1023 Wcm-2, tandis que la production d'anti-matière s'emballe, via un mécanisme de cascade, à partir de 1024 Wcm2. Dans un second temps, nous étudions la génération de positrons lors de la collision frontale entre un faisceau d'électrons ultra-relativistes issu d'un accélérateur plasma et une impulsion laser ultra-intense. Dans une dernière partie, nous considérons un scénario prospectif d'intérêt astrophysique, à savoir la collision de plasmas de paires issus de cibles solides irradiées à 1024 Wcm-2 montrant la croissance rapide d'une instabilité de lamentation magnétique combinée à d'intenses effets radiatifs. / This PhD thesis is concerned with the regime of extreme-intensity laser-matter interaction that should be accessed on upcoming multi-petawatt facilities (e.g. CILEX-Apollon, ELI, IZEST). At intensities IL > 1022 Wcm-2, the relativistic dynamics of the laser-driven electrons becomes significantly modified by high-energy radiation emission through nonlinear inverse Compton scattering. For IL > 1023 Wcm-2, the emitted-ray photons can, in turn, interact with the laser field and decay into electron-positron pairs via the nonlinear Breit-Wheeler process. These quantum electrodynamic processes, which until recently could only be explored on large-scale particle accelerators, can greatly alter the "standard" mechanisms of laser-plasma interaction, and therefore its overall energy budget. In order to model their intricate interplay with the laser-induced plasma processes, they have been implemented within the particle-in-cell code calder developed at CEA. In a first part, we study these QED processes in the interaction of an ultra-intense laser with a micrometric overdense target. It is found that the laser-to--ray energy conversion efficiency can by far exceed 10% for intensities IL > 1023 Wcm-2, while copious pair production (through pair cascading) kicks in for IL > 1024 Wcm-2. In a second part, we consider positron generation in the collision between a GeV electron bunch issued from a laser-wake eld accelerator and a counterpropagating laser pulse. In a third part, we analyze a prospective scheme of astrophysical interest, consisting in the collision between two dense pair plasmas produced from solid targets irradiated at 1024 Wcm-2 showing a fast-growing magnetic lamentation instability amplified by intense synchrotron emission.

Les comportements critiques des systèmes de mécanique statistique en 2 dimensions ou de mécanique quantique en 1+1 dimensions, ainsi que certains aspects des systèmes sans interactions en 2+1 dimensions, sont efficacement décrits par les méthodes de la théorie des champs conforme et de l'intégrabilité, dont le développement a été spectaculaire au cours des 40 dernières années. Plusieurs problèmes résistent cependant toujours à une compréhension exacte, parmi lesquels celui de la transition entre plateaux dans l'Effet Hall Quantique Entier. La raison principale en est que de tels problèmes sont généralement associés à des théories non unitaires, ou théories conformes logarithmiques, dont la classification se révèle être d'une grande difficulté mathématique. Se tournant vers la recherche de modèles discrets (chaînes de spins, modèles sur réseau), dans l'espoir en particulier d'en trouver des représentations en termes de modèles exactement solubles (intégrables), on se heurte à la deuxième difficulté représentée par le fait que les théories associées sont la plupart du temps non compactes, ou en d'autres termes qu'elles donnent lieu à un continuum d'exposants critiques. En effet, le lien entre modèles discrets et théories des champs non compactes est à ce jour loin d'être compris, en particulier il a longtemps été cru que de telles théories ne pouvaient pas émerger comme limites continues de modèles discrets construits à partir d'un ensemble compact de degrés de libertés, par ailleurs les seuls qui donnent a accès à une construction systématique de solutions exactes.Dans cette thèse, on montre que le monde des modèles discrets compacts ayant une limite continue non compacte est en fait beaucoup plus grand que ce que les quelques exemples connus jusqu'ici auraient pu laisser suspecter. Plus précisément, on y présente une solution exacte par ansatz de Bethe d'une famille infinie de modèles(les modèles $a_n^{(2)}$, ainsi que quelques résultats sur les modèles $b_n^{(1)}$, où il est observé que tous ces modèles sont décrits dans un certain régime par des théories conformes non compactes. Parmi ces modèles, certains jouent un rôle important dans la description de phénomènes physiques, parmi lesquels la description de polymères en deux dimensions avec des interactions attractives et des modèles de boucles impliqués dans l'étude de modèles de Potts couplés ou dans une tentative de description de la transition entre plateaux dans l'Effet Hall par un modèle géométrique compact.On montre que l'existence insoupçonnéede limite continues non compacts pour de tels modèles peut avoir d'importantes conséquences pratiques, par exemple dans l'estimation numérique d'exposants critiques ou dans le résultats de simulations de Monte Carlo. Nos résultats sont appliqués à une meilleure compréhension de la transition theta décrivant l'effondrement des polymères en deux dimensions, et des perspectives pour une potentielle compréhension de la transition entre plateaux en termes de modèles sur réseaux sont présentées. / The critical points of statistical mechanical systems in 2 dimensions or quantum mechanical systems in 1+1 dimensions (this also includes non interacting systems in 2+1 dimensions) are effciently tackled by the exact methods of conformal fieldtheory (CFT) and integrability, which have witnessed a spectacular progress during the past 40 years. Several problems have however escaped an exact understanding so far, among which the plateau transition in the Integer Quantum Hall Effect,the main reason for this being that such problems are usually associated with non unitary, logarithmic conformal field theories, the tentative classification of which leading to formidable mathematical dificulties. Turning to a lattice approach, andin particular to the quest for integrable, exactly sovable representatives of these problems, one hits the second dificulty that the associated CFTs are usually of the non compact type, or in other terms that they involve a continuum of criticalexponents. The connection between non compact field theories and lattice models or spin chains is indeed not very clear, and in particular it has long been believed that the former could not arise as the continuum limit of discrete models built out of acompact set of degrees of freedom, which are the only ones allowing for a systematic construction of exact solutions.In this thesis, we show that the world of compact lattice models/spin chains with a non compact continuum limit is much bigger than what could be expected from the few particular examples known up to this date. More precisely we propose an exact Bethe ansatz solution of an infinite family of models (the so-called $a_n^{(2)}$ models, as well as some results on the $b_n^{(1)}$ models), and show that all of these models allow for a regime described by a non compact CFT. Such models include cases ofgreat physical relevance, among which a model for two-dimensional polymers with attractive interactions and loop models involved in the description of coupled Potts models or in a tentative description of the quantum Hall plateau transition by somecompact geometrical truncation. We show that the existence of an unsuspected non compact continuum limit for such models can have dramatic practical effects, for instance on the output of numerical determination of the critical exponents or ofMonte-Carlo simulations. We put our results to use for a better understanding of the controversial theta transition describing the collapse of polymers in two dimensions, and draw perspectives on a possible understanding of the quantum Hall plateautransition by the lattice approach.

Das Zusammenspiel von Hadronen und Modifikationen ihrer Eigenschaften auf der einen Seite und spontaner chiraler Symmetriebrechung und Restauration auf der anderen Seite wird untersucht. Es werden die QCD Summenregeln für D und B Mesonen in kalter Materie berechnet. Wir bestimmen die Massenaufspaltung von D - D-bar und B - B-bar Mesonen als Funktion der Kerndichte und untersuchen den Einfluss verschiedener Kondensate in der Näherung linearer Dichteabhängigkeit. Die Analyse beinhaltet ebenfalls D_s und D^*_0 Mesonen. Es werden QCD Summenregeln für chirale Partner mit offenem Charmfreiheitsgrad bei nichtverschwindenden Nettobaryonendichten und Temperaturen vorgestellt. Es wird die Differenz sowohl von pseudoskalaren und skalaren Mesonen, als auch von Axialvektor- und Vektormesonen betrachtet und die entsprechenden Weinberg-Summenregeln hergeleitet. Basierend auf QCD Summenregeln werden die Auswirkungen eines Szenarios auf das rho Meson untersucht, in dem alle chiral ungeraden Kondensate verschwinden wohingegen die chiral symmetrischen Kondensate ihren Vakuumwert behalten. Die komplementären Folgerungen einer Massenverschiebung und Verbreiterung der rho Mesonanregung werden diskutiert. Ein alternativer Zugang basierend auf gekoppelten Dyson-Schwinger- und Bethe-Salpeter-Gleichungen für Quarkbindungszustände wird untersucht. Zu diesem Zwecke wird die analytische Struktur des Quarkpropagators in der komplexen Ebene numerisch untersucht und die Möglichkeit getestet die Anwendbarkeit auf den Sektor der schwer-leicht Quark Systeme im skalaren und pseudoskalaren Kanal, wie dem D Meson, durch Variation des Impulsteilungsparameters zu erweitern. Die Lösungen der Dyson-Schwinger-Gleichung in der Wigner-Weyl-Phase der chiralen Symmetrie bei nichtverschwindenden Stromquarkmassen wird benutzt um den Fall einer expliziten Symmetriebrechung ohne spontane Symmetriebrechung zu untersuchen. / The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D - D-bar and B - B-bar mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D_s and $D^*_0 mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the rho meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.