Tesis sobre el tema "Géométrie du cordon"
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Cassani, Davide. "Théorie des cordes, compactifications avec flux et géométrie généralisée". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00409105.
Texto completoNous commençons en introduisant les outils mathématiques nécessaires: nous nous concentrons sur les structures SU(3)xSU(3) sur le fibré tangent généralisé T+T*, en analysant leurs déformations. Ensuite nous étudions la théorie de supergravité N=2 quadri-dimensionnelle définie par réduction des théories de type II sur des fonds à structure SU(3)xSU(3) avec flux généraux de NSNS et RR: nous établissons l'action bosonique complète, et nous montrons comment ces donées sont reliées au formalisme de la géométrie généralisée sur T+T*. En particulier, nous trouvons une expression géométrique pour le potentiel scalaire N=2. Puis nous nous concentrons sur les relations entre les descriptions à 10d et à 4d des fonds supersymétriques avec flux: nous dérivons les conditions de vide N=1 dans la théorie N=2 à 4d, ainsi que dans sa troncation N=1, et nous prouvons une correspondance précise avec les équations qui caractérisent les vides N=1 au niveau dix-dimensionnel. Nous terminons en présentant des exemples concrets, basés sur des espaces quotients avec structure SU(3). Nous établissons pour ces espaces la cohérence de la troncation basée sur l'invariance gauche, et nous explorons les vides de la théorie associée, en prenant en compte les corrections des boucles des cordes.
De, Felice Oscar. "Solutions avec flux et géométrie généralisée exceptionnelle". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS041/document.
Texto completoThe main topic of this thesis are flux compactifications. Firstly, we study dimensional reductions of type II and eleven-dimensional supergravities using exceptional generalised geometry. We start by presenting the needed mathematical tools, focusing on G-structures and their extension to generalised geometry. Then, we move our focus on compactifications. In particular, we mainly focus on type IIA, building the version of exceptional generalised geometry adapted to such supergravity and finding the right deformations of generalised Lie derivative to accomodate the Romans mass. We describe the generalised Scherk-Schwarz method to find consistent truncation ansatze preserving the maximal amount of supersymmetry. We apply such a method to several examples of truncations on spheres, we reproduce the truncation ansatz on S6 and the embedding tensor leading to dyonically gauged ISO(7) supergravity in four dimensions. For spheres of dimension d = 2; 3; 4, we find an obstruction to have generalised parallelisations in massive theory, giving the evidence that maximally supersymmetric reductions might not exist. As further point, we study generalised calibrations on AdS backgrounds in type IIB and M-theory. We find these are described by Exceptional Sasaki-Einstein structures and we place the focus on the generalised Reeb vectors. The inequalities for the energy bound are derived by decomposing a _-symmetry condition and equivalently, bispinors in calibration conditions from existing literature. We explain how the closure of the calibration forms is related to the integrability conditions of the Exceptional Sasaki- Einstein structure, in particular for AdS space-filling or point-like branes. Doing so, we show that the form parts of the twisted vector structure in M-theory provides the expected generalised calibrations. The IIB case yields similar results
Wang, Zeya. "Robotisation de la fabrication additive par procédé arc-fil : Identification et amélioration de la commande". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0068.
Texto completoAdditive manufacturing of metallic parts has gained significant popularity in recent years as an important technological solution for the production of complex parts. Among the different processes of metal additive manufacturing, the wire-arc additive manufacturing (WAAM) using CMT (Cold metal transfer) welding is taken for our study because of its high deposition rate, low cost of equipment and little loss of material (low spatter) during manufacturing. In the literature review, it can be noted that one of the most important problems that prevent the industrial application of the WAAM is the poor geometric accuracy of the manufactured parts due to the instability of the process and the lack of reliable control system to deal with irregularities during deposition. The focus of this work is to improve the stability and geometric performance of the process. In this work, an experimental system is implemented to robotize the process and to monitor the geometry of the deposited parts. The process is modeled by artificial neural networks and a control system is developed to regulate the geometry of the deposit and to reduce manufacturing errors. Furthermore, an improvement strategy is applied in order to reduce the geometric instabilities at the ends of the bead; an in-situ monitoring method is also developed to detect the internal defects of deposited parts
Andriot, David. "Solutions avec flux de la théorie des cordes sur tores twistés, et Géométrie Complexe Généralisée". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00497172.
Texto completoBorot, Gaetan. "Quelques problèmes de géométrie énumérative, de matrices aléatoires, d'intégrabilité, étudiés via la géométrie des surfaces de Riemann". Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00625776.
Texto completoBorot, Gaëtan. "Quelques problèmes de géométrie énumérative, de matrices aléatoires, d'intégrabilité, étudiés via la géométrie des surfaces de Riemann". Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112092/document.
Texto completoComplex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory, … All these topics share certain relations, called "loop equations" or "Virasoro constraints". In the simplest case, the complete solution of those equations was found recently : it can be expressed in the framework of differential geometry over a certain Riemann surface which depends on the problem : the "spectral curve". This thesis is a contribution to the development of these techniques, and to their applications.First, we consider all order large N asymptotics in some N-dimensional integrals coming from random matrix theory, or more generally from "log gases" problems. We shall explain how to use loop equations to establish those asymptotics in beta matrix models within a one cut regime. This can be applied in the study of large fluctuations of the maximum eigenvalue in beta matrix models, and lead us to heuristic predictions about the asymptotics of Tracy-Widom beta law to all order, and for all positive beta. Second, we study the interplay between integrability and loop equations. As a corollary, we are able to prove the previous prediction about the asymptotics to all order of Tracy-Widom law for hermitian matrices.We move on with the solution of some combinatorial problems in all topologies. In topological string theory, a conjecture from Bouchard, Klemm, Mariño and Pasquetti states that certain generating series of Gromov-Witten invariants in toric Calabi-Yau threefolds, are solutions of loop equations. We have proved this conjecture in the simplest case, where those invariants coincide with the "simple Hurwitz numbers". We also explain recent progress towards the general conjecture, in relation with our work. In statistical physics on the random lattice, we have solved the trivalent O(n) model introduced by Kostov, and we explain the method to solve more general statistical models.Throughout the thesis, the computation of some "generalized matrices integrals" appears to be increasingly important for future applications, and this appeals for a general theory of loop equations
Orsi, Francesco. "Etude des vides de la théorie des cordes avec flux". Paris 7, 2012. http://www.theses.fr/2012PA077025.
Texto completoThis thesis revolves around investigating some aspects of both supersymmetric and non- supersymmetric flux vacua of type II string theory. After providing the relevant definition of a vacuum in this setting, the framework of Generalized Complex Geometry is exposed: we review in particular the differential conditions for vacua in the presence of fluxes in this language, and we discuss their relation to integrabi-lity of the associated structures. We then survey a natural extension able to include the whole flux con¬tent into a geometrical picture, known as Exceptional Generalized Geometry. Fluxes are recovered in this context as a twisting of the Levi-Civita operator, from which a set of differential equations for the relevant algebraic structures is derived. These are carefully compared with the known supersymmetric constraints that a vacuum should satisfy in both cases of N =1,2 supersymmetries. Motivated by the application of the AdS/CFT correspondence with a reduced amount of supercharges, we obtain an effective five-dimensional supersymmetric theory, and we demonstrate in particular how a specific ansatz largely used in the string theory literature can be naturally embedded in it. We then investigate the su-pergravity dual to a metastable supersymmetry-breaking state by considering the most general first- order deformations of a supersymmetric solution, in order to single out the backreaction of anti-D2 branes. We conclude that unavoidable infrared singularities arise in view of the presence of anti-D2 branes per-turbing the underlying supersymmetric background
Pasqualini, Olivier. "Éléments finis stochastiques étendus pour le calcul en fatigue de joints soudés avec géométries aléatoires". Nantes, 2013. http://www.theses.fr/2013NANT2090.
Texto completoWelded joints are essential components for the construction of various fixed or floating structures. These elements are so important that we need to fully understand the fatigue process in order to foresee the structural behaviour under cyclic loading. The fatigue lifetime computation of a welded joint depends of various parameters such as the geometry of the structure. The stress concentration factor computation Kt is an efficient key parameter to model the fatigue lifetime. It has the advantage to link theoretical stress with the maximum value of local stresses and so with the fatigue lifetime thanks to S-N curves. In order to compute the Kt coefficient from real data and their uncertainties, some measurements along welded joints were realized by using a Non-Destructive Control device with laser process measurement. A statistical analysis of these measures were carried out to model the geometrical parameters by random variables and to identify their probability distribution. Kt-computation were performed by using eXtended Stochastic Finite Element Method; this computation method combines the Stochastic Finite Element Method, efficient to solve problems governed by random physical inputs, and the XFEM, efficient to implicitly define the domain geometry by using level-sets. In particular, we use a non-intrusive method of least-square computation to carry out, with a few numbers of random values, a Kt formulation defined on Polynomial Chaos base. From these results, an original semi-probabilistic model is suggested which introduces the geometrical parameters
Orantin, Nicolas. "Du développement topologique des modèles de matrices à la théorie des cordes topologiques : combinatoire de surfaces par la géométrie algébrique". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00173162.
Texto completoje montre que pour un choix particulier des paramètres, ces objets peuvent être rendus invariants modulaires et sont solutions des équations d'anomalie holomorphe de la théorie de Kodaira-Spencer donnant un nouvel élément vers la preuve de la conjecture de Dijkgraaf-Vafa.
Bordalo, Pedro. "Cordes et champs antisymétriques dans des espaces-temps courbes". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2004. http://tel.archives-ouvertes.fr/tel-00008396.
Texto completoNFidanza, Stéphane. "Rôle(s) du champ de fond antisymétrique en théorie des cordes". Palaiseau, Ecole polytechnique, 2003. https://pastel.archives-ouvertes.fr/pastel-00000709.
Texto completoCassani, Davide. "String theory compactifications with fluxes, and generalized geometry". Paris 6, 2009. https://tel.archives-ouvertes.fr/tel-00409105.
Texto completoAndriot, David. "String theory flux vacua on twisted tori and generalized complex geometry". Paris 6, 2010. http://www.theses.fr/2010PA066144.
Texto completoVey, Dimitri. "Multisymplectic gravity". Paris 7, 2012. http://www.theses.fr/2012PA077261.
Texto completoRThis thesis is contributed to the topic of modern Mathematical Physics differential Geometry in General Relativity, more exactly, to a study of the multisymplectic geometry approach in formulation of various examples of gauge theories, including theory of gravitation. The multisymplectic geometry provides a geometrical framework to formulate classical field theory in a coordinate free manner on arbitrary space-time manifold. Main idea is to construct a Hamiltonian description of classical fields theory compatible with, Principles of special and general relativity and string theories and more generally any effort towards understanding gravitation. Since space¬time should merge out from the dynamics. We need a description without any space-time/field splitting a priori. There is no space-time structure given a priori. Space-time coordinates should merge out from the analysis of what are the observable quantities and from the dynamics
Ntokos, Praxitelis. "Flux backgrounds, AdS/CFT and Generalized Geometry". Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066206/document.
Texto completoThe search for string theory vacuum solutions with non-trivial fluxes is of particular importance for the construction of models relevant for particle physics phenomenology. In the framework of the AdS/CFT correspondence, four-dimensional gauge theories which can be considered to descend from N = 4 SYM are dual to ten- dimensional field configurations with geometries having an asymptotically AdS_5 factor. In this Thesis, we study mass deformations that break supersymmetry (partially or entirely) on the field theory side and which are dual to type IIB backgrounds with non-zero fluxes on the gravity side. The supergravity equations of motion constrain the parameters on the gauge theory side to satisfy certain relations. In particular, we find that the sum of the squares of the boson masses should be equal to the sum of the squares of the fermion masses, making these set-ups problematic for phenomenology applications. The study of the supergravity duals for more general deformations of the conformal field theory requires techniques which go beyond the standard geometric tools. Exceptional Generalized Geometry provides a very elegant way to incorporate the supergravity fluxes in the geometry. We study AdS_5 backgrounds with generic fluxes preserving eight supercharges and we show that these satisfy particularly simple relations which admit a geometrical interpretation in the framework of Generalized Geometry. This opens the way for the systematic study of supersymmetric marginal deformations of the conformal field theory in the context of AdS/CFT
Tourkine, Piotr. "Results in perturbative quantum supergravity from string theory". Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066295/document.
Texto completoSupergravity theories are supersymmetric extensions of General Relativity (GR). They have a better ultraviolet (UV) behavior than GR, due to cancellations between bosons and fermions in loop diagrams. Maximal supergravity is a candidate for a UV finite point-like theory of quantum gravity. Nowadays, the most advanced understanding coming from field theory and string theory indicate that the theory should not be UV finite, and that the first UV divergences should appear at the 7-loop order. This open question constitutes a background in which my PhD thesis can be problematized.In this thesis, our approach consists in using string theory scattering amplitudes and study their point-like limit, in which supergravity amplitudes are expected to be recovered. Very little is known beyond one loop on this limit and in this manuscript I describe first how a recent field of mathematics, tropical geometry, may be used in this process, and mention some applications and open issues.Another way to cross-check the predictions of string theory on the UV behavior of maximal supergravity consists in performing the same analysis in theories of reduced supersymmetry.I discuss the case of half-maximal supergravity theories, and show a non-renormalization theorem in heterotic string which explains the vanishing of the 3-loop divergence of this theory and predicts a 4-loop divergence.The last aspect of my work is focused on a string theoretic understanding on the techniques used in field theory to compute higher loop amplitudes. I describe the first analysis of the so called BCJ double copy construction at one-loop from string theory, and partly explain the origin of the BCJ prescription
Prins, Daniël. "On flux vacua, SU(n)-structures and generalised complex geometry". Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10174/document.
Texto completoUnderstanding supersymmetric flux vacua is essential in order to connect string theory to observable physics. In this thesis, flux vacua are studied by making use of two mathematical frameworks: SU(n)-structures and generalised complex geometry. Manifolds with $SU(n)$ structure are generalisations of Calabi-Yau manifolds. Generalised complex geometry is a geometrical framework that simultaneously generalises complex and symplectic geometry. Classes of flux vacua of type II supergravity and M-theory are given on manifolds with SU(4) structure. The N = (1,1) type IIA vacua uplift to N=1 M-theory vacua, with four-flux that need not be (2,2) and primitive. Explicit vacua are given on Stenzel space, a non-compact Calabi Yau. These are then generalised by constructing families of non-CY SU(4)-structures to find vacua on non-symplectic SU(4)-deformed Stenzel spaces. It is shown that the supersymmetry conditions for N = (2,0) type IIB can be rephrased in the language of generalised complex geometry, partially in terms of integrability conditions of generalised almost complex structures. This rephrasing for d=2 goes beyond the calibration equations, in contrast to d=4,6 where the calibration equations are equivalent to supersymmetry. Finally, Euclidean type II theory is examined on SU(5)-structure manifolds, where generalised equations are found which are necessary but not sufficient to satisfy the supersymmetry equations. Explicit classes of solutions are provided here as well. Contact with Lorentzian physics can be made by uplifting such solutions to d=1, N = 1 M-theory
Metzger, Steffen. "Supersymmetric Gauge Theories from String Theory". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2005. http://tel.archives-ouvertes.fr/tel-00011979.
Texto completoDans une première partie nous étudions la construction d'une théorie Yang-Mills supersymétrique, couplée à un superchamp chiral dans la représentation adjointe, à partir de la théorie des cordes de type IIB sur une variété Calabi-Yau non compacte, avec des D-branes qui enroulent certaines sousvariétés. Les propriétés de
la théorie de jauge sont alors reflétées dans la structure
géométrique de la variété Calabi-Yau. En particulier, on peut calculer en principe le superpotentiel effectif de basse énergie qui décrit la structure des vides de la théorie de jauge en utilisant la théorie des cordes (topologiques). Malheureusement, en pratique, ceci n'est pas faisable. Il est remarquable qu'on puisse cependant montrer que la dynamique de basse énergie de la
théorie de jauge est codée par la géométrie d'une autre variété Calabi-Yau non compacte, reliée à la première par une transition géométrique. La théorie des cordes de type IIB sur cette deuxième variété, dans laquelle sont allumés des flux de fond appropriés, génère une théorie de jauge en quatre dimensions, qui n'est d'autre que la théorie effective de basse énergie de la théorie de
jauge originale. Ainsi, pour obtenir le superpotentiel effectif de basse énergie il suffit simplement de calculer certaines intégrales dans la deuxième géométrie Calabi-Yau, ce qui est faisable, au moins perturbativement. On trouve alors que le problème extrêmement difficile d'étudier la dynamique de basse
énergie d'une théorie de jauge non Abelienne a été réduit à celui de calculer certaines intégrales dans une géométrie connue. On peut démontrer que ces intégrales sont intimement reliées à certaines quantités dans un modèle de matrices holomorphes, et on peut alors calculer le superpotentiel effectif comme fonction de
certaines expressions du model de matrices. Il est remarquable que la série perturbative du modèle de matrices calcule alors le superpotentiel effectif non-perturbatif.
Ces relations étonnantes ont été découvertes et élaborée par plusieurs auteurs au cours des dernières années. Les résultats originaux de cette thèse comprennent la forme précise des relations de la ``géométrie spéciale" sur une variété Calabi-Yau
non compacte. Nous étudions en détail comment ces intégrales géométriques dépendent du cut-off, et leur relation à l'énergie libre du modèle de matrices. En particulier, sur une variété Calabi-Yau non compacte nous proposons une forme bilineaire sur le
produit direct de l'espace des formes avec l'espace des cycles, qui élimine toutes les divergences, sauf la divergence logarithmique. Notre analyse détaillée du modèle de matrices holomorphes clarifie aussi plusieurs aspects reliés à la méthode du col de ce modèle de matrices. Nous montrons en particulier qu'exiger une densité spectrale réelle restreint la forme de la
courbe Riemannienne qui apparaît dans la limite planaire du modèle de matrices. Çela nous donne des contraintes sur la forme du contour sur lequel les valeurs propres sont intégrées. Tous ces
résultats sont utilisés pour calculer explicitement l'énergie libre planaire d'un modèle de matrices avec un potentiel cubique.
La deuxième partie de cette thèse concerne la génération de théories de jauge supersymétriques en quatre dimensions comportant des aspects caractéristiques du modèle standard à partir de
compactifications de la supergravité en onze dimensions sur une variété G_2. Si cette variété contient une singularité conique, des fermions chiraux apparaissent dans la théorie de jauge en quatre dimensions ce qui conduit potentiellement à des anomalies. Nous montrons que, localement à chaque singularité, les anomalies
correspondantes sont annulées par une non-invariance de l'action classique au singularités (``anomaly inflow"). Malheureusement, aucune métrique d'une variété G_2 compacte n'est connue explicitement. Nous construisons ici des familles de métriques sur des variétés compactes faiblement G_2, qui contiennent deux singularités coniques. Les variétés faiblement G_2 ont des propriétés semblables aux propriétés des variétés G_2, et alors ces exemples explicites pourraient être utiles pour mieux comprendre la situation générique. Finalement, nous regardons la
relation entre la supergravité en onze dimensions et la théorie des cordes hétérotiques E_8\times E_8. Nous étudions en détail les anomalies qui apparaissent si la supergravité est formulée sur le produit d'un espace de dix dimensions et un intervalle. Encore une fois nous trouvons que les anomalies s'annulent localement sur
chaque bord de l'intervalle si on modifie l'action classique d'une façon appropriée.
Olivier, Marchal. "Aspects géométriques et intégrables des modèles de matrices aléatoires". Phd thesis, 2010. http://tel.archives-ouvertes.fr/tel-00863625.
Texto completoMarchal, Olivier. "Aspects géométriques et intégrables des modèles de matrices aléatoires". Thèse, 2010. http://hdl.handle.net/1866/6861.
Texto completoThis thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to ``quantum algebraic geometry'' and to the generalization of symplectic invariants to ``quantum curves''. Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold. Since the range of the applications encountered is large, we try to present every domain in a simple way and explain how random matrix models can bring new insights to those fields. The common element of the thesis being matrix models, each part has been written so that readers unfamiliar with the domains of application but familiar with matrix models should be able to understand it.
Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard.