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abstract: Recent developments inspired by string theoretic considerations provide multiple maps between gravitational and non-gravitational degrees of freedom. In this dis- sertation I discuss aspects of three such dualities, the gauge/gravity duality and how it applies to condensed matter systems, the fluid-gravity duality, and the color-kinematics duality. The first of these, colloquially referred to as holography, in its simplest form posits a mapping of d-dimensional conformal field theory (boundary) partition functions onto d+1 dimensional gravitational(bulk) partition functions, where the space-time carries a negative cosmological constant. In this dissertation I discuss the results of our calculations examining the emergence of Fermi-surface like structures in the bulk spacetime despite the absence of explicit Fermions in the theory.Specifically the 4+1 dimensional Einstein-Maxwell-Chern-Simons theory with scalar degrees of freedom, with and without symmetry breaking is considered. These theories are gravity duals to spatially modulated gauge theories. The results of calculations presented here indicate the existence of a rich phase space, most prominently Fermi shells are seen. The second set of dualities considered are the color-kinematic duality, also known as the double-copy paradigm and the fluid-gravity duality. The color-kinematic duality involves identifying spin-2 amplitudes as squares of spin-1 gauge amplitudes. This double copy picture is utilized to construct “single copy” representations for space- times where Einstein’s equations reduce to incompressible Navier-Stokes equations. In this dissertation I show how spacetimes that characterize irrotational fluids and constant vorticity fluids each map to distinct algebraically special spacetimes. The Maxwell fields obtained via the double-copy picture for such spacetimes further provide interesting parallels, for instance, the vorticity of the fluid is proportional to the magnetic field of the associated gauge field. / Dissertation/Thesis / Doctoral Dissertation Physics 2020

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21561号 / 理博第4468号 / 新制||理||1641(附属図書館) / 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 福間 將文, 教授 田中 貴浩, 准教授 國友 浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23546号 / 情博第776号 / 新制||情||132(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 教授 太田 快人, 教授 永持 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

This thesis is devoted to the study of orientifolds and dynamical supersymmetry breaking in configurations of D-branes on toric Calabi-Yau singularities, through the lens of dimer models. We first review the basic ingredients of string theory that led to the formulation of gauge/gravity dualities in terms of dimers. Then, we discuss the non-abelian anomaly cancellation conditions for the supersymmetric gauge theories arising on D-branes and provide necessary geometric criteria to determine whether an orientifold projection can be safely introduced. We also find a new realization of orientifold projection without fixed loci in dimer models and expand on its physical features. We argue that it exhausts the possibilities of orientifolding dimer models. In the subsequent part of the thesis, we investigate dynamical supersymmetry breaking vacua in the same class of models and their typical instability along N=2 Coulomb branches. This leads us to formulate a no-go theorem against their stability based on geometrical features of the singularity, and then to establish a precise way to circumvent it. We eventually find the first instance of stable dynamical supersymmetry breaking vacuum in string theory from D-branes on a toric Calabi-Yau singularity, the Octagon. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

La théorie des cordes est un de nos meilleurs candidats pour une théorie quantique de la gravité. A ce jour elle n'a pas encore été conclusive à propose de ce sujet. Malgré cela, on a réalisé qu'on peut en tirer des informations sur tout une variété de sujets, dont notamment les théories de jauges supersymétriques, en étudiant la limite de basse énergie dans le volume d'univers des branes. Cette immersion des théories de jauges en théorie des cordes nous fournit un autre point de vue. Ce dernier nous permet souvent de prendre une approche plus géométrique pour obtenir de nouveaux résultats sinon inaccessible par des méthodes plus conventionnelles. Même en absence de vérification expérimentale de la supersymétrie, sa présence dans cette classe de théories de jauge nous fournit un terrain de jeux propice pour tester de nouvelles méthodes d'une manière efficace. En effet, la présence de la supersymétrie donne une structure additionnelle qui rend la théorie plus rigide. Cela simplifie les calculs et rend des résultats plus accessibles. On peut oser de dire que si on n'arrive pas à calculer un certain résultat en présence de supersymétrie, il y a très peu de chance d'y arriver sans. L'approche par la théorie des cordes le rend possible de découvrir des symétries cachées ou de comprendre des symétries connues d'une autre manière.Une classe de théories quantique intéressantes qui sont présentes en théories des cordes, c'est les théories de petites cordes. Ces dernières ont été découverte il y a deux décennies. Ces théories en six dimensions ont été construite une première fois comme théories dans le volume d'universe de branes NS5 dans le cadre de la théorie des cordes IIB en prenant la limite du couplage de la corde qui tend vers zéro. Dans cette limite, la théorie résultant reste non-trivial mais les interactions en dehors de la brane sont supprimées, notamment la gravité. Comme le nom le suggère, ces théories contiennent des cordes qu'on appelle petites cordes. La tension des petites cordes est proportionnelle à l'échelle naturelle de la corde. En plus, ces théories profitent de la T-dualité comme les théories de cordes critiques. Elle sont donc des théories quantiques non-locales. Leur complexité se situe entre celle des théories quantiques locales et celle de la théorie des cordes complète. Elles sont donc des candidates intéressantes pour étudier la dynamique dans le volume d'univers de la brane NS5. Pour des énergies inférieures à l'échelle de la corde, elles ont une description en termes de théories de jauges symétriques de type quiver. On peut donc également obtenir des informations sur ces dernières. Cette description locale n'est plus valable une fois l'échelle de la corde atteinte.Le but principal de cette thèse est d'étudier des dualités entre le théories de petites cordes en utilisant différentes constructions disponible en théorie des cordes. Cela nous permet d'attaquer le problème d'angles différents et de faire un lien avec des structures géométriques. En conséquence on peut analyser différentes relation parmi les théories de petites cordes. On confirme ensuite la validité des dualités qu'on obtient en utilisant la fonction de partition instantonique. Cet object est complètement non-perturbative et établit ces dualités comme résultat exact. Cette structure de dualités s'étend naturellement aux descriptions de basse énergie en terme de théories de jauges supersymétriques. De plus, on étudie les conséquences directes du réseaux de dualités qu'on a découvert. / String theory remains one of our best candidates for a theory of quantum gravity. Until now it has not lived up to this goal. However, along the way it was realized that string theory can give us valu-able insights into a variety of subjects among which supersymmetric gauge theories by studying the low-energy worldvolume dynamics of branes. This embedding of gauge theories into string theory provides us with a different viewpoint that often allows us to use powerful geometric considerati-ons in order to obtain new results that are inaccessible from conventional methods. Even in the ab-sence of experimental confirmation of supersymmetry, its presence in this class of gauge theories provides us with a playground where different methods can be tested in an efficient way. Indeed, supersymmetry provides additional structure, rendering the underlying theory more rigid and thus simplifying computations and making results more accessible. One could dare to say that when a certain result can not be calculated in the presence of supersymmetry, there is probably not much hope of achieving it without supersymmetry. This stringy approach to gauge theories makes it pos-sible to unravel hidden dualities or to understand already known ones from a different perspective. An interesting class of quantum theories that are embedded into string theory are the so called little string theories. They have been discovered two decades ago. These six-dimensional theories were first obtained as the worldvolume theory of a stack of NS5 branes in the context of Type II string theory trough a particular decoupling limit that sends the string coupling constant to zero while kee-ping at the same time the string scale finite. In this limit, the resulting theory remains interacting but the bulk dynamics is decoupled, in particular gravity. As their name suggests, they contain strings. The tension of the little strings is proportional to the string scale, which is the only intrinsic scale in the theory. Furthermore, the little string theories enjoy T-duality similar to the critical string theory. They are thus non-local quantum theories. So the complexity of little string theory lies between that of local quantum field theories and full fledged critical string theory. This makes them interesting candidates for studying stringy phenomena in an easier setup where gravity is absent and to learn more about the worldvolume dynamics of the NS5 brane. At energies far below the string scale, they have a low-energy description in terms of quiver gauge theories, so their study can also give us insights into these kinds of theories. This local description breaks down as we reach the string scale and we must rely on the full little string theories. The main goal of this thesis is to study dualities between little string theories by using different dual constructions available in string theory. These allow us to attack the problem from different angles and they establish also a connection to geometric structures. This makes it possible to systematically analyse relations among different little string theories. We then confirm the validity of the newly found duality relations by using the so called instanton partition function. The latter is a completely non-perturbative object allowing us to establish the dualities as an exact result. This duality structure naturally extends to the low-energy description in terms of supersymmetric quiver gauge theories. Furthermore, we study the direct consequences of this duality web. We find interesting cases where the dimensional reduction from six to five dimensions simultaneously reduces the rank of the group and changes the matter content. Another result that we find is the presence of a hidden dihedral symmetry which acts in a highly non-trivial fashion on the spectrum of the underlying gauge theories.

This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions which also reveals some unexpected phenomena. The balance between the intuitionistic and modal languages is restored by adding to the former one more implication.

In this work we introduce some category-theoretical concepts and techniques to study probability distributions on metric spaces and ordered metric spaces. In Chapter 1 we give an overview of the concept of a probability monad, first defined by Giry. Probability monads can be interpreted as a categorical tool to talk about random elements of a space X. We can consider these random elements as formal convex combinations, or mixtures, of elements of X. Spaces where the convex combinations can be actually evaluated are called algebras of the probability monad. In Chapter 2 we define a probability monad on the category of complete metric spaces and 1-Lipschitz maps called the Kantorovich monad, extending a previous construction due to van Breugel. This monad assigns to each complete metric space X its Wasserstein space PX. It is well-known that finitely supported probability measures with rational coefficients, or empirical distributions of finite sequences, are dense in the Wasserstein space. This density property can be translated into categorical language as a colimit of a diagram involving certain powers of X. The monad structure of P, and in particular the integration map, is uniquely determined by this universal property. We prove that the algebras of the Kantorovich monad are exactly the closed convex subsets of Banach spaces. In Chapter 3 we extend the Kantorovich monad of Chapter 2 to metric spaces equipped with a partial order. The order is inherited by the Wasserstein space, and is called the stochastic order. Differently from most approaches in the literature, we define a compatibility condition of the order with the metric itself, rather then with the topology it induces. We call the spaces with this property L-ordered spaces. On L-ordered spaces, the stochastic order induced on the Wasserstein spaces satisfies itself a form of Kantorovich duality. The Kantorovich monad can be extended to the category of L-ordered metric spaces. We prove that its algebras are the closed convex subsets of ordered Banach spaces, i.e. Banach spaces equipped with a closed cone. The category of L-ordered metric spaces can be considered a 2-category, in which we can describe concave and convex maps categorically as the lax and oplax morphisms of algebras. In Chapter 4 we develop a new categorical formalism to describe operations evaluated partially. We prove that partial evaluations for the Kantorovich monad, or partial expectations, define a closed partial order on the Wasserstein space PA over every algebra A, and that the resulting ordered space is itself an algebra. We prove that, for the Kantorovich monad, these partial expectations correspond to conditional expectations in distribution. Finally, we study the relation between these partial evaluation orders and convex functions. We prove a general duality theorem extending the well-known duality between convex functions and conditional expectations to general ordered Banach spaces.

A common phenomenon is that larger cities have different place identities; therefore, this thesis is based on the case of Malmö since it is Sweden's third largest city. The purpose was to explore how Malmö’s place image coheres to its place identity, and how the duality of Malmö influences the place image.   The research was based on a qualitative case study with an abductive approach since the purpose was explorative. Furthermore, the developed conceptual framework of this thesis was based on previous research regarding place branding, more specifically, place image and place identity. The empirical material in this thesis was collected through a comprehensive user-generated content analysis of Instagram posts as well as through two semis-structured focus groups with people living outside of Malmö.   Findings revealed that the place image and place identity cohered in some aspects, while in other aspects the place image differs from the place identity. Furthermore, the findings revealed a complex duality within the city; thus, the place identity of Malmö sends out dual messages which influenced the place image that strengthened the duality of Malmö.   The findings of this thesis have contributed with insights to the field of place branding since the concept of place image has not been related to dualities within cities in previous research.The limitations of this thesis were that the participants in the focus groups were from the same university which might have influenced their perception. Another limitation was that only people aged 35 or younger participated. Due to Covid-19, it was hard to find people older than 35 to the focus groups and the result could receive a broader perspective if the participants were older. These limitations could be considered in future research to receive the place image of a broader age range. Furthermore, future research could consider complementing the method of this thesis with focus groups to expose both the positive and negative side of Malmö.

Nous avons investigué les propriétés des champs de jauge de spin élevé libres à travers une étude de divers aspects de leur dynamique hamiltonienne. Pour des champs se propageant sur un espace-temps plat, les contraintes issues de l'analyse hamiltonienne de ces théories de jauge ont été identifiées et résolues par l'introduction de prépotentiels, dont l'invariance de jauge comprend, de façon intrigante, à la fois des difféomorphismes linéarisés généralisés et des transformations d'échelle de Weyl généralisées et linéarisées. Cela a motivé notre étude systématique des invariants conformes pour les spins élevés. Les invariants correspondants ont été construits à l'aide du tenseur de Cotton, dont nous avons établi les propriétés essentielles (symétrie, conservation, trace nulle; invariance, complétude). Avec ces outils géométriques, l'analyse hamiltonienne a pu être complétée et une action du premier ordre écrite en termes des prépotentiels. Nous avons constaté que cette action possédait une invariance manifeste par dualité électromagnétique; cette invariance, combinée à l'invariance de jauge des prépotentiels, fixe d'ailleurs uniquement l'action. En outre, de façon générale, cette action s'est révélée être exactement celle obtenue à travers une réécriture des équations du mouvement des spins élevés comme des conditions d'auto-dualité tordue (non manifestement covariantes).Avec un intérêt pour les extensions supersymétriques, nous avons amorcé la généralisation de cette étude aux champs fermioniques. Le champ de masse nulle libre de spin 5/2 a été soumis à la même analyse, et son prépotentiel s'est révélé partager l'invariance de jauge conforme déjà observée dans le cas bosonique général. Le supermultiplet incorporant les spins 2 et 5/2 a ensuite été considéré, et une symétrie rigide de son action, combinant une transformation de dualité électromagnétique du spin 2 avec une transformation de chiralité du spin 5/2 a été construite pour commuter avec la supersymétrie. Dans une autre direction, nous avons étudié les propriétés d'un champ tensoriel chiral de symétrie mixte dans un espace-temps plat à six dimensions: une (2,2)-forme. Son analyse hamiltonienne a été réalisée, des prépotentiels introduits et l'action de premier ordre obtenue s'est encore une fois révélée être la même que celle obtenue à travers une réécriture des équations du mouvement comme des conditions d'auto-chiralité (non manifestement covariante).Finalement, nous nous sommes penchés sur les charges de surface des champs fermioniques et bosoniques de spin élevé se propageant sur un espace-temps à courbure constante. Cela a été réalisé par une analyse hamiltonienne de ces systèmes, les contraintes étant identifiées aux générateurs des transformations de jauge. Injectant dans ces générateurs des valeurs des paramètres des transformations de jauge correspondant à des transformations impropres de jauge (imposant une réelle variation physique sur les champs) a ensuite permis d'évaluer la valeur de ces générateurs pour des champs résolvant les équations du mouvement: elle s'est bien révélée finie et non-nulle, constituant les charges de surface de ces théories. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished