Donoghue's effective field theory of quantum gravity is extended to include the interaction of massless particles. The collinear divergences which accompany massless particles are examined first in the context of QED and then in quantum gravity. A result of Weinberg is extended to show how these divergences vanish in the case of gravity. The scattering cross section for hypothetical massless scalar particles is computed first, because it is simpler, and the results are then extended to photons. Some terms in the cross section are shown to correspond to the Aichelburg-Sexl metric surrounding a massless particle and to quantum corrections to that metric. The scattering cross section is also applied to calculate quantum corrections to the bending of starlight, and though small, the result obtained is qualitatively different than in the classical case. Since effective field theory includes the low-energy degrees of freedom which generate collinear divergences, the results presented here will remain relevant in any future quantum theory of gravity.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24168号 / 理博第4859号 / 新制||理||1695(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 笹倉 直樹, 准教授 髙山 史宏, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The Swampland program is way of sorting effective field theories based on conjectures of how an effective field theory consistent with quantum gravity should look like. In this thesis we take a closer look at the No Global Symmetries Conjecture, the Weak Gravity Conjecture, the de Sitter Conjecture and the Trans-Planckian Censorship Conjecture. The Weak Gravity Conjecture generalized to arbitrary dimensions and p-forms is tested under dimensional reduction and its sharpened version is used to discuss how under this conjecture non-supersymmetric AdS geometries are unstable. The de Sitter Conjecture and the Trans-Planckian Censorship Conjecture are compared to show that they give similar predictions based on different assumptions. Lastly we provide an example of a theory emerging from the swampland that utilizes the instability of AdS geometries to model our universe as the boundary of a higher dimensional expanding bubble. / Swampland-programmet är ett sätt att sortera effektiva fältteorier baserat på antaganden om hur en effektiv fältteori förenlig med kvantgravitation bör se ut. I den här avhandlingen tittar vi närmare på No Global Symmetries-antagandet, Weak Gravity-antagandet, de Sitter-antagandet och Trans-Planckian Censorship-antagandet. Weak gravity-antagandet generaliserat till godtyckliga dimensioner och p-former testas under dimensionsreduktion och dess skärpta version används för att diskutera hur man via detta antagande finner en instabilitet i icke-supersymmetriska AdS-geometrier. De sitter-antagandet och Trans-Planckian Censorship-antagandet jämförs för att visa att de ger liknande förutsägelser baserat på olika frågeställningar. Slutligen ger vi ett exempel på en teori som växer fram ur programmet som använder instabiliteten hos AdS-geometrier genom att modellera vårt universum som randen på en expanderande bubbla i högre dimensioner.

Cette thèse présente une étude détaillée de la structure de théories appelées GFT ("Group Field Theory" en anglais),à travers le prisme de la renormalisation. Ce sont des théories des champs issues de divers travaux en gravité quantique, parmi lesquels la gravité quantique à boucles et les modèles de matrices ou de tenseurs. Elles sont interprétées comme desmodèles d'espaces-temps quantiques, dans le sens où elles génèrent des amplitudes de Feynman indexées par des triangulations,qui interpolent les états spatiaux de la gravité quantique à boucles. Afin d'établir ces modèles comme des théories deschamps rigoureusement définies, puis de comprendre leurs conséquences dans l'infrarouge, il est primordial de comprendre leur renormalisation. C'est à cette tâche que cette thèse s'attèle, grâce à des méthodes tensorielles développées récemment,et dans deux directions complémentaires. Premièrement, de nouveaux résultats sur l'expansion asymptotique (en le cut-off) des modèles colorés de Boulatov-Ooguri sont démontrés, donnant accès à un régime non-perturbatif dans lequel une infinité de degrés de liberté contribue. Secondement, un formalisme général pour la renormalisation des GFTs dites tensorielles (TGFTs) et avec invariance de jauge est mis au point. Parmi ces théories, une TGFT en trois dimensions et basée sur le groupe de jauge SU(2) se révèle être juste renormalisable, ce qui ouvre la voie à l'application de ce formalisme à la gravité quantique. / In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory.Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand,and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. The question of renormalizability is crucial if one wants to establish interesting GFTs as well-defined (perturbative) quantum field theories, and in a second step connect them to known infrared gravitational physics. Relying on recently developed tensorial tools, this thesis explores the GFT formalism in two complementary directions. First, new results on the large cut-off expansion of the colored Boulatov-Ooguri models allow to explore further a non-perturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of so-called Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a non-trivial 3d TGFT with gauge group SU(2) is proven just-renormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity.

Les trous noirs sont étudiés d'un point de vue théorique. Les propriétés thermodynamiques et quantiques des trous noirs sont abordées à travers des nouvelles perspectives. On explore différents problèmes logiquement reliés: depuis les lois de la mécanique des trous noirs, en passant par la function partition Euclidienne des trous noirs, jusqu'aux modèles microscopiques quantiques et granulaires.L'approche repose sur deux principes: la thermodynamique importante pour les trous noirs se situe près de l'horizon et la géométrie quantique de l'espace-temps est granuleuse.On examine la première loi de la mécanique des trous noirs avec une perspective quasilocal basée sur des observateurs près de l'horizon. Il s'avère que la première loi peut être simplement reformulée comme la variation de l'aire de l'horizon. Ensuite, on examine la fonction de partition Euclidienne à partir de la nouvelle perspective quasilocal, et on reproduit l'entropie de Bekenstein-Hawking ainsi que l'energie quasilocal nouvellement introduite.L'approche quasilocal peut être abordée par un point de vue basé sur les Horizons Isolés. Dans ce cadre, on explore la quantification de l'Horizon Isolé rotatoire, en analysant la structure symplectique, et en utilisant l'espace de Hilbert de la Gravitation Quantique à Boucles.Finalement, on étudie les conséquences macroscopiques du modèle granulaire quantique basé sur la Gravitation Quantique à Boucles. L'accent est mis sur le modèle de trou noir en rotation, les résultats ne sont pas concluants du fait que plusieurs hypothèses doivent être posées. Cependant, la perspective est prometteuse. Certains des résultats, comme l'entropie, peuvent être reproduits. / Black holes are studied from a theoretical point of view. The thermodynamics and quantum properties are addressed from a new perspective. A range of logically connected problems are explored: Starting from the laws of black hole mechanics, going through the Euclidean partition function, to the microscopic quantum granular models.The approach is supported by two guiding principles: What is physically relevant for black hole thermodynamics lays close to the horizon and the quantum geometry of the spacetime is coarse-grained.The first law of black hole mechanics is reviewed from the new quasilocal perspective based on near horizon observers. It turns out that the first law can be reformulated as variations of the area of the horizon. On the same grounds, the semiclassical Euclidean partition function is reviewed from the new quasilocal perspective. The framework reproduces the classic Bekenstein-Hawking entropy and the newly introduced quasilocal energy.The quasilocal approach can also be addressed by using Isolated Horizons. The quantization procedures are explored for the rotating Isolated Horizon starting from a symplectic structure analysis, and using the Loop Quantum Gravity Hilbert space. Finally, through a statistical analysis, the macroscopic consequences of the quantum granular model based on the Loop Quantum Gravity approach are studied. Special emphasis is put on the rotating quantum black hole model, however the results are not conclusive as several assumptions should be made on the way. Nevertheless, the perspective is promising as some of the semiclassical results, for instance the entropy, can be reproduced.

Estudamos duas classes de teorias de campos com métrica indefinida: os modelos sigma não linear não-compactos e as teorias quárticas da gravitação. Mostramos que a prova da unitariedade para os modelos sigma de simetria não compacta é a mesma que para os modelos compactos nas regiões fisicamente relevantes. Além disso, analisamos a possibilidade de ocorrer geração dinâmica de massa nos modelos sigma sob influência de temperatura finita, em várias dimensões. No que se refere às teorias quárticas da gravitação, calculamos o valor esperado no vácuo da função de dois pontos com inserção da relação de Gauss-Bonnet. Encontramos que a identidade clássica não é preservada quando empregamos a regularização dimensional, mesmo num espaço sem singularidades. Isto revela o surgimento de anomalias gravitacionais / Two classes of field theories with indefinite metric are studied: noncompact nonlinear sigma models and higher-derivative quantum gravity. We show that the proof of unitarity for noncompact sigma models is the same as the one for compact models in the physically relevant regions. Moreover, we analyze the possibility of dynamical mass generation at finite temperature in various space-time dimensions. Concerning to the higher-derivative quantum gravity, we calculate the vacuum expectation value of the two-point function with the insertion of Gauss-Bonnet Relation. In the quantum context, we also show, using dimensional regularization, that the Gauss-Bonnet relation is not satisfied due to gravitational anomalies.

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-07-04T18:29:04Z No. of bitstreams: 1 Guilherme Silva de Araújo Sadovski - Dissertação.pdf: 806650 bytes, checksum: 333998d8c772954dd2891f36903361eb (MD5) / Made available in DSpace on 2017-07-04T18:29:04Z (GMT). No. of bitstreams: 1 Guilherme Silva de Araújo Sadovski - Dissertação.pdf: 806650 bytes, checksum: 333998d8c772954dd2891f36903361eb (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O objetivo principal desta dissertação é o de testarmos a consistência em larga-escala de um modelo de gravidade quântica. Este modelo consiste de uma teoria de YangMills para o grupo de calibre SO(m, n) escrita em um espaço-tempo euclidiano quadridimensional. Ao tomarmos o limite infravermelho, a álgebra do grupo SO(m, n) sofre uma contra¸c˜ao de Inönü-Wigner e é deformada na álgebra de Poincaré, quebrando, assim, a simetria de calibre. Como consequências, temos o surgimento das simetrias locais de Lorentz e a identificação dos campos de calibre com a vierbein, e(x), e a conexão de spin, ω(x). A gravidade resultante é uma teoria efetiva tipo-Einstein-Cartan que contém termos de correção ultravioleta e campo de torção propagante. Uma vantagem deste modelo de gravidade induzida é o surgimento natural de uma constante cosmológica gravitacional que, junto com a constante de Newton, G, pode ser calculada perturbativamente. Utilizamos a métrica FLRW e o ansatz de um espaço-tempo riemanniano para demonstramos que esta gravidade efetiva possui o Modelo Cosmológico Padrão como seu limite infravermelho. Além disso, o setor ultravioleta de teoria prevê uma fase de Sitter hiper-acelerada que pode vir a ser associada à inflação e prevê também a presença de matéria exótica no Universo primordial. / Our main go in this thesis is to test the large-scale consistency of a quantum gravity model. This model consists of a Yang-Mills theory with gauge group SO(m, n) written in a four-dimensional euclidean space-time. In the infrared limit, the SO(m, n) algebra undergoes an In¨on¨u-Wigner contraction to Poincaré algebra and the gauge symmetry is broken. As consequence, Lorentz local symmetries arise and the gauge fields can be identified with a vierbein field, e(x), and a spin connection field, ω(x). The resulting gravity is an effective Einstein-Cartan-like theory with ultraviolet correction terms and propagating torsion field. An advantage of this model is the natural appearance of a gravitational cosmological constant that, along with Newton’s gravitational constant, G, can be calculated perturbatively. Making use of the FLRW metric and the ansatz of a riemannian spacetime we demonstrate that this effective gravity has the Standard Cosmological Model in its infrared sector. Furthermore, the ultraviolet regime foresee a hyper-accelerated de Sitter phase that may prove to be inflationary and also foresee the presence of exotic matter in the early Universe.

La théorie de cordes unifie de façon naturelle les théories de jauge, qui décrivent les interactions entre les particules élémentaires, avec une théorie quantique de la gravitation. Ces dernières années ont apporté de grands progrès dans la compréhension des états non-perturbatifs de la théorie, ses aspects holographiques, ainsi que la construction de modèles proches du Modèle Standard. Néanmoins, il reste des défis pour la théorie de cordes, qui incluent une définition non-perturbative, une meilleure compréhension de l'holographie, et le problème de la constante cosmologique. Ma recherche s'est concentrée sur des aspects formels des théories de gravitation quantique, qui incluent les trous noirs, la dépendance du temps, et l'holographie. Gr^ace à de nouveaux résultats dans le domaine de la théorie conforme avec spectre continu, mes collaborateurs et moi-m^eme avons avancé dans la compréhension de l'holographie dans des fonds avec dilaton linéaire, ainsi que dans le plongement de théories de jauge supersymétriques dans la théorie de cordes. En particulier, on a étudié des théories conformes supersymétriques avec spectre continu que l'on utilise pour construire des fonds de théories de cordes non-compacts et courbés. Les résultats obtenus nous ont permis de décrire des exemples explicites de symétrie miroir pour des fonds non-compacts. En introduisant des bords dans les théories conformes, on a analysé des états non-perturbatifs de la théorie de cordes, les D-branes. A basse énergie, les degrés de liberté sur les D-branes interagissent par des interactions de jauge. Avec ces outils, on a réussi à plonger une dualité infrarouge de théorie de jauge supersymétrique dans la théorie de cordes, et on a montré que la dualité correspond à une monodromie pour les états de bord dans l'espace de modules de la théorie conforme.<br><br> Dans cette thèse, on discute de nombreux autres liens entre la théorie conforme, la théorie de jauge et la gravitation. La plupart des contributions décrites étaient motivées par la théorie de cordes. Des exemples sont l'analyse d'états qui préservent la supersymétrie et leur lien avec les algèbres affines, la dépendance du temps et le dictionnaire holographique, l'analyse directe de la quantification de la gravité en présence d'un trou noir, la réalisation du scenario sans-bord pour la fonction d'onde de l'univers en théorie de cordes, une formule de Verlinde pour les théories conformes non-rationnelles et la construction de solutions non-géometriques à la supergravité. Dans d'autres travaux, je me suis concentré sur des théories qui quantifient la gravité plus directement, mais qui pourraient avoir moins de succès dans le problème de l'unification des forces en quatre dimensions. Ces théories ont quand-m^eme le potentiel de nous apprendre des aspects communs à toute théorie de gravitation quantique. Par exemple, on a analysé les degrés de liberté responsables de l'entropie d'un trou noir en trois dimensions, et nous avons argumenté sur la difficulté de reconcilier l'invariance modulaire avec l'unitarité en dehors de la théorie de cordes. On a aussi discuté la diffusion de ces trous noirs. D'autres contributions à la théorie de jauge non-commutative, la théorie de jauge supersymétrique, la production de paires dans un espace courbe, et cetera, sont aussi relativement indépendantes du cadre de la théorie de cordes.<br><br> Il me semble qu'il reste intéressant d'étudier des questions difficiles sur la théorie de jauge et la gravitation quantique, dans la cadre de la théorie de cordes, et en dehors de ce cadre, et d'^etre guidé par des problèmes ouverts durs qui doivent mener à un progrès concret par incréments ou par sauts.

In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. Recently, a new natural ultraviolet cutoff that is fully covariant was proposed. In the literature, most studies of ultraviolet cutoffs are concerned with Lorentz-violating ultraviolet cutoffs. The difficulty in making a minimum length cutoff covariant is rooted in the fact that any given length scale can be further Lorentz contracted. It was shown that this problem is avoided by the proposed covariant cutoff by allowing field modes with arbitrarily small wavelengths to still exist, albeit with exceedingly small, covariantly-determined bandwidths. In other words, the degrees of freedom of sub-Planckian modes in time are highly suppressed. The effects of this covariant ultraviolet cutoff on the kinematics of a scalar quantum field are well understood. There is much to learn, however, about the effects on a field’s dynamics. These effects are of great interest, as their presence may have direct observational consequences in cosmology. As such, this covariant ultraviolet cutoff offers the tantalizing prospect of experimental access to physics at the Planck scale. In cosmology, the energy scales that are probed by measurements of cosmic microwave background (CMB) statistics are the closest that we can get to the Planck scale. In particular, the statistics of the CMB encodes information about the quantum fluctuations of the scalar inflaton field. A measure of the strength of a field’s quantum fluctuations is in turn given by the magnitude of the field’s Feynman propagator. To this end, in this thesis I study how this covariant ultraviolet cutoff modifies the Feynman propagator of a scalar quantum field. In this work, I first calculate the cutoff Feynman propagator for a scalar field in flat spacetime, and then I address the cutoff Feynman propagator of a scalar field in curved spacetime. My studies culminate with an explicit calculation for the case of a power-law Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. This last calculation is cosmologically significant, as power-law FLRW spacetime is a prototypical and realistic model for early-universe inflation. In preparation for studying the covariant cutoff on curved spacetime, I will review the necessary back- ground material as well as the kinematic influence of the covariant cutoff. I will also discuss several side results that I have obtained on scalar quantum field theories in spacetimes which possess a finite start time.

In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. Recently, a new natural ultraviolet cutoff that is fully covariant was proposed. In the literature, most studies of ultraviolet cutoffs are concerned with Lorentz-violating ultraviolet cutoffs. The difficulty in making a minimum length cutoff covariant is rooted in the fact that any given length scale can be further Lorentz contracted. It was shown that this problem is avoided by the proposed covariant cutoff by allowing field modes with arbitrarily small wavelengths to still exist, albeit with exceedingly small, covariantly-determined bandwidths. In other words, the degrees of freedom of sub-Planckian modes in time are highly suppressed. The effects of this covariant ultraviolet cutoff on the kinematics of a scalar quantum field are well understood. There is much to learn, however, about the effects on a field’s dynamics. These effects are of great interest, as their presence may have direct observational consequences in cosmology. As such, this covariant ultraviolet cutoff offers the tantalizing prospect of experimental access to physics at the Planck scale. In cosmology, the energy scales that are probed by measurements of cosmic microwave background (CMB) statistics are the closest that we can get to the Planck scale. In particular, the statistics of the CMB encodes information about the quantum fluctuations of the scalar inflaton field. A measure of the strength of a field’s quantum fluctuations is in turn given by the magnitude of the field’s Feynman propagator. To this end, in this thesis I study how this covariant ultraviolet cutoff modifies the Feynman propagator of a scalar quantum field. In this work, I first calculate the cutoff Feynman propagator for a scalar field in flat spacetime, and then I address the cutoff Feynman propagator of a scalar field in curved spacetime. My studies culminate with an explicit calculation for the case of a power-law Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. This last calculation is cosmologically significant, as power-law FLRW spacetime is a prototypical and realistic model for early-universe inflation. In preparation for studying the covariant cutoff on curved spacetime, I will review the necessary back- ground material as well as the kinematic influence of the covariant cutoff. I will also discuss several side results that I have obtained on scalar quantum field theories in spacetimes which possess a finite start time.