Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-05-15T19:23:47Z No. of bitstreams: 1 tiberiodepaulanetto.pdf: 1926871 bytes, checksum: 17bceffda5c85de37a0d50a14f4f3f04 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-22T14:37:09Z (GMT) No. of bitstreams: 1 tiberiodepaulanetto.pdf: 1926871 bytes, checksum: 17bceffda5c85de37a0d50a14f4f3f04 (MD5) / Made available in DSpace on 2018-05-22T14:37:09Z (GMT). No. of bitstreams: 1 tiberiodepaulanetto.pdf: 1926871 bytes, checksum: 17bceffda5c85de37a0d50a14f4f3f04 (MD5) Previous issue date: 2017-02-22 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese, exploram-se diferentes aspectos e aplicações das teorias gravitacionais com correções quânticas. O texto é dividido em três partes principais. Na primeira parte, são consideradas as soluções linearizadas em diferentes teorias de gravitação com derivadas superiores. O potencial Newtoniano é calculado nos modelos locais, super-renormalizáveis no nível quântico, e mostra-se que a singularidade Newtoniana é cancelada devido a contribuição dos modos massivos extras. Logo depois, o colapso gravitacional de uma pequena massa é estudado na gravitação não-local livre de fantasmas, sendo o principal resultado a ausência da singularidade na solução do campo gravitacional e a possibilidade da não formação do miniburaco negro como resultado do colapso. Na segunda parte, algumas questões sobre a inflação induzida pela anomalia conforme são estudadas. É discutida a possibilidade da transição entre os períodos de inflação estável para instável. É mostrado que esta transição é automática se as correções quânticas nesse período forem desprezadas. Em seguida, considera-se o efeito de termos que violam as simetrias de CPT e Lorentz na inflação induzida pela anomalia conforme. É demonstrado que os novos termos responsáveis por violar essas simetrias não afetam a dinâmica do fator de escala da métrica. Por fim, na terceira parte as correções quânticas para o modelo dos Galileons e para as teorias dos campos massivos tensoriais antissimétricos são obtidas. É mostrado que o propagador da teoria dos Galileons recebe correções quânticas com derivadas superiores e que o teorema de não-renormalização do modelo dos Galileons permanece, de uma maneira generalizada, válido na região das baixas energias. Depois, por meio de cálculos explícitos das correções quânticas semiclássicas não-locais é confirmada a equivalência quântica entre os modelos dos campos tensoriais antissimétricos massivos com a teoria de Proca e com o modelo do campo escalar massivo mínimo. / In this thesis, different aspects and applications of gravitational theories with quan-tum corrections are explored. The text is divided into three main parts. In the first part, the linearized solutions in different gravity theories with higher derivatives are considered. The Newtonian potential is calculated in the local models, super-renormalizable at the quantum level, and it is shown that the Newtonian singularity is cancelled due to the contributions of the extra massive modes. Then the gravitational collapse of a small mass is studied in non-local ghost-free gravity, being the main result the absence of singularity in the gravitational field solution and the possibility of non-mini black hole formation as the collapse result. In the second part, some issues about anomaly-induced inflation are studied. It is discussed the possibility of the transition between stable to unstable periods of inflation. It is shown that this transition is automatic if the quantum corrections in this period are neglected. In the following, we consider the effect of CPT and Lorentz-violating terms in the conformal anomaly-induced inflation. It is shown the new terms responsible to violate these symmetries do not affect the dynamics of the metric scale factor. Finally, in the third part, the quantum corrections for the Galileon model and for the theory of the massive antisymmetric tensor fields are obtained. It is shown that the propaga-tor of Galilean theory receives quantum corrections with higher derivatives and that the non-renormalization theorem for Galileon models remains, in a generalized way, valid in the low-energy region. Then, by means of explicit calculations of non-local semiclassical quantum corrections, the quantum equivalence between the massive antisymmetric tensor field models with the Proca theory and minimal massive scalar field model is confirmed.

The idea of holography [1, 2] finds a concrete realization in form of the AdS/CFT correspondence [3, 4]. This duality relates a field theory with conformal symmetries to quantum gravity living in one higher dimension. In this thesis we study aspects of black hole quasinormal modes, higher spin theories and entanglement entropy in the context of this duality. In almost all cases we have been able to subject the duality to some precision tests. Quasinormal modes encode the spectrum of black holes and the time-scale of pertur- bations therein [5]. From the dual CFT viewpoint they are the poles of retarded Green's function (or peaks in the spectral function) [6]. Quasinormal modes were previously studied for scalar, gauge field and fermion fluctuations [7]. We solve for these quasinormal modes of higher spin (s _ 2) fields in the background of the BTZ black hole [8, 9]. We obtain an exact solution for a field of arbitrary spin s (integer or half-integer) in the BTZ background. This implies that the BTZ is perhaps the only known black hole background where such an analysis can be done analytically for all bosonic and fermionic fields. The quasinormal modes are shown to match precisely with the poles of the corresponding Green's function in the CFT living on the boundary. Furthermore, we show that one-loop determinants of higher spin fields can also be written as a product form [10] in terms of these quasinormal modes and this agrees with the same obtained by integrating the heat-kernel [11]. We then turn our attention to dualities relating higher-spin gravity to CFTs with W algebra symmetries. Since higher spin gravity does go beyond diffeomorphism invariance, one needs re_ned notions of the usual concepts in differential geometry. For example, in general relativity black holes are defined by the presence of the horizon. However, higher spin gravity has an enlarged group of symmetries of which the diffeomorphisms form a subgroup. The appropriate way of thinking of solutions in higher spin gravity is via characterizations which are gauge invariant [12, 13]. We study classical solutions embedded in N = 2 higher spin supergravity. We obtain a general gauge-invariant condition { in terms of the odd roots of the superalgebra and the eigenvalues of the holonomy matrix of the background { for the existence of a Killing spinor such that these solutions are supersymmetric [14]. We also study black holes in higher spin supergravity and show that the partition function of these black holes match exactly with that obtained from a CFT with the same asymptotic symmetry algebra [15]. This involved studying the asymptotic symmetries of the black hole and thereby developing the holographic dictionary for the bulk charges and chemical potentials with the corresponding quantities of the CFT. We finally investigate entanglement entropy in the AdS3/CFT2 context. Entanglement entropy is an useful non-local probe in QFT and many-body physics [16]. We analytically evaluate the entanglement entropy of the free boson CFT on a circle at finite temperature (i.e. on a torus) [17]. This is one of the simplest and well-studied CFTs. The entanglement entropy is calculated via the replica trick using correlation functions of bosonic twist operators on the torus [18]. We have then set up a systematic high temperature expansion of the Renyi entropies and determined their finite size corrections. These _nite size corrections both for the free boson CFT and the free fermion CFT were then compared with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces (replica geometry) as its boundary [19]. One-loop corrections in these geometries are entirely determined by the spectrum of the excitations present in the bulk. It is shown that the leading _nite size corrections obtained by evaluating the one-loop determinants on these handlebody geometries exactly match with those from the free fermion/boson CFTs. This provides a test for holographic methods to calculate one-loop corrections to entanglement entropy. We also study conformal field theories in 1+1 dimensions with W-algebra symmetries at _nite temperature and deformed by a chemical potential (_) for a higher spin current. Using OPEs and uniformization techniques, we show that the order _2 correction to the Renyi and entanglement entropies (EE) of a single interval in the deformed theory is universal [20]. This universal feature is also supported by explicit computations for the free fermion and free boson CFTs { for which the EE was calculated by using the replica trick in conformal perturbation theory by evaluating correlators of twist fields with higher spin operators [21]. Furthermore, this serves as a verification of the holographic EE proposal constructed from Wilson lines in higher spin gravity [22, 23]. We also examine relative entropy [24] in the context of higher-spin holography [25]. Relative entropy is a measure of distinguishability between two quantum states. We confirm the expected short-distance behaviour of relative entropy from holography. This is done by showing that the difference in the modular Hamiltonian between a high-temperature state and the vacuum matches with the difference in the entanglement entropy in the short-subsystem regime.

Algebraic Quantum Field Theory (AQFT) is a mathematically rigorous framework that was developed to model the interaction of quantum mechanics and relativity. In AQFT, quantum mechanics is modelled by C*-algebras of observables and relativity is usually modelled in Minkowski space. In this thesis we will consider a generalization of AQFT which was inspired by the work of Abramsky and Coecke on abstract quantum mechanics [1, 2]. In their work, Abramsky and Coecke develop a categorical framework that captures many of the essential features of finite-dimensional quantum mechanics. In our setting we develop a categorified version of AQFT, which we call premonoidal C*-quantum field theory, and in the process we establish many analogues of classical results from AQFT. Along the way we also exhibit a number of new concepts, such as a von Neumann category, and prove several properties they possess. We also establish some results that could lead to proving a premonoidal version of the classical Doplicher-Roberts theorem, and conjecture a possible solution to constructing a fibre-functor. Lastly we look at two variations on AQFT in which a causal order on double cones in Minkowski space is considered.

In this work the extension of the criterion for local thermal equilibrium by Buchholz, Ojima and Roos to curved spacetime as introduced by Schlemmer is investigated. Several problems are identified and especially the instability under time evolution which was already observed by Schlemmer is inspected. An alternative approach to local thermal equilibrium in quantum field theories on curved spacetimes is presented and discussed. In the following the dynamic system of the linear field and matter perturbations in the generic model of inflation is studied in the view of ambiguity of quantisation. In the last part the compatibility of the temperature fluctuations of the cosmic microwave background radiation with local thermal equilibrium is investigated.:1. Introduction 5 2. Technical Background 10 2.1. The Free Scalar Field on a Globally Hyperbolic Spacetime . . . . . . 10 2.1.1. Construction of the Scalar Field . . . . . . . . . . . . . . . . . 10 2.1.2. Algebra of Wick Products . . . . . . . . . . . . . . . . . . . . 13 2.1.3. Local Covariance Principle . . . . . . . . . . . . . . . . . . . . 17 2.2. Local Thermal Equilibirum . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1. Global Thermodynamic Equilibrium - KMS States . . . . . . 21 2.2.2. Local Thermal Observables . . . . . . . . . . . . . . . . . . . 24 2.2.3. LTE on Flat Spacetime . . . . . . . . . . . . . . . . . . . . . . 29 2.2.4. LTE in Cosmological Spacetimes . . . . . . . . . . . . . . . . 32 2.3. Linear Scalar Cosmological Perturbations . . . . . . . . . . . . . . . . 34 2.3.1. Robertson-Walker Cosmology . . . . . . . . . . . . . . . . . . 35 2.3.2. Mathematical Background . . . . . . . . . . . . . . . . . . . . 38 2.3.3. Technical Framework and Formulae . . . . . . . . . . . . . . . 40 2.3.4. The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . 46 2.3.5. The Sachs-Wolfe Effect for Adiabatic Perturbations . . . . . . 49 3. Towards a Refinement of the LTE Condition on Curved Spacetimes 54 3.1. Non-Minimal Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.1. Commutator Distribution . . . . . . . . . . . . . . . . . . . . 55 3.1.2. KMS Two-Point Function . . . . . . . . . . . . . . . . . . . . 57 3.1.3. Balanced Derivatives . . . . . . . . . . . . . . . . . . . . . . . 61 3.2. Conformally Static Spacetimes . . . . . . . . . . . . . . . . . . . . . . 65 3.2.1. Conformal KMS States . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2. Extrinsic LTE in de Sitter Spacetime . . . . . . . . . . . . . . 71 3.3. Massive Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3.1. Properties of the Model . . . . . . . . . . . . . . . . . . . . . 78 3.3.2. Bogoliubov Transformation . . . . . . . . . . . . . . . . . . . 80 3.3.3. Thermal Observables . . . . . . . . . . . . . . . . . . . . . . . 82 3.4. Towards an Alternative Concept . . . . . . . . . . . . . . . . . . . . . 91 3.4.1. Problems and Open Questions Concerning LTE . . . . . . . . 92 3.4.2. Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4.3. Positivity Inequalities . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.4. Macroobservable Interpretation . . . . . . . . . . . . . . . . . 100 3.5. An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4. Cosmological Perturbation Theory 105 4.1. Dynamics of Perturbations in Inflation . . . . . . . . . . . . . . . . . 106 4.1.1. CCR Quantisation is Ambiguous . . . . . . . . . . . . . . . . 106 4.1.2. Canonical Symplectic Form . . . . . . . . . . . . . . . . . . . 111 4.1.3. The Algebraic Point of View . . . . . . . . . . . . . . . . . . . 117 4.2. LTE States in Cosmology . . . . . . . . . . . . . . . . . . . . . . . . 120 4.2.1. The Link to Fluid Dynamics . . . . . . . . . . . . . . . . . . . 120 4.2.2. Incompatibility of LTE with Sachs-Wolfe Effect . . . . . . . . 125 5. Conclusion and Outlook 131 A. Technical proofs 136 A.1. Proof of Lemma 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.2. Proof of Lemma 3.2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 A.3. Proof of Lemma 3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.4. Idea of Proof for Conjecture 3.4.3 . . . . . . . . . . . . . . . . . . . . 144 B. Introduction to Probability Theory 146 Bibliography 150 Correction of Lemma 3.1.2 155 / In dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft.:1. Introduction 5 2. Technical Background 10 2.1. The Free Scalar Field on a Globally Hyperbolic Spacetime . . . . . . 10 2.1.1. Construction of the Scalar Field . . . . . . . . . . . . . . . . . 10 2.1.2. Algebra of Wick Products . . . . . . . . . . . . . . . . . . . . 13 2.1.3. Local Covariance Principle . . . . . . . . . . . . . . . . . . . . 17 2.2. Local Thermal Equilibirum . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1. Global Thermodynamic Equilibrium - KMS States . . . . . . 21 2.2.2. Local Thermal Observables . . . . . . . . . . . . . . . . . . . 24 2.2.3. LTE on Flat Spacetime . . . . . . . . . . . . . . . . . . . . . . 29 2.2.4. LTE in Cosmological Spacetimes . . . . . . . . . . . . . . . . 32 2.3. Linear Scalar Cosmological Perturbations . . . . . . . . . . . . . . . . 34 2.3.1. Robertson-Walker Cosmology . . . . . . . . . . . . . . . . . . 35 2.3.2. Mathematical Background . . . . . . . . . . . . . . . . . . . . 38 2.3.3. Technical Framework and Formulae . . . . . . . . . . . . . . . 40 2.3.4. The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . 46 2.3.5. The Sachs-Wolfe Effect for Adiabatic Perturbations . . . . . . 49 3. Towards a Refinement of the LTE Condition on Curved Spacetimes 54 3.1. Non-Minimal Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.1. Commutator Distribution . . . . . . . . . . . . . . . . . . . . 55 3.1.2. KMS Two-Point Function . . . . . . . . . . . . . . . . . . . . 57 3.1.3. Balanced Derivatives . . . . . . . . . . . . . . . . . . . . . . . 61 3.2. Conformally Static Spacetimes . . . . . . . . . . . . . . . . . . . . . . 65 3.2.1. Conformal KMS States . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2. Extrinsic LTE in de Sitter Spacetime . . . . . . . . . . . . . . 71 3.3. Massive Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3.1. Properties of the Model . . . . . . . . . . . . . . . . . . . . . 78 3.3.2. Bogoliubov Transformation . . . . . . . . . . . . . . . . . . . 80 3.3.3. Thermal Observables . . . . . . . . . . . . . . . . . . . . . . . 82 3.4. Towards an Alternative Concept . . . . . . . . . . . . . . . . . . . . . 91 3.4.1. Problems and Open Questions Concerning LTE . . . . . . . . 92 3.4.2. Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4.3. Positivity Inequalities . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.4. Macroobservable Interpretation . . . . . . . . . . . . . . . . . 100 3.5. An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4. Cosmological Perturbation Theory 105 4.1. Dynamics of Perturbations in Inflation . . . . . . . . . . . . . . . . . 106 4.1.1. CCR Quantisation is Ambiguous . . . . . . . . . . . . . . . . 106 4.1.2. Canonical Symplectic Form . . . . . . . . . . . . . . . . . . . 111 4.1.3. The Algebraic Point of View . . . . . . . . . . . . . . . . . . . 117 4.2. LTE States in Cosmology . . . . . . . . . . . . . . . . . . . . . . . . 120 4.2.1. The Link to Fluid Dynamics . . . . . . . . . . . . . . . . . . . 120 4.2.2. Incompatibility of LTE with Sachs-Wolfe Effect . . . . . . . . 125 5. Conclusion and Outlook 131 A. Technical proofs 136 A.1. Proof of Lemma 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.2. Proof of Lemma 3.2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 A.3. Proof of Lemma 3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.4. Idea of Proof for Conjecture 3.4.3 . . . . . . . . . . . . . . . . . . . . 144 B. Introduction to Probability Theory 146 Bibliography 150 Correction of Lemma 3.1.2 155

The question of the possibility of intelligent machines is fundamentally intertwined with the machines’ ability to reason. Or not. The developments of the recent years point in a completely different direction : What we need is simple, generic but scalable algorithms that can keep learning on their own. This thesis is an attempt to find theoretical explanations to the findings of recent years where empirical evidence has been presented in support of phase transitions in neural networks, power law behavior of various entities, and even evidence of algorithmic universality, all of which are beautifully explained in the context of statistical physics, quantum field theory and statistical field theory but not necessarily in the context of deep learning where no complete theoretical framework is available. Inspired by these developments, and as it turns out, with the overly ambitious goal of providing a solid theoretical explanation of the empirically observed power laws in neu- ral networks, we set out to substantiate the claims that renormalization group theory may be the sought-after theory of deep learning which may explain the above, as well as what we call algorithmic universality. / La question de la possibilité de machines intelligentes est intimement liée à la capacité de ces machines à raisonner. Ou pas. Les développements des dernières années indiquent une direction complètement différente : ce dont nous avons besoin sont des algorithmes simples, génériques mais évolutifs qui peuvent continuer à apprendre de leur propre chef. Cette thèse est une tentative de trouver des explications théoriques aux constatations des dernières années où des preuves empiriques ont été présentées en faveur de transitions de phase dans les réseaux de neurones, du comportement en loi de puissance de diverses entités, et même de l'universialité algorithmique, tout cela étant parfaitement expliqué dans le contexte de la physique statistique, de la théorie quantique des champs et de la théorie statistique des champs, mais pas nécessairement dans le contexte de l'apprentissage profond où aucun cadre théorique complet n'est disponible. Inspiré par ces développements, et comme il s'avère, avec le but ambitieux de fournir une explication théorique solide des lois de puissance empiriquement observées dans les réseaux de neurones, nous avons entrepris de étayer les affirmations selon lesquelles la théorie du groupe de renormalisation pourrait être la théorie recherchée de l'apprentissage profond qui pourrait expliquer cela, ainsi que ce que nous appelons l'universialité algorithmique.

Cette thèse exploite les liens profonds entre la physique des systèmes quantiques locaux, les propriétés non locales de leurs états fondamentaux et le contenu en information de ces états. Les deux premiers chapitres sont consacrés à l’application des systèmes quantiques locaux pour les fins d’une tâche informationnelle précise, soit le calcul quantique. Au terme d’un bref survol de la théorie, nous proposons un patron pour le calcul quantique universel et évolutif pouvant être réalisé sur une grande variété de plateformes physiques, et démontrons qu’il est particulièrement résilient face à un bruit anisotrope. Les quatre derniers chapitres sont pour leur part consacrés à l’approche informationnelle des systèmes quantiques à corps multiples. Nous décrivons les principales propriétés des corrélations et de l’intrication dans les états fondamentaux des systèmes de dimensions réduites les plus courants, en distinguant systèmes non critiques et systèmes critiques. Nous montrons que ces propriétés sont fortement modifiées par la présence de frustration géométrique dans les chaînes de spins. Enfin, nous réalisons une analyse exhaustive des corrélations et de l’intrication dans les états fondamentaux de deux théories quantiques de champs non triviales. / This thesis exploits the deep connections between the physics of local quantum systems, the nonlocal features in their ground states, and the information content of these states. The first two chapters are dedicated to the application of local quantum systems for the purpose of a definite information-theoretical task, namely quantum computation. After a brief survey of the theory, we propose a scheme for scalable universal quantum computation that, we argue, could be implemented on a wide variety of physical platforms, and show that it is particularly resilient to anisotropic noise. The last four chapters are dedicated to the information-theoretical approach of many-body quantum systems. We describe the main properties of correlations and entanglement in the ground states of the most common low-dimensional many-body systems, distinguishing between noncritical systems and critical ones. We show how these properties can be dramatically modified by the presence of geometric frustration in spin chains. Finally, we perform an intensive study of correlations and entanglement in the ground states of two nontrivial one-dimensional quantum field theories.

An evaluation of how sensitive some ATLAS searches for new physics are to a new beyond standard model (BSM) vector-like quark (VLQ) and a pseudo Nambu-Goldstone boson (pNGB) scalar. This was done by simulating a signal containing these new particles and making a recast of it onto existing verified ATLAS searches for new physics at center-of-mass (CM) energy of 13 TeV (Run 2) at the Large Hadron Collider (LHC). Signals for recasting were tailored such that their final states would be appropriate in relation to each respective ATLAS search in order to use the same selection criteria as applied in the existing searches. The results are summarized in the form of significances (Z) for each masspoint of the new top-partner and S particle. Significances did not show any expectiation of excluding any masspoint in the examined mass range for the recasts at 95% CL. This suggests that a dedicated search for these particles in the considered masspoints would be required.