Der Renormierungsgruppen-Fluß der konform-reduzierten Quantengravitation

Wir analysieren die Rolle von "Hintergrundunabhängigkeit" im Zugang der effektiven Mittelwertwirkung zur Quantengravitation. Wenn der nicht-störungstheoretische Renormierungsgruppen-(RG)-Fluß "hintergrundunabhängig" ist, muß die Vergröberung durch eine nicht spezifizierte, variable Metrik definiert werden. Die Forderung nach "Hintergrundunabhängigkeit" in der Quantengravitation führt dazu, daß die funktionale RG-Gleichung von zusätzlichen Feldern abhängt; dadurch unterscheidet sich der RG-Fluß in der Quantengravitation deutlich von dem RG-Fluß einer gewöhnlichen Quantentheorie, deren Moden-Cutoff von einer starren Metrik abhängt. Beispielsweise kann in der "hintergrundunabhängigen" Theorie ein Nicht-Gauß'scher Fixpunkt existieren, obwohl die entsprechende gewöhnliche Quantentheorie keinen solchen entwickelt. Wir untersuchen die Bedeutung dieses universellen, rein kinematischen Effektes, indem wir den RG-Fluß der Quanten-Einstein-Gravitation (QEG) in einem "konform-reduzierten" Zusammenhang untersuchen, in dem wir nur den konformen Faktor der Metrik quantisieren. Alle anderen Freiheitsgrade der Metrik werden vernachlässigt. Die konforme Reduktion der Einstein-Hilbert-Trunkierung zeigt exakt dieselben qualitativen Eigenschaften wie in der vollen Einstein-Hilbert-Trunkierung. Insbesondere besitzt sie einen Nicht-Gauß'schen Fixpunkt, der notwendig ist, damit die Gravitation asymptotisch sicher ist. Ohne diese zusätzlichen Feldabhängigkeiten ist der RG-Fluß dieser Trunkierung der einer gewöhnlichen $phi^4$-Theorie. Die lokale Potentialnäherung für den konformen Faktor verallgemeinert den RG-Fluß in der Quantengravitation auf einen unendlich-dimensionalen Theorienraum. Auch hier finden wir sowohl einen Gauß'schen als auch einen Nicht-Gauß'schen Fixpunkt, was weitere Hinweise dafür liefert, daß die Quantengravitation asymptotisch sicher ist. Das Analogon der Metrik-Invarianten, die proportional zur dritten Potenz der Krümmung ist und die die störungstheoretische Renormierbarkeit zerstört, ist unproblematisch für die asymptotische Sicherheit der konform-reduzierten Theorie. Wir berechnen die Skalenfelder und -imensionen der beiden Fixpunkte explizit und diskutieren mögliche Einflüsse auf die Vorhersagekraft der Theorie. Da der RG-Fluß von der Topologie der zugrundeliegenden Raumzeit abhängt, diskutieren wir sowohl den flachen Raum als auch die Sphäre. Wir lösen die Flußgleichung für das Potential numerisch und erhalten Beispiele für RG-Trajektorien, die innerhalb der Ultraviolett-kritischen Mannigfaltigkeit des Nicht-Gauß'schen Fixpunktes liegen. Die Quantentheorien, die durch einige solcher Trajektorien definiert sind, zeigen einen Phasenübergang von der bekannten (Niederenergie-) Phase der Gravitation mit spontan gebrochener Diffeomorphismus-Invarianz zu einer neuen Phase von ungebrochener Diffeomorphismus-Invarianz. Diese Hochenergie-Phase ist durch einen verschwindenden Metrik-Erwartungswert charakterisiert.

Tensorial group field theories

In questa tesi il Gruppo di Rinormalizzazione non-perturbativo (FRG) viene applicato ad una particolare classe di modelli rilevanti in Gravit`a quantistica, conosciuti come Tensorial Group Field Theories (TGFT). Le TGFT sono teorie di campo quantistiche definite sulla variet`a di un gruppo G. In ogni dimensione esse possono essere espanse in grafici di Feynman duali a com- plessi simpliciali casuali e sono caratterizzate da interazioni che implementano una non-localit`a combinatoriale. Le TGFT aspirano a generare uno spaziotempo in un contesto background independent e precisamente ad ottenere una descrizione con- tinua della sua geometria attraverso meccanismi fisici come le transizioni di fase. Tra i metodi che meglio affrontano il problema di estrarre le transizioni di fase e un associato limite del continuo, uno dei pi` u efficaci `e il Gruppo di Rinormalizzazione non-perturbativo. In questo elaborato ci concentriamo su TGFT definite sulla variet`a di un gruppo non-compatto (G = R) e studiamo il loro flusso di Rinormalizzazione. Identifichiamo con successo punti fissi del flusso di tipo IR, e una superficie critica che suggerisce la presenza di transizioni di fase in regime Infrarosso. Ci`o spinge ad uno stu- dio per approfondire la comprensione di queste transizioni di fase e della fisica continua che vi `e associata. Affrontiamo inoltre il problema delle divergenze Infrarosse, tramite un processo di regolarizzazione che definisce il limite termodinamico appropriato per le TGFT. Infine, applichiamo i metodi precedentementi sviluppati ad un modello dotato di proiezione sull’insieme dei campi gauge invarianti. L’analisi, simile a quella applicata al modello precedente, conduce nuovamente all’identificazione di punti fissi (sia IR che UV) e di una superficie critica. La presenza di transizioni di fasi `e, dunque, evidente ancora una volta ed `e possibile confrontare il risultato col modello senza proiezione sulla dinamica gauge invariante.

Planck stars: theory and phenomenology

General Relativity (GR) is one of the greatest scientific achievements of the 20th century along with quantum theory. Despite the elegance and the accordance with experimental tests, these two theories appear to be utterly incompatible at fundamental level. Black holes provide a perfect stage to point out these difficulties. Indeed, classical GR fails to describe Nature at small radii, because nothing prevents quantum mechanics from affecting the high curvature zone, and because classical GR becomes ill-defined at r = 0 anyway. Rovelli and Haggard have recently proposed a scenario where a negative quantum pressure at the Planck scales stops and reverts the gravitational collapse, leading to an effective “bounce” and explosion, thus resolving the central singularity. This scenario, called Black Hole Fireworks, has been proposed in a semiclassical framework. The purpose of this thesis is twofold: - Compute the bouncing time by means of a pure quantum computation based on Loop Quantum Gravity; - Extend the known theory to a more realistic scenario, in which the rotation is taken into account by means of the Newman-Janis Algorithm.

Holographic renormalization for z = 2 Lifshitz spacetimes from AdS

Lifshitz spacetimes with the critical exponent z = 2 can be obtained by the dimensional reduction of Schrödinger spacetimes with the critical exponent z = 0. The latter spacetimes are asymptotically AdS solutions of AdS gravity coupled to an axion–dilaton system and can be uplifted to solutions of type IIB supergravity. This basic observation is used to perform holographic renormalization for four-dimensional asymptotically z = 2 locally Lifshitz spacetimes by the Scherk–Schwarz dimensional reduction of the corresponding problem of holographic renormalization for five-dimensional asymptotically locally AdS spacetimes coupled to an axion–dilaton system. We can thus define and characterize a four-dimensional asymptotically locally z = 2 Lifshitz spacetime in terms of five-dimensional AdS boundary data. In this setup the four-dimensional structure of the Fefferman–Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed. We find that for asymptotically locally z = 2 Lifshitz spacetimes obtained in this way, there are two anomalies each with their own associated nonzero central charge. Both anomalies follow from the Scherk–Schwarz dimensional reduction of the five-dimensional conformal anomaly of AdS gravity coupled to an axion–dilaton system. Together, they make up an action that is of the Horava–Lifshitz type with a nonzero potential term for z = 2 conformal gravity.

ATLAS search for new phenomena in dijet mass and angular distributions using pp collisions at sqrts=7 TeV

Mass and angular distributions of dijets produced in LHC proton-proton collisions at a centre-of-mass energy root s = 7TeV have been studied with the ATLAS detector using the full 2011 data set with an integrated luminosity of 4.8 fb(-1). Dijet masses up to similar to 4.0TeV have been probed. No resonance-like features have been observed in the dijet mass spectrum, and all angular distributions are consistent with the predictions of QCD. Exclusion limits on six hypotheses of new phenomena have been set at 95% CL in terms of mass or energy scale, as appropriate. These hypotheses include excited quarks below 2.83 TeV, colour octet scalars below 1.86TeV, heavy W bosons below 1.68 TeV, string resonances below 3.61 TeV, quantum black holes with six extra space-time dimensions for quantum gravity scales below 4.11 TeV, and quark contact interactions below a compositeness scale of 7.6 TeV in a destructive interference scenario.

Uniqueness of black holes with bubbles in minimal supergravity

We generalize uniqueness theorems for non-extremal black holes with three mutually independent Killing vector fields in five-dimensional minimal supergravity in order to account for the existence of non-trivial two-cycles in the domain of outer communication. The black hole space-times we consider may contain multiple disconnected horizons and be asymptotically flat or asymptotically Kaluza–Klein. We show that in order to uniquely specify the black hole space-time, besides providing its domain structure and a set of asymptotic and local charges, it is necessary to measure the magnetic fluxes that support the two-cycles as well as fluxes in the two semi-infinite rotation planes of the domain diagram.

Lorentz invariant intrinsic decoherence

We present a Lorentz invariant extension of a previous model for intrinsic decoherence (Milburn 1991 Phys. Rev. A 44 5401). The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, similar to modifications suggested by quantum gravity and string theory, but without sacrificing Lorentz invariance. Some observational signatures are discussed.

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

New design of electrostatic mirror actuators for application in high-precision interferometry

We describe a new geometry for electrostatic actuators to be used in sensitive laser interferometers, suited for prototype and table top experiments related to gravitational wave detection with mirrors of 100 g or less. The arrangement consists of two plates at the sides of the mirror (test mass), and therefore does not reduce its clear aperture as a conventional electrostatic drive (ESD) would do. Using the sample case of the AEI-10 m prototype interferometer, we investigate the actuation range and the influence of the relative misalignment of the ESD plates with respect to the test mass. We find that in the case of the AEI-10 m prototype interferometer, this new kind of ESD could provide a range of 0.28 mu m when operated at a voltage of 1 kV. In addition, the geometry presented is shown to provide a reduction factor of about 100 in the magnitude of the actuator motion coupling to the test mass displacement. We show that therefore in the specific case of the AEI-10 m interferometer, it is possible to mount the ESD actuators directly on the optical table without spoiling the seismic isolation performance of the triple stage suspension of the main test masses.

Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors

The most promising concept for low frequency (millihertz to hertz) gravitational wave observatories are laser interferometric detectors in space. It is usually assumed that the noise floor for such a detector is dominated by optical shot noise in the signal readout. For this to be true, a careful balance of mission parameters is crucial to keep all other parasitic disturbances below shot noise. We developed a web application that uses over 30 input parameters and considers many important technical noise sources and noise suppression techniques to derive a realistic position noise budget. It optimizes free parameters automatically and generates a detailed report on all individual noise contributions. Thus one can easily explore the entire parameter space and design a realistic gravitational wave observatory. In this document we describe the different parameters, present all underlying calculations, and compare the final observatory's sensitivity with astrophysical sources of gravitational waves. We use as an example parameters currently assumed to be likely applied to a space mission proposed to be launched in 2034 by the European Space Agency. The web application itself is publicly available on the Internet at http://spacegravity.org/designer. Future versions of the web application will incorporate the frequency dependence of different noise sources and include a more detailed model of the observatory's residual acceleration noise.

Design of a speed meter interferometer proof-of-principle experiment

The second generation of large scale interferometric gravitational wave (GW) detectors will be limited by quantum noise over a wide frequency range in their detection band. Further sensitivity improvements for future upgrades or new detectors beyond the second generation motivate the development of measurement schemes to mitigate the impact of quantum noise in these instruments. Two strands of development are being pursued to reach this goal, focusing both on modifications of the well-established Michelson detector configuration and development of different detector topologies. In this paper, we present the design of the world's first Sagnac speed meter (SSM) interferometer, which is currently being constructed at the University of Glasgow. With this proof-of-principle experiment we aim to demonstrate the theoretically predicted lower quantum noise in a Sagnac interferometer compared to an equivalent Michelson interferometer, to qualify SSM for further research towards an implementation in a future generation large scale GW detector, such as the planned Einstein telescope observatory.

Centre-of-mass motion in multi-particle Schrodinger-Newton dynamics

We investigate the implication of the nonlinear and non-local multi-particle Schrodinger-Newton equation for the motion of the mass centre of an extended multi-particle object, giving self-contained and comprehensible derivations. In particular, we discuss two opposite limiting cases. In the first case, the width of the centre-of-mass wave packet is assumed much larger than the actual extent of the object, in the second case it is assumed much smaller. Both cases result in nonlinear deviations from ordinary free Schrodinger evolution for the centre of mass. On a general conceptual level we include some discussion in order to clarify the physical basis and intention for studying the Schrodinger-Newton equation.