A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Erste Messung der Pi-0-Photoproduktion an transversal polarisierten Protonen nahe der Schwelle

Diese Arbeit befasst sich mit der photoinduzierten Erzeugung neutraler Pionen, sehr nahe an der Schwellenenergie. Dabei werden zwei Ziele verfolgt: Zum einen die Überprüfung von Vorhersagen dieser effektiven Theorien und Modelle, zum anderen werden hier erstmals alle relevanten Partialwellenamplituden modellunabhängig aus gemessenen Observablen bestimmt. Diese Methode soll in Zukunft auch bei höheren Energien im Bereich der Nukleonresonanzen Anwendung finden. rnrnKonkret wird die Durchführung und Analyse eines Experiments vorgestellt, welches am Mainzer Mikrotron (MAMI) in den Jahren 2010 bis 2013 mit zirkular polarisiertem Photonenstrahl stattfand. Der Photonenstrahl wurde an einer Anlage zur Erzeugung energiemarkierter Bremsstrahlung aus dem Elektronenstrahl von MAMI gewonnen. Zum Nachweis der Reaktionsprodukte diente das hermetische 4pi CB/TAPS-Detektorsystem. Erstmalig standen bei derartigen Messungen auch transversal polarisierte Protonen zur Verfügung. Dazu wird Butanol in einer speziellen Apparatur dynamisch polarisiert. Molekularer Wasserstoff lässt sich aufgrund der para-Konfiguration nicht polarisieren. Wegen der Verwendung von Butanol als Targetmaterial, bei dem weniger als 5% aller erzeugten Pionen an polarisierten Protonen produziert wurden, ist die Behandlung des Untergrunds eine zentrale Aufgabe. rnrnEs werden zwei Methoden der Untergrundseparation vorgestellt, wovon die bessere in der Analyse angewendet wurde. Abschließend findet eine ausführliche Bewertung systematischer Fehler statt.rnrnDie erstmalige Verwendung transversal polarisierter Protonen ermöglicht den Zugang zu bisher nicht gemessenen Spin"=Freiheitsgraden. In Kombination mit einem komplementären Vorläufer-Experiment aus dem Jahr 2008 mit linear polarisiertem Photonenstrahl konnten aus den gewonnenen Daten erstmals alle komplexen s- und p-Partialwellenamplituden modellunabhängig bestimmt werden. rnrnDarüber hinaus wurden im Rahmen dieser Arbeit wesentliche Verbesserungen am apparativen Aufbau erzielt. Beispiele sind ein Elektronenstrahl-Polarimeter, ein zellularer CB-Multiplizitätstrigger, sowie signifikante Verbesserungen der Datennahmeelektronik und des Triggersystems, die teilweise in dieser Arbeit vorgestellt werden.

Reliability and consistency affect the integration of visual depth cues

Abstract Originalsprache (englisch) Visual perception relies on a two-dimensional projection of the viewed scene on the retinas of both eyes. Thus, visual depth has to be reconstructed from a number of different cues that are subsequently integrated to obtain robust depth percepts. Existing models of sensory integration are mainly based on the reliabilities of individual cues and disregard potential cue interactions. In the current study, an extended Bayesian model is proposed that takes into account both cue reliability and consistency. Four experiments were carried out to test this model's predictions. Observers had to judge visual displays of hemi-cylinders with an elliptical cross section, which were constructed to allow for an orthogonal variation of several competing depth cues. In Experiment 1 and 2, observers estimated the cylinder's depth as defined by shading, texture, and motion gradients. The degree of consistency among these cues was systematically varied. It turned out that the extended Bayesian model provided a better fit to the empirical data compared to the traditional model which disregards covariations among cues. To circumvent the potentially problematic assessment of single-cue reliabilities, Experiment 3 used a multiple-observation task, which allowed for estimating perceptual weights from multiple-cue stimuli. Using the same multiple-observation task, the integration of stereoscopic disparity, shading, and texture gradients was examined in Experiment 4. It turned out that less reliable cues were downweighted in the combined percept. Moreover, a specific influence of cue consistency was revealed. Shading and disparity seemed to be processed interactively while other cue combinations could be well described by additive integration rules. These results suggest that cue combination in visual depth perception is highly flexible and depends on single-cue properties as well as on interrelations among cues. The extension of the traditional cue combination model is defended in terms of the necessity for robust perception in ecologically valid environments and the current findings are discussed in the light of emerging computational theories and neuroscientific approaches.

On the flavor problem in strongly coupled theories

rnThis thesis is on the flavor problem of Randall Sundrum modelsrnand their strongly coupled dual theories. These models are particularly wellrnmotivated extensions of the Standard Model, because they simultaneously address rntherngauge hierarchy problem and the hierarchies in the quarkrnmasses and mixings. In order to put this into context, special attention is given to concepts underlying therntheories which can explain the hierarchy problem and the flavor structure of the Standard Model (SM). ThernAdS/CFTrnduality is introduced and its implications for the Randall Sundrum model withrnfermions in the bulk andrngeneral bulk gauge groups is investigated. It will be shown that the differentrnterms in the general 5D propagator of a bulk gauge field can be related tornthe corresponding diagrams of the strongly coupled dual, which allows for arndeeperrnunderstanding of the origin of flavor changing neutral currents generated by thernexchange of the Kaluza Klein excitations of these bulk fields.rnIn the numerical analysis, different observables which are sensitive torncorrections from therntree-levelrnexchange of these resonances will be presented on the basis of updatedrnexperimental data from the Tevatron and LHC experiments. This includesrnelectroweak precision observables, namely corrections to the S and Trnparameters followed by corrections to the Zbb vertex, flavor changingrnobservables with flavor changes at one vertex, viz. BR (Bd -> mu+mu-) and BR (Bs -> mu+mu-), and two vertices,rn viz. S_psiphi and |eps_K|, as well as bounds from direct detectionrnexperiments. rnThe analysis will show that all of these bounds can be brought in agreement withrna new physics scale Lambda_NP in the TeV range, except for the CPrnviolating quantity |eps_K|, which requires Lambda_NP= Ord(10) TeVrnin the absencernof fine-tuning. The numerous modifications of the Randall Sundrum modelrnin the literature, which try to attenuate this bound are reviewed andrncategorized.rnrnSubsequently, a novel solution to this flavor problem, based on an extendedrncolor gauge group in the bulk and its thorough implementation inrnthe RS model, will be presented, as well as an analysis of the observablesrnmentioned above in the extended model. This solution is especially motivatedrnfromrnthe point of view of the strongly coupled dual theory and the implications forrnstrongly coupled models of new physics, which do not possess a holographic dual,rnare examined.rnFinally, the top quark plays a special role in models with a geometric explanation ofrnflavor hierarchies and the predictions in the Randall-Sundrum model with andrnwithout the proposed extension for the forward-backward asymmetryrnA_FB^trnin top pair production are computed.

Describing and explaining the foreign expansion of network managing electronic business companies (NM-EBCs)

This study deals with the internationalization behavior of a new and specific type of e-business company, namely the network managing e-business company (NM-EBC). The business model of such e-business companies is based on providing a platform and applications for users to connect and interact, on gathering and channeling the inputs provided by the users, and on organizing and managing the cross-relationships of the various participants. Examples are online communities, matching platforms, and portals. Since NM-EBCs internationalize by replicating their business model in a foreign market and by building up and managing a network of users, who provide input themselves and interact with each other, they have to convince users in foreign markets to join the network and hence to adopt their platform. We draw upon Rogers’ Diffusion of Innovations Theory and Network Theory to explain the internationalization behavior of NM-EBCs. These two theories originate from neighboring disciplines and have not yet been used to explain the internationalization of firms. We combine both theories and formulate hypotheses about which strategies NM-EBCs may choose to expand abroad. To test the applicability of our theory and to gain rich data about the internationalization behavior of these firms, we carried out multiple case studies with internationally active Germany-based NM-EBCs.

Aircraft-based in-situ aerosol mass spectrometry: Chemical characterization and source identification of submicron particulate matter in the free and upper troposphere and lower stratosphere

The composition of the atmosphere is frequently perturbed by the emission of gaseous and particulate matter from natural as well as anthropogenic sources. While the impact of trace gases on the radiative forcing of the climate is relatively well understood the role of aerosol is far more uncertain. Therefore, the study of the vertical distribution of particulate matter in the atmosphere and its chemical composition contribute valuable information to bridge this gap of knowledge. The chemical composition of aerosol reveals information on properties such as radiative behavior and hygroscopicity and therefore cloud condensation or ice nucleus potential. rnThis thesis focuses on aerosol pollution plumes observed in 2008 during the POLARCAT (Polar Study using Aircraft, Remote Sensing, Surface Measurements and Models, of Climate, Chemistry, Aerosols, and Transport) campaign over Greenland in June/July and CONCERT (Contrail and Cirrus Experiment) campaign over Central and Western Europe in October/November. Measurements were performed with an Aerodyne compact time-of-flight aerosol mass spectrometer (AMS) capable of online size-resolved chemical characterization of non-refractory submicron particles. In addition, the origins of pollution plumes were determined by means of modeling tools. The characterized pollution episodes originated from a large variety of sources and were encountered at distinct altitudes. They included pure natural emissions from two volcanic eruptions in 2008. By the time of detection over Western Europe between 10 and 12 km altitude the plume was about 3 months old and composed to 71 % of particulate sulfate and 21 % of carbonaceous compounds. Also, biomass burning (BB) plumes were observed over Greenland between 4 and 7 km altitude (free troposphere) originating from Canada and East Siberia. The long-range transport took roughly one and two weeks, respectively. The aerosol was composed of 78 % organic matter and 22 % particulate sulfate. Some Canadian and all Siberian BB plumes were mixed with anthropogenic emissions from fossil fuel combustion (FF) in North America and East Asia. It was found that the contribution of particulate sulfate increased with growing influences from anthropogenic activity and Asia reaching up to 37 % after more than two weeks of transport time. The most exclusively anthropogenic emission source probed in the upper troposphere was engine exhaust from commercial aircraft liners over Germany. However, in-situ characterization of this aerosol type during aircraft chasing was not possible. All long-range transport aerosol was found to have an O:C ratio close to or greater than 1 implying that low-volatility oxygenated organic aerosol was present in each case despite the variety of origins and the large range in age from 3 to 100 days. This leads to the conclusion that organic particulate matter reaches a final and uniform state of oxygenation after at least 3 days in the free troposphere. rnExcept for aircraft exhaust all emission sources mentioned above are surface-bound and thus rely on different types of vertical transport mechanisms, such as direct high altitude injection in the case of a volcanic eruption, or severe BB, or uplift by convection, to reach higher altitudes where particles can travel long distances before removal mainly caused by cloud scavenging. A lifetime for North American mixed BB and FF aerosol of 7 to 11 days was derived. This in consequence means that emission from surface point sources, e.g. volcanoes, or regions, e.g. East Asia, do not only have a relevant impact on the immediate surroundings but rather on a hemispheric scale including such climate sensitive zones as the tropopause or the Arctic.