Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Comparative functional analysis of factors controlling glial differentiation in Drosophila and mouse

The present study is a comparative functional analysis of three factors controlling glial differentiation in mouse (Fyn Src kinase, hnRNPF/H and NG2) and their homologues in Drosophila (Src42A and 64B, Glorund and Kon-tiki (Kon)). In Drosophila, mutations in any of these genes were not associated with major embryonic neurodevelopmental phenotypes. Src kinases and Glorund were shown to be ubiquitously expressed, whereas kon mRNA showed selective expression in muscles as well as in central and peripheral glia. Kon was also shown to be expressed in L3 larvae with high levels of protein accumulation at the neuromuscular junction (NMJ) and in muscles in the form of speckles. Knockdown of kon in glia resulted in NMJ phenotypes, mainly characterized by a significant increase in bouton number and a reduction in α-Konecto staining intensity at the NMJ. From the three glial layers ensheathing the peripheral nervous system, subperineurial glial showed to be the one contributing the most to kon knockdown dependent NMJ phenotypes, while perineurial glia only had a minor role. The knockdown of kon in glia also showed to affect Glutamate receptor subunit (α-GluRIIA) clustering in the postsynapse, same as microtubule arrangement in the presynapse, as seen by α-Futsch pattern interruptions and alterations. kon knockdown in glia also resulted in impaired axonal transport, as seen by the accumulation of Bruchpilot-positive vesicles along the nerves, abnormal formation of neuronal derived protrusions and swellings, filled with vacuole-like structures. Glia number along the peripheral nerves is also reduced as consequence of kon knockdown. Muscle derived Kon was shown to accumulate at the NMJ and play a role in bouton consolidation and to interfere with phagocytosis of ghost boutons. NMJ bouton and branch number was also significantly increased in Kon overexpression in glia. The overexpression of Kon in glia also resulted in a massive elongation of the ventral nerve cord, which served in a suppressor screen to identify intracellular interaction partners of Kon in glia. It was shown that Kon is processed in glia and preliminary results indicate that the metalloendopeptidase Kuzbanian (the fly homologue of ADAM10) may play a role in the shedding of Konecto. In the present work, Kon is shown as a multifunctional gene with various roles in glia-neuron and glia-neuron-muscle interaction.