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.

Deriving Deligne-Mumford stacks with perfect obstruction theories

Intersection theory on moduli spaces has lead to immense progress in certain areas of enumerative geometry. For some important areas, most notably counting stable maps and counting stable sheaves, it is important to work with a virtual fundamental class instead of the usual fundamental class of the moduli space. The crucial prerequisite for the existence of such a class is a two-term complex controlling deformations of the moduli space. Kontsevich conjectured in 1994 that there should exist derived version of spaces with this specific property. Another hint at the existence of these spaces comes from derived algebraic geometry. It is expected that for every pair of a space and a complex controlling deformations of the space their exists, under some additional hypothesis, a derived version of the space having the chosen complex as cotangent complex. In this thesis one version of these additional hypothesis is identified. We then show that every space admitting a two-term complex controlling deformations satisfies these hypothesis, and we finally construct the derived spaces.

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.

Host race formation in Hyalesthes obsoletus (Signoret 1865)

Die Winden-Glasflügelzikade Hyalesthes obsoletus (Cixiidae, Glasflügelzikaden) nutzte in Deutschland ursprünglich die Ackerwinde Convolvulus arvensis als Wirtspflanze, allerdings nahm in den letzten zwei Dekaden die Abundanz auf der Großen Brennnessel Urtica dioica stark zu, zusammen mit der Inzidenz der Schwarzholzkrankheit Bois noir auf Weinreben. Bois noir wird durch ein Phytoplasma verursacht, das durch H. obsoletus von C. arvensis und U. dioica auf Weinreben übertragen wird. Es stellte sich daher die Frage, ob H. obsoletus Wirtsrassen entwickelt hat, die möglicherweise die Bois noir-Epidemiologie beeinflussen. In der vorliegenden Studie wurden folgende Fragestellungen bearbeitet: rn(1) Gibt es in Deutschland und Europa genetisch unterscheidbare Wirtsrassen von H. obsoletus auf den beiden Wirtspflanzen C. arvensis und U. dioica? Es wurden sieben Mikrosatellitenmarker entwickelt und etabliert, um H. obsoletus Populationen aus Deutschland und Europa genetisch zu analysieren. Es zeigte sich eine deutliche Differenzierung zwischen Populationen von beiden Wirtspflanzen in Deutschland, jedoch nicht in den historischen Ursprungsgebieten der deutschen Populationen, in der Schweiz, Italien oder Slovenien.rn(2) Wo sind die deutschen Wirtsrassen von H. obsoletus entstanden? Eine Einwanderung von südlichen, bereits an U. dioica angepassten Individuen stand einer lokalen Wirtsrassenevolution gegenüber. Die engere genetische Verwandtschaft der deutschen Population auf U. dioica zu denen auf C. arvensis, im Vergleich zu den übrigen Populationen auf U. dioica, impliziert einen lokalen Prozess im nördlichen Verbreitungsgebiet. Eine Immigration südlicher Tiere scheint nicht zur Diversifizierung beigetragen zu haben, führte aber möglicherweise einen U. dioica-spezifischen Phytoplasma-Stamm ein. Durch Wirtsrassenevolution entwickelten sich spezifische, vektorbasierte epidemiologische Kreisläufe der Schwarzholzkrankheit Bois noir. rn(3) Welche Präferenzen zeigen die beiden Wirtsrassen von H. obsoletus für die Wirtspflanzen C. arvensis und U. dioica und unterscheiden sich diese? Die Präferenz von H. obsoletus aus beiden deutschen Wirtsrassen in Bezug auf den Geruch der Wirtspflanzen wurde in einem Y-Olfaktometer untersucht, zusätzlich wurden beide Pflanzen direkt zur Wahl gestellt. Bei beiden Untersuchungen zeigte die Population von C. arvensis eine signifikante Präferenz für ihre native Wirtspflanze. Die Population von U. dioica wies dagegen keine Präferenz für den Geruch einer Wirtspflanze auf, bevorzugte im direkten Test jedoch signifikant ihre native Wirtspflanze. Dies weist darauf hin, dass die Anpassung an den „neuen“ Wirt noch nicht vollständig ist.rn

Gender und Genre in melodramatischen Literaturverfilmungen der Gegenwart - Far From Heaven, The Hours, A Single Man

Die Dissertation Gender und Genre in melodramatischen Literaturverfilmungen der Gegenwart untersucht das Medium Film anhand von Todd Haynes’ Far from Heaven (2002), Stephen Daldrys The Hours (2002) und Tom Fords A Single Man (2009) als Quelle des Wissens über gesellschaftlich-normierte Geschlechterrollen und sozialkonstruierte Genderkonzepte. Die Arbeit versteht sich als eine nachhaltige Schnittstellenforschung zwischen Gender-, Literatur-, Film- und Medienwissenschaften und zeigt die Öffnung der Germanistik für den medial geprägten Kulturwandel, welcher den deutschen bzw. den deutschsprachigen Kulturraum betrifft. Gender und Geschlecht destabilisieren die Gesellschaft und die „heterosexuelle Matrix“ durch das individuelle Suchen, Finden, Konstruieren und Anerkennen einer eigenen, individuellen Genderidentität. Dieser Prozess kann unter Zuhilfenahme des Erzählens von Geschlecht im Film verdeutlicht werden, denn die audiovisuelle Fiktion modelliert Wirklichkeitsvorstellungen und das Wirklichkeitsverständnis der Rezipienten. Wobei offen bleibt, ob die Fiktion die Realität oder die Realität die Fiktion imitiert. Denn es gibt nicht nur eine Wahrheit, sondern mehrere, vielleicht unzählige Bedeutungszuschreibungen. Die drei paradigmatischen Literaturverfilmungen wurden jeweils in Bezug zu ihren Literaturvorlagen von Virginia Woolf, Michael Cunningham und Christopher Isherwood gesetzt. Sie können als Beispiele für ein wissendes, postmodernes Pastiche des Themen-Clusters Diskriminierung/Homophobie/Homosexualität/„Rasse“ gelten. Alle drei Filme verhandeln durch gemeinsame, melodramatische Motive (Spiegel, Telefon, Krieg, Familie) die Darstellbarkeit von Emotionen, Begehren, Sehnsüchten, Einsamkeit und dem Verlust der Liebe. Durch Verbindungslinien zu den Melodramen von Douglas Sirk und mittels den Theorien von u.a. Judith Butler, Stanley Cavell, Carolin Emcke, Thomas Elsaesser, Sigmund Freud, Hermann Kappelhoff und Laura Mulvey wurde das Begriffspaar Genre und Gender her-ausgestellt und im zeitgenössischen Geschlechter-Diskurs verortet. Das im Verlauf der Arbeit erarbeitete Wissen zu Gender, Sexualität, Körper und Geschlecht wurde als ein Gender-Genre-Hybrid verstanden und im Genre des queeren bzw. homosexuellen Melodrams (gay melodrama) neu verortet. Die drei Filme sind als ein Wiederbelebungsversuch bzw. ein Erweiterungsversuch des melodramatischen Genres unter dem Genderaspekt anzusehen. Die Analyse und Dekonstruktion feststehender Begriffe im Kontext der Gender- und Gay Studies und dem Queer Cinema lösen produktive Krisen und damit emanzipierte Verfahren aus. Diese müssen immer wieder neu beschrieben werden, damit sie wahrgenommen und verstanden werden. Daher sind die drei melodramatischen Literaturverfilmungen ein fiktionales Dokumentationsmodell gesellschaftlicher Konflikte, welches anhand individueller Schicksale verdeutlicht wird.

The performativity of nonviolent protest in South Asia (1918 - 1948)

This study seeks to address a gap in the study of nonviolent action. The gap relates to the question of how nonviolence is performed, as opposed to the meaning or impact of nonviolent politics. The dissertation approaches the history of nonviolent protest in South Asia through the lens of performance studies. Such a shift allows for concepts such as performativity and theatricality to be tested in terms of their applicability and relevance to contemporary political and philosophical questions. It also allows for a different perspective on the historiography of nonviolent protest. Using concepts, modes of analysis and tropes of thinking from the emerging field of performance studies, the dissertation analyses two different cases of nonviolent protest, asking how politics is performatively constituted. The first two sections of this study set out the parameters of the key terms of the dissertation: nonviolence and performativity, by tracing their genealogies and legacies as terms. These histories are then located as an intersection in the founding of the nonviolent. The case studies at the analytical core of the dissertation are: fasting as a method in Gandhi's political arsenal, and the army of nonviolent soldiers in the North-West Frontier Province, known as the Khudai Khidmatgar. The study begins with an overview of current theorisations of nonviolence. The approach to the subject is through an investigation of commonly held misconceptions about nonviolent action, such as its supposed passivity, the absence of violence, its ineffectiveness and its spiritual basis. This section addresses the lacunae within existing theories of nonviolence and points to possible fertile spaces for further exploration. Section 3 offers an overview of the different shades of the concept of performativity, asking how it is used in various contexts and how these different nuances can be viewed in relation to each other. The dissertation explores how a theory of performativity may be correlated to the theorisation of nonviolence. The correlations are established in four boundary areas: action/inaction, violence/absence of violence, the actor/opponent and the body/spirit. These boundary areas allow for a theorising of nonviolent action as a performative process. The first case study is Gandhi's use of the fast as a method of nonviolent protest. Using a close reading of his own writings, speeches and letters, as well as a reading of responses to his fast in British newspapers and within India, the dissertation asks what made fasting into Gandhi's most favoured mode of protest and political action. The study reconstructs his unique praxis of the fast from a performative perspective, demonstrating how display and ostentation are vital to the political economy of the fast. It also unveils the cultural context and historical reservoir of body practices, which Gandhi drew from and adapted into 'weapons' of political action. The relationship of Gandhian nonviolence to the body forms a crucial part of the analysis. The second case study is the nonviolent army of the Pashtuns, Khudai Khidmatgar (KK), literally Servants of God. This anti-imperialist movement in the North-West Frontier Province of what is today the border between Pakistan and Afghanistan existed between 1929 and 1948. The movement adopted the organisational form of an army. It conducted protest activities against colonial rule, as well as social reform activities for the Pashtuns. This group was connected to the Congress party of Gandhi, but the dissertation argues that their conceptualisation and praxis of nonviolence emerged from a very different tradition and worldview. Following a brief introduction to the socio-political background of this Pashtun movement, the dissertation explores the activities that this nonviolent army engaged in, looking at their unique understanding of the militancy of an unarmed force, and their mode of combat and confrontation. Of particular interest to the analysis is the way the KK re-combined and mixed what appear to be contradictory ideologies and acts. In doing so, they reframed cultural and historical stereotypes of the Pashtuns as a martial race, juxtaposing the institutional form of the army with a nonviolent praxis based on Islamic principles and social reform. The example of the Khudai Khidmatgar is used to explore the idea that nonviolence is not the opposite of violent conflict, but in fact a dialectical engagement and response to violence. Section 5, in conclusion, returns to the boundary areas of nonviolence: action, violence, the opponent and the body, and re-visits these areas on a comparative note, bringing together elements from Gandhi's fasts and the practices of the KK. The similarities and differences in the two examples are assessed and contextualised in relation to the guiding question of this study, namely the question of the performativity of nonviolent action.