Auf sehr kleinen Längenskalen erlaubt die Weltflächenbeschreibung über zweidimensionale konforme Feldtheorien eine störungstheoretische Definition der String-Theorie. Viele strukturelle Eigenschaften und phänomenologische Implikationen der letzteren können mit Hilfe von D(irichlet)-Branen untersucht werden, die in der zugrunde liegenden Weltflächentheorie durch konforme Randbedingungen beschrieben werden. Etliche interessante Hintergründe für die String-Theorie erhält man über Gruppenmannigfaltigkeiten und Coset-Modelle. Neben wichtigen Beispielen wie SL(2,R), SU(2) und Gepner-Modellen, die für AdS- und Calabi-Yau-Kompaktifizierungen eine Rolle spielen, beinhalten sie außerdem weitere Beispiele wie den Nappi-Witten-Hintergrund oder den Raum T^11, die über eine asymmetrische Wirkung der Eichgruppe definiert sind und eine kosmologische Raumzeit mit Urknall- und Weltsturz-Singularitäten bzw. die Basis des Conifolds beschreiben. Die vorliegende Arbeit bietet eine umfassende, auf den exakten Methoden der konformen Feldtheorie beruhende Analyse von asymmetrischen Coset-Modellen. Wegen der heterotischen Natur der zugrundeliegenden Symmetriealgebra erlauben diese Modelle nur Randbedingungen, die einen Teil der Symmetrie brechen. Nach einer allgemeinen Erläuterung der Grundidee für die Konstruktion von symmetriebrechenden Randbedingungen richtet sich das Hauptaugenmerk auf WZNW- und asymmetrische Coset-Modelle, die das Fundament nahezu aller bekannten konformen Feldtheorien bilden. Mit Hilfe der erzielten Ergebnisse werden die Struktur sowie die Geometrie von D-Branen in den Gruppen SL(2,R) und SU(2), im Hintergrund AdS_3 x S^3, in der kosmologischen Nappi-Witten-Raumzeit und in T^pq-Räumen untersucht. Die Techniken, die in dieser Arbeit entwickelt werden, erlauben jedoch ebenso die Behandlung von Rändern und Kontaktstellen in (1+1)- oder 2-dimensionalen kritischen Systemen, die in der Festkörpertheorie oder der statistischen Physik auftreten. Insbesondere können Defektlinien beschrieben werden, die weder totale Reflexion noch völlige Transmission aufweisen. / At very small length scales, the world sheet approach in terms of two-dimensional conformal field theories provides a perturbative definition of string theory. Many structural properties and phenomenological implications of the latter can be explored using D(irichlet)-branes which may be identified with conformal boundary conditions in the underlying world sheet theory. Several interesting backgrounds in string theory arise from group manifolds and coset theories. Apart from prominent examples such as SL(2,R), SU(2) and Gepner models which play a role in AdS and Calabi-Yau compactifications, they also include further instances like the Nappi-Witten background or the space T^11 which are constructed using an asymmetric action of the gauge group and which describe a cosmological space-time with big-bang and big-crunch singularities and the base of the conifold, respectively. The present thesis provides a comprehensive analysis of asymmetric cosets based on the exact methods of boundary conformal field theory. Due to the heterotic nature of the underlying symmetry algebra, the models only allow for conformal boundary conditions which break parts of the bulk symmetry. The universal ideas for the construction of symmetry breaking boundary conditions are indicated and applied in detail to WZNW and asymmetric coset theories which provide the basic building blocks of almost all known conformal field theories. The general results are used to investigate the structure and shape of D-branes in the group manifolds SL(2,R) and SU(2), the background AdS_3 x S^3, the cosmological Nappi-Witten space-time and T^pq-spaces. The techniques developed in this thesis also allow for a treatment of boundaries and junctions in (1+1)- or 2-dimensional critical systems in condensed matter theory and statistical physics. In particular, they enable us to describe defect lines which go beyond full reflection or transmission.

In dieser Arbeit beschreibe ich verschiedene Aspekte der Kompaktifizierung der String Theorie, insbesondere auf nichttrivialen Mannigfaltigkeiten. Im ersten Teil betrachte ich K-Theorie und ihre Anwendung in der Untersuchung von D-Branen. Es handelt sich um eine verallgemeinerte Kohomologietheorie welche die möglichen Ladungen für eine gegebene Raumzeitmannigfaltigkeit klassifiziert. Eine natürliche Fragestellung ist inwiefern sich diese Beschreibung von der üblichen mit (de Rahm) Kohomologie/Homologie unterscheidet. Hierzu gebe ich eine Calabi-Yau Mannigfaltigkeit an die den Unterschied illustriert. Anstatt der Kompaktifizierung auf einer komplizierten glatten Mannigfaltigkeit kann man auch Orbifolds von einfachen Mannigfaltigkeiten studieren um interessante Kompaktifizierungen zu erhalten. Dies wird mit äquivarianter K-Theorie beschrieben. Um dies mit physikalischen vorhersagen zu vergleichen berechne ich alle KO_{Z_2}(R^{p,q}). Darueberhinaus kann man Orientifolds betrachten, diese führen auf die Definition von neuen K-Theorien. Ich beschreibe einfache Eigenschaften dieser Theorien. Im zweiten Teil präsentiere ich Kompaktifizierungen auf G_2 und Spin(7) Mannigfaltigkeiten und ihre Beschreibung als Gepner Modelle. Die SCFT und die geometrische Beschreibung unterscheiden sich, und ich gebe eine Erklärung für dieses Phänomen. / In this thesis I consider various aspects of string theory compactifications, especially for nontrivial internal manifolds. The first part is dedicated to the application of K-theory to the study of D-branes. It is the generalized cohomology theory which classifies the possible charges on a given spacetime. A natural question is whether there is any difference between K-theory and the usual description via (de Rahm) cohomology/homology. For this I present a Calabi-Yau manifold which illustrates this difference. Instead of compactifying on a complicated smooth manifold one can also consider orbifolds of simple manifolds to get interesting compactifications. These are described by equivariant K-theory. To be able to compare this with the physical prediction I calculate all KO_{Z_2}(R^{p,q}). Furthermore one can consider orientifolds, which suggests the definition of new K-theories. I investigate simple properties of these. In the second part I present compactifications on G_2 and Spin(7) manifolds and their description as Gepner models. The SCFT and the geometric description disagree. An explanation for this phenomenon is offered.

<p>For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level.</p><p>A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only.</p><p>We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.</p>

<p>String theory has proved to be a valuable theoretical laboratory for probing gravity and gauge theory in a unified framework. In this thesis some of the exciting spin-offs of string theory such as branes and higher spin are studied. After a review of the basics of string theory the four papers of the thesis are discussed. In the first paper we support the equivalence between two descriptions of non-commutative open strings by calculating scattering amplitudes in both approaches. The second paper gives a physical interpretation of the fact that Ramond-Ramond charge in string theory on SU(2) is only defined modulo an integer. In the third paper we calculate contributions to the stress-energy tensor of higher-spin theory in four dimensional AdS space, and in the last paper of the thesis we compare the free energy of the two dimesional type 0A extremal blackhole and find agreement with the corresponding quantity in a deformed matrix model.</p>

For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level. A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only. We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.

String theory has proved to be a valuable theoretical laboratory for probing gravity and gauge theory in a unified framework. In this thesis some of the exciting spin-offs of string theory such as branes and higher spin are studied. After a review of the basics of string theory the four papers of the thesis are discussed. In the first paper we support the equivalence between two descriptions of non-commutative open strings by calculating scattering amplitudes in both approaches. The second paper gives a physical interpretation of the fact that Ramond-Ramond charge in string theory on SU(2) is only defined modulo an integer. In the third paper we calculate contributions to the stress-energy tensor of higher-spin theory in four dimensional AdS space, and in the last paper of the thesis we compare the free energy of the two dimesional type 0A extremal blackhole and find agreement with the corresponding quantity in a deformed matrix model.

We discuss certain aspects of string field theory and its applications in exploring the land- scape of classical string theory vacua. We start by giving a brief overview of various tree-level string field theories, as well as of some relevant mathematical background. As a byproduct of our general discussion of observables, we present a new gauge-invariant quantity for the A∞ formulation of open superstring field theory. Putting particular emphasis on perturba- tive methods, we proceed to review in detail the construction of tree-level effective actions governing the dynamics of a certain subset of degrees of freedom. In light of recent devel- opments, we also discuss efficient methods for evaluating certain vertices of zero-momentum effective actions for open superstring and heterotic string field theories in the presence of a global N = 2 worldsheet superconformal symmetry. We show how to apply this perturbative approach to study dynamics of the D(−1)/D3 system (both with and without a B-field), while also discussing a number of more complicated Dp-brane configurations. At generic points in their moduli spaces, such bound states of Dp-branes clearly cannot be described in terms of simple Dirichlet or Neumann boundary conditions. The rest of this thesis is therefore devoted to developing analytic...

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20904号 / 理博第4356号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 杉本 茂樹, 教授 川合 光, 准教授 國友 浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In den letzten Jahren hat die Erforschung von Branen zu vielen neuen Einsichten in String- und M-Theorie geführt. Ein Großteil dieser Forschung behandelte den Fall großen Volumens, wo geometrische Methoden zuverlässige Informationen liefern. Die Extrapolation in den Bereich, wo die endliche Ausdehnung des Strings wichtig wird (`stringy regime'), erfordert gewöhnlich neue Methoden aus der konformen Feldtheorie mit Randbedingungen. Branen auf Gruppenmannigfaltigkeiten ermöglichen einen guten Zugang zu diesem Problem. Obwohl sie nichttriviale Hintergründe beschreiben, was zu vielen interessanten Effekten führt, sind sie immer noch gut beherrschbar. Sie dienen auch als Bausteine bei den Restklassen- und Orbifoldkonstruktionen von im Wesentlichen allen bekannten konformen Modellen. Die vorliegende Arbeit untersucht die Dynamik von Branen auf Gruppenmannigfaltigkeiten und Restklassenmodellen. In einem bestimmten Grenzfall wird die Dynamik von nichtkommutativen Eichtheorien regiert. Viele der Prozesse lassen sich in den Bereich extrapolieren, wo Stringeffekte eine Rolle spielen. Sie äußern sich als Renormierungsgruppenflüsse auf den zweidimensionalen Weltflächentheorien mit Rändern. Solche Flüsse sind auch von Interesse in der Festkörpertheorie, wo sie Randphänomene in eindimensionalen Systemen beschreiben. Wesentliche Daten über diese dynamischen Prozesse sind in Ladungen von D-Branen kodiert. Wir werden die Resultate, die wir über Prozesse zwischen verschiedenen Brankonfigurationen erhalten, mit der Vermutung vergleichen, dass die Ladungen Werte in getwisteten K-Gruppen annehmen. / In recent years, the study of branes has led to many new insights into string and M-theory. Much of this study was done in the large-volume regime where geometric techniques provide reliable information. The extrapolation into the stringy regime usually requires new methods from boundary conformal field theory. Branes on group manifolds give us a good handle on this issue. Although they describe non-trivial backgrounds leading to many interesting effects, they are still tractable. They also serve as building blocks in the coset and orbifold constructions of essentially all known conformal models. The present thesis investigates the dynamics of branes on group manifolds and coset models. In some limiting regime, the dynamics are governed by non-commuta\-tive gauge theories. Many of the processes can be extrapolated to the stringy regime. They manifest themselves as renormalization group flows on the two-dimensional worldsheet theories with boundaries. Such flows are of interest also in condensed matter theory where they describe boundary phenomena in one-dimensional systems. Essential data on these dynamical processes are encoded in D-brane charges. We will compare the obtained results on processes between brane configurations with the conjecture that the charges take their values in twisted K-groups.

In dieser Arbeit stellen wir verschiedene Tests der (M)atrixtheorie-Vermutung vor. Die (M)atrixtheorievermutung besagt, dass die Dynamik von M-Theorie, der Urtheorie, die alle bekannten Stringtheorien und auch elfdimensionale Supergravitation als bestimmte Grenzfaelle enthalten soll, durch ein quantenmechanisches Matrixmodell gegeben ist. Insbesondere untersuchen wir Streuprozesse sowohl aus Sicht des Matrixmodells, als auch aus Sicht der Supergravitation, und vergleichen die resultierenden S-Matrixelemente. Wir finden beeindruckende Uebereinstimmung zwischen den beiden Theorien, solange wir uns auf klassische Supergravitation beschraenken. Sobald wir auch Quanteneffekte auf der Supergravitationsseite einbeziehen, hat diese Uebereinstimmung keinen Bestand. Des weiteren untersuchen wir die Frage, ob Loesungen der klassischen Matrixmodell-Bewegungsgleichungen mit Impulsuebertrag existieren, und finden eine negative Antwort. / In this thesis, we present several tests of the M(atrix)-Model conjecture that asserts that the dynamics of M-Theory, the eleven-dimensional Ur-theory containing all known string theories and also eleven-dimensional supergravity in specific limits, is given by a quantum mechanical matrix model. In particular, scattering processes are analyzed both from the M(atrix)-Model and from the supergravity perspective and the corresponding S-matrix elements are compared. We find impressive agreement between these two theories as long as only classical supergravity is considered. If one includes also quantum effects on the supergravity side, the agreement does not persist. In addition to these calculations, the question of the existence of classical solutions to the M(atrix)-Model equations of motion with momentum transfer is addressed and answered negatively.