Supersymmetric Gauge Theories from String Theory

The subject of this thesis are various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain subcycles. The low energy limit of this non-Abelian gauge theory can be obtained from a second non-compact Calabi-Yau geometry, which is related to the first one through a geometric transition. In particular, the effective superpotential governing the vacuum structure of the gauge theory can be obtained from integrals on a Calabi-Yau manifold. These integrals in turn are related to matrix model quantities and one therefore can use the matrix model to learn something about the gauge theory vacua. The second part of this work covers the generation of four-dimensional supersymmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G_2-manifolds. We discuss anomaly cancellation through inflow in the case of conical singularities, present an explicit compact manifold with two conical singularities and weak G_2-holonomy, and review the anomaly cancellation mechanism in the context of M-theory on the interval.Comment: PhD-thesis; 224 pages, 17 figure

User-centric knowledge extraction and maintenance

An ontology is a machine readable knowledge collection. There is an abundance of information available for human consumption. Thus, large general knowledge ontologies are typically generated tapping into this information source using imperfect automatic extraction approaches that translate human readable text into machine readable semantic knowledge. This thesis provides methods for user-driven ontology generation and maintenance. In particular, this work consists of three main contributions: 1. An interactive human-supported extraction tool: LUKe. The system extends an automatic extraction framework to integrate human feedback on extraction decisions and extracted information on multiple levels. 2. A document retrieval approach based on semantic statements: S3K. While one application is the retrieval of documents that support extracted information to verify the correctness of the piece of information, another application in combination with an extraction system is a fact based indexing of a document corpus allowing statement based document retrieval. 3. A method for similarity based ontology navigation: QBEES. The approach enables search by example. That is, given a set of semantic entities, it provides the most similar entities with respect to their semantic properties considering different aspects. All three components are integrated into a modular architecture that also provides an interface for third-party components.Eine Ontologie ist eine Wissenssammlung in maschinenlesbarer Form. Da eine große Bandbreite an Informationen nur in natürlichsprachlicher Form verfügbar ist, werden maschinenlesbare Ontologien häufig durch imperfekte automatische Verfahren erzeugt, die eine Übersetzung in eine maschinenlesbare Darstellung vornehmen. In der vorliegenden Arbeit werden Methoden zur menschlichen Unterstützung des Extraktionsprozesses und Wartung der erzeugten Wissensbasen präsentiert. Dabei werden drei Beiträge geleistet: 1. Zum ersten wird ein interaktives Extraktionstool (LUKe) vorgestellt. Hierfür wird ein bestehendes Extraktionssystem um die Integration von Nutzerkorrekturen auf verschiedenen Ebenen der Extraktion erweitert und an ein beispielhaftes Szenario angepasst. 2. Zum zweiten wird ein Ansatz (S3K) zur Dokumentsuche basierend auf faktischen Aussagen beschrieben. Dieser erlaubt eine aussagenbasierte Suche nach Belegstellen oder weiteren Informationen im Zusammenhang mit diesen Aussagen in den Dokumentsammlungen die der Wissensbasis zugrunde liegen. 3. Zuletzt wird QBEES, eine Ähnlichkeitssuche in Ontologien, vorgestellt. QBEES ermöglicht die Suche bzw. Empfehlung von ähnlichen Entitäten auf Basis der semantischen Eigenschaften die sie mit einer als Beispiel angegebenen Menge von Entitäten gemein haben. Alle einzelnen Komponenten sind zudem in eine modulare Gesamtarchitektur integriert

Relating prepotentials and quantum vacua of N=1 gauge theories with different tree-level superpotentials

We consider N=1 supersymmetric U(N) gauge theories with Z_k symmetric tree-level superpotentials W for an adjoint chiral multiplet. We show that (for integer 2N/k) this Z_k symmetry survives in the quantum effective theory as a corresponding symmetry of the effective superpotential W_eff(S_i) under permutations of the S_i. For W(x)=^W(h(x)) with h(x)=x^k, this allows us to express the prepotential F_0 and effective superpotential W_eff on certain submanifolds of the moduli space in terms of an ^F_0 and ^W_eff of a different theory with tree-level superpotential ^W. In particular, if the Z_k symmetric polynomial W(x) is of degree 2k, then ^W is gaussian and we obtain very explicit formulae for F_0 and W_eff. Moreover, in this case, every vacuum of the effective Veneziano-Yankielowicz superpotential ^W_eff is shown to give rise to a vacuum of W_eff. Somewhat surprisingly, at the level of the prepotential F_0(S_i) the permutation symmetry only holds for k=2, while it is anomalous for k>2 due to subtleties related to the non-compact period integrals. Some of these results are also extended to general polynomial relations h(x) between the tree-level superpotentials.Comment: 27 pages, 10 figures, modified version to appear in JHEP, discussion of the physical meaning of the Z_k symmetry adde

Anomalies in M-theory on singular G_2-manifolds

When M-theory is compactified on G_2-holonomy manifolds with conical singularities, charged chiral fermions are present and the low-energy four-dimensional theory is potentially anomalous. We reconsider the issue of anomaly cancellation, first studied by Witten. We propose a mechanism that provides local cancellation of all gauge and mixed gauge-gravitational anomalies, i.e. separately for each conical singularity. It is similar in spirit to the one used to cancel the normal bundle anomaly in the presence of five-branes. It involves smoothly cutting off all fields close to the conical singularities, resulting in an anomalous variation of the 3-form C and of the non-abelian gauge fields present if there are also ADE singularities.Comment: 29 pages; references added, version to appear in Nucl.Phys.

Compact weak G_2-manifolds with conical singularities

We construct 7-dimensional compact Einstein spaces with conical singularities that preserve 1/8 of the supersymmetries of M-theory. Mathematically they have weak G_2-holonomy. We show that for every non-compact G_2-holonomy manifold which is asymptotic to a cone on a 6-manifold Y, there is a corresponding weak G_2-manifold with two conical singularities which, close to the singularities, looks like a cone on Y. Our construction provides explicit metrics on these weak G_2-manifolds. We completely determine the cohomology of these manifolds in terms of the cohomology of Y.Comment: 26 pages, Latex, version to be published in Nucl. Phys. B, minor changes, one appendix adde

Anomaly cancellation in M-theory: a critical review

We carefully review the basic examples of anomaly cancellation in M-theory: the 5-brane anomalies and the anomalies on S^1/Z_2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly fix all coefficients and signs, proper attention is paid to issues of orientation, chirality and the Euclidean continuation. Independent of the conventions chosen, the Chern-Simons and Green-Schwarz terms must always have the same sign. The reanalysis of the reduction to the heterotic string on S^1/Z_2 yields a surprise: a previously neglected factor forces us to slightly modify the Chern-Simons term, similar to what is needed for cancelling the normal bundle anomaly of the 5-brane. This modification leads to a local cancellation of the anomaly, while maintaining the periodicity on S^1.Comment: 35 page