New N=1 Superconformal Field Theories and their Supergravity Description

In this note we construct a new class of superconformal field theories as mass deformed N=4 super Yang-Mills theories. We will argue that these theories correspond to the fixed points which were recently found by Khavaev, Pilch and Warner studying the deformations of the dual IIB string theory on AdS_5\times S^5.Comment: LaTeX2e; v2: 2 references added; v3: discussion about selfduality correcte

N=1 Supersymmetric Gauge Theories and Supersymmetric 3-cycles

In this paper we discuss the strong coupling limit of chiral N=1 supersymmetric gauge theory via their embedding into M-theory. In particular we focus on the brane box models of Hanany and Zaffaroni and show that after a T-duality transformation their M-theory embedding is described by supersymmetric 3-cycles; its geometry will encode the holomorphic non-perturbative information about the gauge theory.Comment: 36 pages, LaTeX2e, 10 figures, additional references added, minor correction

Mirror Symmetries for Brane Configurations and Branes at Singularities

We study local mirror symmetry on non-compact Calabi-Yau manifolds (conifold type of singularities) in the presence of D3 brane probes. Using an intermediate brane setup of NS 5-branes `probed' by D4 resp. D5 branes, we can explicitly T-dualize three isometry directions to relate a non-compact Calabi-Yau manifold to its local mirror. The intermediate brane setup is the one that is best suited to read off the gauge theory on the probe. Both intervals and boxes of NS 5-branes appear as brane setups. Going from one to the other is equivalent to performing a conifold transition in the dual geometry. One result of our investigation is that the brane box rules as they have been discussed so far should be generalized. Our new rules do not need diagonal fields localized at the intersection. The old rules reappear on baryonic branches of the theory.Comment: LaTeX2e, 36 pages; typos corrected and 3 references adde

Killing Spinor Equations from Nonlinear Realisations

Starting from a nonlinear realisation of eleven dimensional supergravity based on the group G11, whose generators appear as low level generators of E11, we present a super extended algebra, which leads to a covariant derivative of spinors identical to the Killing spinor equation of this theory. A similar construction leads to the Killing spinor equation of N=1 pure supergravity in ten dimensions.Comment: 16 pages, typos correcte

CFT/CFT interpolating RG flows and the holographic c-function

We consider holographic RG flows which interpolate between non-trivial ultra-violet (UV) and infra-red (IR) conformal fixed points. We study the ``superpotentials'' which characterize different flows and discuss their expansions near the fixed points. Then we focus on the holographic $c$-function as defined from the two-point function of the stress-energy tensor. We point out that the equation for the metric fluctuations in the background flow is equivalent to a scattering problem and we use this to obtain an expression for the $c$-function in terms of the associated Jost functions. We propose two explicit models that realize UV-IR flows. In the first example we consider a thin wall separating two AdS spaces with different radii, while in the second one the UV region is replaced with an asymptotically AdS space. We find that the holographic $c$-function obeys the expected properties. In particular it reduces to the correct -- nonzero -- central charge in the IR limit.Comment: 20 pages, discussion at the end of sec. 3 and sec. 4.1 change

Branes between geometry and gauge theory

Der Gegenstand dieser Arbeit ist Bestandteil der Stringtheorie und betrifft insbesondere die geometrischen Aspekte der Realisierung von Eichtheorien innerhalb der Stringtheorie. Wir studieren die Eichtheorie von D3-Branes an verallgemeinerten Singularitaeten wie der Orbifold- oder Conifold-Singularitaet. Die Einfuehrung der sogenannten Branediamanten fuehrt auf ein konsistentes Bild. Fuer diese Klasse von Modellen wird die Wirkung der Mirrorsymmetrie diskutiert. Im zweiten Teil untersuchen wir die Feldtheorie der M5-Brane auf der Grundlage des Supereinbettungsformalismus. Das Hauptresultat dieses Kapitels ist eine explizite Identifikation der selbstdualen 3-Form mit den Parametern der komplexen Struktur des Einbettungsraumes. Das heuristische Material, das in den vorangegangenen Kapiteln angesammelt wurde, weist darauf hin, dass die Informationen, die ein supersymmetrischer 3-Zykel enthaelt, zumindest teilweise auf supersymmetrische 2-Zykel zurueckgefuehrt werden koennen. Daher studieren wir den Fall von Brane-Boxen, die durch Ueberlagerung von gewoehnlichen N=2 Systemen aus D4 und NS5-Branes gewonnen werden koennen. Diese Konfigurationen erfuellen die Bedingung des `uniform bending' und der Lift auf einen supersymmetrischen 3-Zykel kann explizit ausgefuehrt werden. Im letzten Teil konstruieren wir eine neue superkonforme N=1 Eichtheorie, die aus einer Massendeformation der N=4 SYM entsteht und eine duale Supergravitationsbeschreibung durch die AdS/CFT-Korrespondenz besitzt.The subject of this work is part of the theory of strings and in particular concerned with geometrical aspects of the realization of gauge theory within string theory. In particular we study the gauge theory of D3-branes at generalised singularities like orbifolds and the orbifolded conifold singularities. The introduction of the so called diamonds leads to a consistent picture. The action of mirror symmetry for this class of models is discussed. In a second part the field theory of the M5-brane will be investigated on the basis of the superembedding approach. The main result here will be a rather explicit identification of the self dual three form field with the parameters of the complex structure of the embedding space. The heuristic material collected from the previous chapters states that the information contained in supersymmetric 3-cycles can be partially extracted from supersymmetric 2-cycles. Thus we study the case of brane boxes, which can be obtained by sewing together usual N=2 setups of D4 and NS5-branes. These systems satisfy the condition of uniform bending and the lift to a supersymmetric 3-cycle can be performed explicitly. In the last part a new superconformal N=1 gauge theories will be constructed which arise as certain deformations of N=4 SYM and have a dual description due to the AdS/CFT correspondence