This series consists of talks in the area of Superstring Theory.
Geometries produced by brane intersections preserving eight supercharges are constructed. Typical examples of such configurations are given by fundamental strings ending on D branes and by brane webs. Consistency conditions of supergravity are shown to impose certain requirements on the locations of the sources, and these restrictions are found to be in a perfect agreement with results of the probe analysis. This agreement serves as a nontrivial test of the duality between open and closed strings. Some applications to AdS/CFT correspondence are also discussed.
F-theory compactifications on Calabi-Yau fourfolds provide one way to obtain N=1 supersymmetric grand unified models of particle physics from string theory. With this motivation in mind, I will consider F-theory on a particularly simple class of local Calabi-Yau fourfolds, for which a low-energy analysis based upon topological gauge theory is valid. For these models, I will explain how the geometry of the fourfold determines the spectrum of massless charged matter and the effective superpotential in four dimensions.
We consider the large N limit of a class of fourdimensional supersymmetric theories in conjunction with a limit in their parameter space towards singular points where extra baryonic states become light, which causes the low-energy description to break down. However, this can be cured by defining a large N double scaling limit where one approaches the singularity by keeping the mass M of these states fixed. This limit has several interesting features.