Quantum Fields and Strings

The rich network of string dualities provides powerful constraints in the structure of the theory. The connection of ten-dimensional type II theories to eleven-dimensional supergravity compactified on a circle and on a torus allows one to compute many perturbative high genus terms as well as the complete sum of non-perturbative contributions to a given higher derivative coupling of the string effective action. The same duality connection leads to a series of surprising non-renormalization theorems. These control the UV behavior of maximal supergravity in lower dimensions, and indicate that N=8 supergravity in four dimensions might be a finite quantum gravity 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. If time permits, I will also discuss the relation between certain surface operators in gauge theory and brane recombination in F-theory.