Quantum Fields and Strings

We discuss recent developments in the study of black holes and similar compact objects in string theory. The focus is on how these solutions are effected by higher-derivative terms in an effective action. The setting of this investigation is an off-shell formulation of five-dimensional supergravity, including terms of order four-derivatives whose precise form are determined by embedding this theory in M-theory. We find that certain singular solutions are fully regularized by the higher-derivative terms and that generic solutions receive calculable corrections to the entropy, or other relevant quantities such as the dual central charge. A particular solution studied corresponds to the geometry sourced by a fundamental string and may set the stage for a new and exciting example of holography.

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.