Lectures on Warped Compactifications and Stringy Brane Constructions

TL;DR

This paper reviews warped compactifications in 5d gravity and string theory brane constructions, discussing their implications for hierarchy and cosmological problems, and explores stringy calculations related to D-branes on Calabi-Yau manifolds.

Contribution

It provides a comprehensive overview of warped compactifications and detailed methods for computing superpotentials in string theory brane setups, advancing understanding of supersymmetry breaking and moduli stabilization.

Findings

Warped compactifications can address hierarchy and cosmological constant problems.

String theory D-brane calculations inform supersymmetry breaking mechanisms.

Probing quantum geometry of Calabi-Yau spaces through superpotential computations.

Abstract

In these lectures, two different aspects of brane world scenarios in 5d gravity or string theory are discussed. In the first two lectures, work on how warped compactifications of 5d gravity theories can change the guise of the hierarchy problem and the cosmological constant problem is reviewed, and a discussion of several issues which remain unclear in this context is provided. In the next two lectures, microscopic constructions in string theory which involve D-branes wrapped on cycles of Calabi-Yau manifolds are described. The focus is on computing the superpotential in the brane worldvolume field theory. Such calculations may be a necessary step towards understanding e.g. supersymmetry breaking and moduli stabilization in stringy realizations of such scenarios, and are of intrinsic interest as probes of the quantum geometry of the Calabi-Yau space.