|abstract ||A promising candidate for a fundamental theory of nature, incorporating both general relativity and quantum mechanics, is string theory. This theory is based on one-dimensional extended objects that move through spacetime. However, string theory is most naturally formulated in ten dimensions. To consider string theory in four dimensions one can compactify six dimensions (by making them very small) and compute the effect on the theory. This yields a certain four-dimensional theory. Furthermore, string theory contains also extended objects of higher dimensions, these are called D-branes (think for example of a membrane). Their effect on the four-dimensional theory should be considered as well. This is what we have done, in a certain setting, and the results are presented in this thesis.
We work in the supergravity approximation, which means that we restrict ourselves to length scales (much) smaller than the string length. In this approximation the D-branes are described by solitonic solutions to the supergravity equations of motion. We consider the N=2 supergravity theory in four dimensions resulting from compactifying type IIA supergravity (the low energy limit of type IIA string theory) on a six-dimensional Calabi-Yau manifold. Furthermore we consider the membrane and NS five-brane. In the four-dimensional theory they can be described by finite action solutions to the equations of motion. We then construct the effective action which incorporates the effects of the membrane and the five-brane, respectively. The effective N=2 supergravity action (the supergravity multiplet coupled to a hypermultiplet) in four dimensions incorporating the one-loop effects in the background of a NS five-brane is computed by a 'traditional' instanton calculation. The effective action incorporating the one-loop effect in the presence of a membrane is computed using knowledge of the symmetries of the action and their breaking by the membrane.
These nonperturbative corrections affect the hypermultiplet sector of the N=2 supergravity theory. Furthermore, we gauge an isometry of the hypermultiplet sector. This produces a potential. This potential has certain minima and the effect of the nonperturbative membrane corrections is to produce a metastable minimum which can have a positive value: a de Sitter minimum.|