Strings and membranes in curved space

Abstract

The extension of Polyakov string theory to curved target spaces is considered. At the classical level, the close connection between string theory and the mathematical theories of minimal surfaces and harmonic mappings is exhibited. It is shown that only trivial classical solutions exist for Euclidian target spaces. A discussion of the existence of non-trivial classical solutions for curved target spaces is presented. Certain classical solutions are selected and a background field approach is used to develop a toy model of strings in S3, which is then extended to a simple (time-sliced) model of cosmological membranes in S3*R. It is found that a non-trivial cosmological membrane theory can be derived in S3*R without the addition of a cosmological term to the action.