String Theory and Spacetime Geometry
The basic ideas underlying string theory are described, first for the example of bosonic string theory and then for superstrings. In the supersymmetric case it is explained how one can read off the topology of the spacetime geometry from the superconformal world-sheet description, and to which extent this identification is ambiguous (mirror symmetry). I also explain how open strings (and the associated D-branes) can be included into this framework, and how, at least for certain classes of Calabi-Yau backgrounds, they can be elegantly described in terms of matrix factorisations of the superpotential.
I thank my collaborators Marco Baumgartl, Ilka Brunner, Stefan Fredenhagen and Christoph Keller for enjoyable collaborations on which some of this work is based. My research has been partially supported by the Swiss National Science Foundation, as well as the Marie Curie network ‘Constituents, Fundamental Forces and Symmetries of the Universe’ (MRTN-CT-2004-005104).
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