### Lectures on D-branes and SheavesLectures on D-branes and Sheaves

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 Author Sharpe, E. Source arXiv.org Content type Text File Format PDF Date of Submission 2003-07-24 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics Subject Keyword High Energy Physics - Theory ♦ physics:hep-th Abstract These notes are a writeup of lectures given at the twelfth Oporto meeting on Geometry, Topology, and Physics,'' and at the Adelaide workshop Strings and Mathematics 2003,'' primarily geared towards a physics audience. We review current work relating boundary states in the open string B model on Calabi-Yau manifolds to sheaves. Such relationships provide us with a mechanism for counting open string states in situations where the physical spectrum calculation is nearly intractable -- after translating to mathematics, such calculations become easy. We describe several different approaches to these models, and also describe how these models are changed by varying physical circumstances -- flat B field backgrounds, orbifolds, and nonzero Higgs vevs. We also discuss mathematical interpretations of operator products, and how such mathematical interpretations can be checked physically. One of the motivations for this work is to understand the precise physical relationship between boundary states in the open string B model and derived categories in mathematics, and we outline what is currently known of the relationship. Educational Use Research Learning Resource Type Article Page Count 87