Topological Sigma Models and Generalized Geometries

Citation

Li, Yi (2005) Topological Sigma Models and Generalized Geometries. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RMHE-4185. https://resolver.caltech.edu/CaltechETD:etd-05262005-154458

Abstract

We study the relation between topological sigma models and generalized geometries. The existence conditions for the most general type of topological sigma models obtained from twisting the N=(2,2) supersymmetric sigma model are investigated, and are found to be related to twisted generalized Calabi-Yau structures. The properties of these topological sigma models are analyzed in detail. The observables are shown to be described by the cohomology of a Lie algebroid, which is intrinsically associated with the twisted generalized Calabi-Yau structure. The Frobenius structure on the space of states and the effects of instantons are analyzed. We also study D-branes in these topological sigma models, and demonstrate that they also admit descriptions in terms of generalized geometries.

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