Topological Sigma Models and Generalized Geometries

Author: Li, Yi

Year: 2005

Degree: Dissertation (Ph.D.)

Advisor: Kapustin, Anton N.

Committee Members: Kapustin, Anton N.; Porter, Frank C.; Ooguri, Hirosi; Schwarz, John H.

Option: Physics

DOI: 10.7907/RMHE-4185

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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