Topological Sigma Models and Generalized Geometries

D-brane;differential geometry;generalized geometry;sigma model;topological field theory

Li, Yi ; Kapustin, Anton N.

University:California Institute of Technology

Department:Physics, Mathematics and Astronomy

关键词: D-brane;    differential geometry;    generalized geometry;    sigma model;    topological field theory;   

Others  :  https://thesis.library.caltech.edu/2098/1/thesis.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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.