Twisted Generalized Calabi-Yau Manifolds and Topological Sigma Models with Flux (Part 1)

          @misc{ pirsa_PIRSA:05020017,
            doi = {},
            url = {https://pirsa.org/05020017},
            author = {Li, Yi},
            keywords = {},
            language = {en},
            title = {Twisted Generalized Calabi-Yau Manifolds and Topological Sigma Models with Flux (Part 1)},
            publisher = {Perimeter Institute},
            year = {2005},
            month = {feb},
            note = {PIRSA:05020017 see, \url{https://pirsa.org}}
          }
          

Abstract

In these lectures, we examine how twisted generalized Calabi-Yau (GCY) manifolds arise in the construction of a general class of topological sigma models with non-trivial three-form flux. The topological sigma model defined on a twisted GCY can be regarded as a simultaneous generalization of the more familiar A-model and B-model. Emphasis will be given to the relation between topological observables of the sigma model and a Lie algebroid cohomology intrinsically associated with the twisted GCY. If time permits, we shall also discuss topological D-branes in this more general setting, and explain how the viewpoint from the Lie algebroid helps to elucidate certain subtleties even for the conventional A-branes and B-branes. The lectures will be physically motivated, although I will try to make the presentation self-contained for both mathematicians and physicists.