Veranstaltung

Vortrag
Mirror symmetry and the topological A- and B-model
Prof. Dr. Albrecht Klemm, University of Wisconsin/ Madison
9.1.2006, 14:00 Uhr – 15:00 Uhr

Mirror symmetry on CY manifolds exchanges the symplectic structure on M, actually a complexified Kähler structure, with the complex structure on a mirror dual CY manifold W. The deformation theory of each of these structures can be described by a topological string theory called the topological A- and the B-model respectively. These models are cohomological theories defined by nilpotent operators QA and QB. We will show that QA exists on every symplectic manifold while QB exists only on CY manifolds and certain generalizations thereof. The latter fact is related to the Tian & Todorov theorem on the unobstructedness of complex structure deformations on CY spaces and generalizations by Hitchin. We will then discuss properties of cohomological theories theories notably the descend- and topological recursion relations. The solution of the topological B-model using these recursion relations and some classical methods of complex structure deformation theory on W is worked out and related by mirror symmetry to the Gromov-Witten theory captured by the topological A-model on M.