Albrecht KLEMM
(Humboldt University, Berlin)
Mirror Symmetry and the Topological String
We review the topological calculations in supersymmetric
field theories in 0,1 and 2 dimensions, with special emphasis
on the non-linear s model case. Then we define
the A-model
on general symplectic manifolds and the B-model on Calabi-Yau manifolds.
We describe selected results in mirror symmetry on CY manifolds, such
as the mirror symmetry predictions for the Gromow-Witten invariants and
the definition of integer invariants for closed an open topological
strings in (non-compact) Calabi-Yau backgrounds (with branes).
Finally we describe aspects of the large N relation between topological
gauge systems and the topological string and review what these theories
calculate in the topological sector of 4d supersymmetric theories.