Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications

Understand

We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations.

• Starting from a geometric Gauss-Manin connection for B type branes we study the integrability and flatness conditions.
• The B model geometry defines an interesting ring structure of operators.
• For the mirror A model this indicates the existence of an open-string extension of the so-called A model connection, whereas the discovered ring structure should be part of the open-string A model quantum cohomology.