Off Shell Mirror Symmetry

In these projects we performed a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifications. Starting from a geometric Gauss-Manin connection for B type branes we studied 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. We obtained predictions for genuine Ooguri-Vafa invariants for Lagrangian branes on the quintic in P4 that pass some non-trivial consistency checks. We discussed the lift of the brane compactifications to F-theory on Calabi-Yau 4-folds and the effective couplings in the effective supergravity action as determined by the N = 1 special geometry of the open-closed deformation space.

Further Literature

Lecture Notes