Edward Witten named two topological field theories for Calabi-Yau threefolds A and B models respectively in his explanation of mirror symmetry. In the current context, A model is the Gromov-Witten theory and B model the variation of Hodge structure. All known examples of (simply-connected) Calabi-Yau threefolds are connected by a special kind of surgery, called transition. The most basic case of transitions is called conifold transitions.
In this talk, I will explain a phenomenon of partial exchange of A and B models when the Calabi-Yau threefold undergoes a conifold transition. This suggests that there might be an A+B theory which is invariant under transitions and is therefore equivalent for all (simply-connected) Calabi-Yau threefolds.
This talk is based on joint work with H.-W. Lin and C.-L. Wang.