Mathematics

It is known that low energy limits of superstring compactifications over Calabi-Yau variesties give rise to effective quantum gravity with matter which can be used to construct semi-realistic theories. One of the important ingredients is Special Kahler Geometry which describes two-point functions of the matter fields. Mathematically they are natural metrics on the corresponding Calabi-Yau variety moduli spaces. The first exact computation was done by Candelas et al. in the wonderful paper where they predicted Gromov-Witten invariants of the Quintic threefold using complicated geometry of the Calabi-Yau variety. In the talk I plan to explain the recent advances in this direction, where using connection with Landau-Ginzburg models we managed to compute the Special geometry for large classes of examples and for higher dimensional moduli spaces. I plan to illustrate it on the Quintic threefold example, where we can compute the geometry on the 101-dimensional moduli space compared to the previously known 1-dimensional subspace. The presentation will be as elementary and self-contained as possible.