Mathematics

Partition functions of N=(2,2) supersymmetric two-dimensional gauge linear sigmamodels on a sphere can be computed exactly. When vacua manifold of the model is a Calabi-Yaumanifold it was conjectured that the partition function computes special Kahlergeometry (in particular Gromow-Witten invariants) on the quantum moduli space ofKahler class deformations of the Calabi-Yau.In the talk I will present the mirror symmetric version of this conjecture andprove it for a class of Calabi-Yau manifolds. In particular, I will show thatnatural gauge theory couplings are most easily connected with complex structuredeformations rather than with the Kahler class deformations.