2018/08/14 by Alexander Belavin, Belavin, Alexander
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.1808.05470
Contribution to Proceedings of International Congress of Mathematicians 2018,Rio de Janeiro,(2018). arXiv admin note: substantial text overlap with arXiv:1710.11609
arxiv created 2018/08/14 · arxiv updated 2018/08/17
The moduli spaces of Calabi--Yau (CY) manifolds are the special Kähler manifolds. The special Kähler geometry determines the low-energy effective theory which arises in Superstring theory after the compactification on a CY manifold. For the cases, where the CY manifold is given as a hypersurface in the weighted projective space, a new procedure for computing the Kähler potential of the moduli space has been proposed in \cite AKBA1,AKBA2, AKBA3. The method is based on the fact that the moduli space of CY manifolds is a marginal subspace of the Frobenius manifold which arises on the deformation space of the corresponding Landau--Ginzburg superpotential. I review this approach and demonstrate its efficiency by computing the Special geometry of the 101-dimensional moduli space of the quintic threefold around the orbifold point \cite AKBA3.