A new approach for computing the geometry of the moduli spaces for a Calabi–Yau manifold

Konstantin Aleshkin, Alexander Belavin
2018 Journal of Physics A: Mathematical and Theoretical  
It is known that moduli spaces of Calabi-Yau (CY) manifolds are special K\"ahler manifolds. This structure determines the corresponding low-energy effective theory which arises in superstring compactifications on CY manifolds. In the case, where CY manifold is given as a hypersurface in the weighted projective space, we propose a new procedure for computing the K\"ahler potential of the moduli space. Our method is based on the fact that the moduli space of CY manifolds is a marginal subspace of
more » ... arginal subspace of the Frobenius manifold which arises on the deformation space of the corresponding Landau--Ginzburg superpotential.
doi:10.1088/1751-8121/aa9e7a fatcat:me567ztfe5h6lgdug5og74uera