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

Abstract

It is known that moduli spaces of Calabi-Yau (CY) manifolds are special Kähler 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 Kähler potential of the moduli space. Our 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.

References in corpus (7)

• A Generalized Construction of Mirror Manifolds
• Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence
• Minimal Liouville Gravity correlation numbers from Douglas string equation
• Unitary Minimal Liouville Gravity and Frobenius Manifolds
• Recent Efforts in the Computation of String Couplings:
• Flat coordinates for Saito Frobenius manifolds and String theory
• Flat structures on the deformations of Gepner chiral rings

Cited by in corpus (8)

• The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
• Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold
• Calabi-Yau CFTs and Random Matrices
• Special geometry on the 101 dimesional moduli space of the quintic threefold
• Exact computation of the Special geometry for Calabi-Yau hypersurfaces of Fermat type
• Partition functions of $\mathcal{N}=(2,2)$ supersymmetric sigma models and Special geometry for the two-moduli non-Fermat Calabi-Yau manifold
• On Calabi-Yau manifolds in weighted projective spaces and their mirror GLSMs
• The Implications of N = 2 Supergravity Cosmology On the Topology of the Calabi-Yau Manifold