On Calabi-Yau manifolds in weighted projective spaces and their mirror GLSMs

Abstract

The goal of the present paper is to calculate the complex structure moduli space Kähler potentials for hypersurfaces in weighted projective spaces and compare with the partition functions of their mirror GLSMs. We explicitly perform the Kähler potential computation and show that the corresponding formula is well-defined in case of quasismooth hypersurfaces. We then construct the mirror GLSM with an appropriate number of Kähler parameters and discuss the interpretation of its partition function in terms of mirror symmetry. Namely, it is shown that different contributions to the partition function are related to various charts of the complex structure moduli space.

arXiv comment20 pages, improved the display of references

References in corpus (13)

• Phases of $N=2$ Theories In Two Dimensions
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• A Generalized Construction of Mirror Manifolds
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• On the Classification of Quasihomogeneous Functions
• Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory
• Periods for Calabi--Yau and Landau--Ginzburg Vacua
• A new approach for computing the geometry of the moduli spaces for a Calabi-Yau manifold
• Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau
• 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
• On the equivalence of Batyrev and BHK Mirror symmetry constructions