Partition Functions of \(\mathcal{N}=(2,2)\) Supersymmetric Sigma Models and Special Geometry on the Moduli Spaces of Calabi-Yau Manifolds

Abstract

We study a new example of a mirror relation between the exact partition functions of \(\mathcal{N}=(2,2)\) super-symmetric gauged linear sigma models on the sphere S² and the special Kähler geometry on the moduli spaces of Calabi-Yau manifolds. Using exact calculations, we show this relation indeed holds for Calabi-Yau manifolds of the Berglund-Hubsch type with two moduli.