Construction of Supersymmetric Nonlinear Sigma Models on Noncompact Calabi-Yau Manifolds with Isometry

TL;DR

This paper constructs N=2 supersymmetric nonlinear sigma models on noncompact Ricci-flat Kähler manifolds, specifically complex line bundles over hermitian symmetric spaces, with explicit metrics and resolution parameters.

Contribution

It introduces a new class of models on noncompact Calabi-Yau manifolds with explicit Kähler potentials and Ricci-flat metrics using supersymmetric gauge theory techniques.

Findings

Explicit Ricci-flat metrics with isometries are derived.

Metrics depend on a resolution parameter controlling the base manifold size.

Conical singularities appear when the resolution parameter vanishes.

Abstract

We propose a class of N=2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these manifolds with isometries are explicitly constructed by using the techniques of supersymmetric gauge theories. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the conical singularity appears when the parameter vanishes.