Ricci-flat Kahler Manifolds from Supersymmetric Gauge Theories

TL;DR

This paper constructs Ricci-flat Kähler metrics on non-compact manifolds using supersymmetric gauge theory techniques, resolving conical singularities with Hermitian symmetric spaces and analyzing the role of resolution parameters.

Contribution

It introduces a method to derive Ricci-flat metrics on complex line bundles over Hermitian symmetric spaces via supersymmetric gauge theories, addressing singularity resolution.

Findings

Derived explicit Ricci-flat metrics on non-compact Kähler manifolds.

Demonstrated the role of resolution parameters in controlling singularity size.

Connected gauge theory techniques with geometric metric construction.

Abstract

Using techniques of supersymmetric gauge theories, we present the Ricci-flat metrics on non-compact Kahler manifolds whose conical singularity is repaired by the Hermitian symmetric space. These manifolds can be identified as the complex line bundles over the Hermitian symmetric spaces. 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.