A Note on Conifolds

TL;DR

This paper constructs the Ricci-flat metric and Kähler potential on the conifold with O(N) symmetry, demonstrating how the conical singularity is smoothed by the complex quadric surface Q^{N-2}.

Contribution

It provides explicit Ricci-flat metrics and Kähler potentials on conifolds with O(N) symmetry, incorporating the resolution of singularities via complex quadrics.

Findings

Explicit Ricci-flat metric derived for the conifold with O(N) symmetry.

Kähler potential formulated for the conifold with singularity resolution.

Demonstration of the smoothing of conical singularity using complex quadric surfaces.

Abstract

We present the Ricci-flat metric and its Kahler potential on the conifold with the O(N) isometry, whose conical singularity is repaired by the complex quadric surface Q^{N-2} = SO(N)/SO(N-2)xU(1).