Trivializing and Orbifolding the Conifold's Base

TL;DR

This paper explicitly trivializes the sphere bundle structure of the conifold's base, enabling detailed topological analysis of orbifolds and linking Betti numbers to gauge theory ranks.

Contribution

It provides an explicit trivialization of the conifold's base sphere bundle and relates its topology to dual gauge theory properties.

Findings

Explicit trivialization of the conifold's base sphere bundle.

Topological characterization of orbifold bases.

Correlation between Betti numbers and gauge theory ranks.

Abstract

The conifold is a cone over the space T^11, which is known to be topologically S^2xS^3. The coordinates used in the literature describe a sphere-bundle which can be proven to be topologically trivializable. We provide an explicit trivialization of this bundle, with simultaneous global coordinates for both spheres. Using this trivialization we are able to describe the topology of the base of several infinite families of chiral and non-chiral orbifolds of the conifold. We demonstrate that in each case the 2nd Betti number of the base matches the number of independent ranks in the dual quiver gauge theory.