The orbifold DT/PT vertex correspondence

TL;DR

This paper develops an orbifold topological vertex formalism for PT invariants of toric Calabi-Yau 3-orbifolds with $A_{n-1}$ singularities, proving a correspondence between orbifold DT and PT invariants and deriving explicit formulas.

Contribution

It introduces a new orbifold topological vertex formalism and proves the orbifold DT/PT Calabi-Yau correspondence, providing explicit formulas for the PT $bZ_{n}$-vertex.

Findings

Established the orbifold DT/PT vertex correspondence.

Derived explicit formulas for the PT $bZ_{n}$-vertex.

Proved the multi-regular orbifold DT/PT correspondence.

Abstract

We present an orbifold topological vertex formalism for PT invariants of toric Calabi-Yau 3-orbifolds with transverse $A_{n-1}$ singularities. We give a proof of the orbifold DT/PT Calabi-Yau topological vertex correspondence. As an application, we derive an explicit formula for the PT $\mathbb{Z}_{n}$-vertex in terms of loop Schur functions and prove the multi-regular orbifold DT/PT correspondence.