The Gerby Gopakumar-Mari\~no-Vafa Formula

TL;DR

This paper establishes a new formula relating cubic Z_n-Hodge integrals to loop Schur functions and uses it to prove the Gromov-Witten/Donaldson-Thomas correspondence for local Z_n-gerbes over the projective line.

Contribution

It introduces a novel formula connecting cubic Z_n-Hodge integrals with loop Schur functions and applies it to prove a significant correspondence in enumerative geometry.

Findings

Proved a formula for cubic Z_n-Hodge integrals in terms of loop Schur functions.

Established the Gromov-Witten/Donaldson-Thomas correspondence for local Z_n-gerbes over P^1.

Abstract

We prove a formula for certain cubic $\Z_n$-Hodge integrals in terms of loop Schur functions. We use this identity to prove the Gromov-Witten/Donaldson-Thomas correspondence for local $\Z_n$-gerbes over $\proj^1$.