A Formula of the One-leg Orbifold Gromov-Witten Vertex and Gromov-Witten Invariants of the Local $\cB\bZ_m$ Gerbe

TL;DR

This paper derives a formula for the orbifold Gromov-Witten vertex with a gerby leg and applies it to compute invariants of the local Z_m gerbe, including specific Hodge integrals.

Contribution

It introduces a new formula for the one-leg orbifold Gromov-Witten vertex with gerby legs and computes related Gromov-Witten invariants.

Findings

Derived a formula for the orbifold Gromov-Witten vertex with gerby leg.

Computed Gromov-Witten invariants of the local Z_m gerbe.

Evaluated specific degree 1 and degree 2 Z_2-Hodge integrals.

Abstract

We give a formula of the framed one-leg orbifold Gromov-Witten vertex where the leg is gerby with isotropy group $\bZ_m$. Then we use this formula to compute the Gromov-Witten invariants of the local $\cB\bZ_m$ gerbe. We will also compute some examples of the degree 1 and degree 2 $\bZ_2$-Hodge integrals.