On an equivalence of divisors on $\bar{M}_{0,n}$ from Gromov-Witten theory and conformal blocks

TL;DR

This paper explores the relationship between two classes of divisors on the moduli space of stable n-pointed rational curves, linking Gromov-Witten theory and conformal blocks, and proves their equivalence under certain conditions.

Contribution

The paper reduces a conjecture relating divisors from Gromov-Witten theory and conformal blocks to the case n=4, and proves it for a large class of cases with conditions for non-vanishing.

Findings

Reduced the conjecture to the case n=4

Proved the conjecture for a large class of divisors

Provided conditions for non-vanishing of divisors

Abstract

We consider a conjecture that identifies two types of base point free divisors on $\bar{M}_{0,n}$. The first arises from Gromov-Witten theory of a Grassmannian. The second comes from first Chern classes of vector bundles associated to simple Lie algebras in type A. Here we reduce this conjecture on $\bar{M}_{0,n}$ to the same statement for $n=4$. A reinterpretation leads to a proof of the conjecture on $\bar{M}_{0,n}$ for a large class, and we give sufficient conditions for the non-vanishing of these divisors.