GW/PT descendent correspondence via vertex operators

TL;DR

This paper establishes an explicit vertex operator formula for the GW/PT descendent correspondence in stationary cases of nonsingular projective 3-folds, proving it for all toric cases and setting the stage for future applications.

Contribution

It introduces a new explicit formula using vertex operators for the GW/PT descendent correspondence in stationary cases, proven for all nonsingular projective toric 3-folds.

Findings

Formula proven for all nonsingular projective toric 3-folds

Uses 1-leg geometry to derive the vertex operator expression

Lays groundwork for Virasoro constraints in future work

Abstract

We propose an explicit formula for the GW/PT descendent correspondence in the stationary case for nonsingular projective 3-folds. The formula, written in terms of vertex operators, is found by studying the 1-leg geometry. We prove the proposal for all nonsingular projective toric 3-folds. An application to the Virasoro constraints for the stationary descendent theory of stable pairs will appear in a sequel.