GW/PT Descendent Correspondence via Vertex Operators

@article{Oblomkov2018GWPTDC,
  title={GW/PT Descendent Correspondence via Vertex Operators},
  author={Alexei Oblomkov and Andrei Okounkov and Rahul Pandharipande},
  journal={Communications in Mathematical Physics},
  year={2018},
  volume={374},
  pages={1321-1359}
}
We propose an explicit formula for the $${{\mathsf {GW}}}/{\mathsf {PT}}$$ GW / PT descendent correspondence in the stationary case for nonsingular connected projective threefolds. 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 threefolds. An application to the Virasoro constraints for the stationary descendent theory of stable pairs will appear in a sequel. 
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