Difference equation for the Gromov-Witten potential of the resolved conifold
Murad Alim
TL;DR
This paper proves a difference equation for the Gromov-Witten potential of the resolved conifold and shows similar equations hold for the genus zero Gopakumar-Vafa contributions across Calabi-Yau threefolds.
Contribution
It introduces a difference equation framework for the Gromov-Witten potential of the resolved conifold and extends this to genus zero Gopakumar-Vafa invariants in Calabi-Yau threefolds.
Findings
Proved a difference equation for the Gromov-Witten potential of the resolved conifold.
Demonstrated that similar difference equations apply to genus zero Gopakumar-Vafa contributions.
Connected Gromov-Witten invariants with difference equations across Calabi-Yau threefolds.
Abstract
A difference equation is proved for the Gromov-Witten potential of the resolved conifold. Using the Gopakumar-Vafa resummation of the Gromov-Witten invariants of any Calabi-Yau threefold, it is further shown that similar difference equations are satisfied by the part of the resummed potential containing the contribution of the genus zero GV invariants.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics