Open topological recursion relations in genus and integrable systems
arXiv:2008.06922 · doi:10.1007/JHEP01(2021)048
Abstract
The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation up to genus 1 the exponent of an open descendent potential satisfies a system of explicitly constructed linear evolutionary PDEs with one spatial variable.
v4: correction of the spelling of the name of one of the authors, 12 pages