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arXiv · 2008.06922

Open topological recursion relations in genus $1$ and integrable systems

Oscar Brauer·Alexandr Buryak
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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.

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Oscar Brauer, Alexandr Buryak. 2020-08-16. Open topological recursion relations in genus $1$ and integrable systems. https://doi.org/10.1007/jhep01(2021)048

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