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arXiv · 1901.10393

Open WDVV equations and Virasoro constraints

Alexey Basalaev·Alexandr Buryak
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Abstract

In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the Virasoro equations for the genus 0 Gromov-Witten invariants, proved the Virasoro equations for a descendent potential in genus 0 of an arbitrary conformal Frobenius manifold. More recently, a remarkable system of partial differential equations, called the open WDVV equations, appeared in the work of A. Horev and J. P. Solomon. This system controls the genus 0 open Gromov-Witten invariants. In our paper, for an arbitrary solution of the open WDVV equations, satisfying a certain homogeneity condition, we construct a descendent potential in genus 0 and prove an open analog of the Virasoro equations. We also present conjectural open Virasoro equations in all genera and discuss some examples.

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Alexey Basalaev, Alexandr Buryak. 2019-01-29. Open WDVV equations and Virasoro constraints. https://arxiv.org/abs/1901.10393

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