# Open WDVV equations and Virasoro constraints

## TL;DR

This paper constructs a genus 0 descendent potential satisfying open Virasoro equations for solutions of open WDVV equations and discusses conjectural extensions to all genera.

## Contribution

It introduces an open Virasoro framework for solutions of open WDVV equations and proposes conjectures for higher genus cases.

## Key findings

- Constructed genus 0 descendent potential for open WDVV solutions.
- Proved an open Virasoro equation analog in genus 0.
- Presented conjectures for open Virasoro equations in all genera.

## 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.