Open WDVV Equations and Virasoro Constraints

Alexey Basalaev, Alexandr Buryak

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In their fundamental work, Dubrovin and 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 Horev and 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.

Original languageEnglish
Pages (from-to)145-186
Number of pages42
JournalArnold Mathematical Journal
Issue number2-3
Publication statusPublished - 1 Nov 2019


  • Moduli space
  • Riemann surface
  • WDVV equations


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