Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary

Abstract

In a recent paper R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. The authors conjectured KdV and Virasoro type equations that completely determine all intersection numbers. In this paper we study these equations in detail. In particular, we prove that the KdV and the Virasoro type equations for the intersection numbers on the moduli space of Riemann surfaces with boundary are equivalent.

Revised version, 16 pages, to appear in Letters in Mathematical Physics

Cited by in corpus (6)

• Double ramification cycles and integrable hierarchies
• Matrix models and a proof of the open analog of Witten's conjecture
• Higher Airy structures and topological recursion for singular spectral curves
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Open intersection numbers and free fields
• From minimal gravity to open intersection theory