Intersection theory on moduli of disks, open KdV and Virasoro

Rahul Pandharipande, Jake P. Solomon, Ran J. Tessler

Research output: Contribution to journalArticlepeer-review

Abstract

We define a theory of descendent integration on the moduli spaces of stable pointed disks. The descendent integrals are proved to be coefficients of the -function of an open KdV hierarchy. A relation between the integrals and a representation of half the Virasoro algebra is also proved. The construction of the theory requires an in-depth study of homotopy classes of multivalued boundary conditions. Geometric recursions based on the combined structure of the boundary conditions and the moduli space are used to compute the integrals. We also provide a detailed analysis of orientations. Our open KdV and Virasoro constraints uniquely specify a theory of higher-genus open descendent integrals. As a result, we obtain an open analog (governing all genera) of Witten’s conjectures concerning descendent integrals on the Deligne-Mumford space of stable curves.

Original languageEnglish
Pages (from-to)2483-2567
Number of pages85
JournalGeometry and Topology
Volume28
Issue number6
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 Mathematical Sciences Publisher.

Keywords

  • boundary condition
  • descendent
  • KdV
  • multisection
  • open Gromov–Witten
  • relative Euler class
  • topological recursion relations
  • Virasoro
  • WDVV

Fingerprint

Dive into the research topics of 'Intersection theory on moduli of disks, open KdV and Virasoro'. Together they form a unique fingerprint.

Cite this