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Intersection theory on
moduli of disks, open KdV and Virasoro
Rahul Pandharipande, Jake P Solomon and Ran J Tessler |
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Geometry & Topology 28 (2024) 2483–2567
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Abstract |
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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. |
Keywords
open Gromov–Witten, descendent, relative Euler class,
boundary condition, KdV, Virasoro, topological recursion
relations, WDVV, multisection
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Mathematical Subject Classification
Primary: 14H15, 32G15
Secondary: 14N35, 37K20, 53D45
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References |
Publication
Received: 3 December 2015
Revised: 10 December 2022
Accepted: 9 February 2023
Published: 21 October 2024
Proposed: Jim Bryan
Seconded: Yakov Eliashberg, Gang Tian
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Authors |
| Rahul Pandharipande | |
| Departement Mathematik ETH Zürich Zürich Switzerland |
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| Jake P Solomon | |
| Institute of Mathematics Hebrew University Jerusalem Israel |
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| Ran J Tessler | |
| Department of Mathematics Weizmann Institute of Science Rehovot Israel |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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