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Open FJRW theory and
mirror symmetry
Mark Gross, Tyler L. Kelly and Ran J. Tessler |
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Geometry & Topology 30 (2026) 2779–2960
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Abstract |
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We construct an open enumerative theory for the Landau–Ginzburg (LG) model . The invariants are defined as integrals of multisections of a Witten bundle with descendents over a moduli space that is a real orbifold with corners. In turn, a generating function for these open invariants yields the mirror LG model and a versal deformation of it with flat coordinates. After establishing an open topological recursion result, we prove an LG/LG open mirror symmetry theorem in dimension two with all descendents. The open invariants we define are not unique but depend on boundary conditions that, when altered, exhibit wall-crossing phenomena for the invariants. We describe an LG wall-crossing group classifying the wall-crossing transformations that can occur. |
Keywords
mirror symmetry, open enumerative geometry, Landau–Ginzburg
models, FJRW theory, wall-crossing, open topological
recursion relations
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Mathematical Subject Classification
Primary: 14H15, 14J33, 14N35, 53D37, 53D45
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References |
Publication
Received: 7 June 2023
Revised: 1 April 2026
Accepted: 1 May 2026
Published: 30 August 2026
Proposed: Jim Bryan
Seconded: Gang Tian, Robert Lipshitz
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Authors |
| Mark Gross | |
| Department of Pure Mathematics and
Mathematical Statistics University of Cambridge Cambridge United Kingdom |
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| Tyler L. Kelly | |
| School of Mathematical
Sciences Queen Mary University of London London United Kingdom |
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| Ran J. Tessler | |
| Department of Mathematics Weizmann Institute of Science Rehovot Israel |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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