|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Higher genus FJRW
invariants of a Fermat cubic
Jun Li, Yefeng Shen and Jie Zhou |
|
Geometry & Topology 27 (2023) 1845–1890
|
 |
Abstract |
|
We reconstruct all-genus Fan–Jarvis–Ruan–Witten invariants of a Fermat cubic Landau–Ginzburg space from genus-one primary invariants, using tautological relations and axioms of cohomological field theories. The genus-one primary invariants satisfy a Chazy equation by the Belorousski–Pandharipande relation. They are completely determined by a single genus-one invariant, which can be obtained from cosection localization and intersection theory on moduli of three-spin curves. We solve an all-genus Landau–Ginzburg/Calabi–Yau correspondence conjecture for the Fermat cubic Landau–Ginzburg space using Cayley transformation on quasimodular forms. This transformation relates two nonsemisimple CohFT theories: the Fan–Jarvis–Ruan–Witten theory of the Fermat cubic polynomial and the Gromov–Witten theory of the Fermat cubic curve. As a consequence, Fan–Jarvis–Ruan–Witten invariants at any genus can be computed using Gromov–Witten invariants of the elliptic curve. They also satisfy nice structures, including holomorphic anomaly equations and Virasoro constraints. |
Keywords
FJRW invariants, Fermat cubic, quasimodular forms, LG/CY
correspondence
|
Mathematical Subject Classification
Primary: 14N35
|
References |
Publication
Received: 29 September 2020
Revised: 9 November 2021
Accepted: 11 December 2021
Published: 27 July 2023
Proposed: Jim Bryan
Seconded: Paul Seidel, Mark Gross
|
Authors |
| Jun Li | |
| Shanghai Center for Mathematical
Sciences Fudan University Shanghai China |
|
| Yefeng Shen | |
| Department of Mathematics University of Oregon Eugene, OR United States |
|
| Jie Zhou | |
| Yau Mathematical Sciences
Center Tsinghua University Beijing China |
|
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
