The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915653394366464 |
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| author | Rossi, Paolo Shadrin, Sergey Singh, Ishan Jaztar |
| author_facet | Rossi, Paolo Shadrin, Sergey Singh, Ishan Jaztar |
| contents | We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten classes of the elliptic curve and the Hodge class $λ_{g-1}$ together with vanishing results for $λ_{g-2}$ to produce a closed, modular expression for the resulting integrable hierarchy. It is the first explicit nontrivial example of a quantum integrable hierarchy from a cohomological field theory containing fermionic fields, which correspond to the odd classes in the cohomology of the elliptic curve. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves Rossi, Paolo Shadrin, Sergey Singh, Ishan Jaztar Algebraic Geometry Mathematical Physics We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten classes of the elliptic curve and the Hodge class $λ_{g-1}$ together with vanishing results for $λ_{g-2}$ to produce a closed, modular expression for the resulting integrable hierarchy. It is the first explicit nontrivial example of a quantum integrable hierarchy from a cohomological field theory containing fermionic fields, which correspond to the odd classes in the cohomology of the elliptic curve. |
| title | The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves |
| topic | Algebraic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2512.04621 |