The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves

Fuente: arXiv
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Main Authors: Rossi, Paolo, Shadrin, Sergey, Singh, Ishan Jaztar
Format: Preprint
Published: 2025
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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
id 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