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arXiv · 2512.04621

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

Paolo Rossi·Sergey Shadrin·Ishan Jaztar Singh
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Abstract

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 $\lambda_{g-1}$ together with vanishing results for $\lambda_{g-2}$ 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.

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Paolo Rossi, Sergey Shadrin, Ishan Jaztar Singh. 2025-12-04. The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves. https://doi.org/10.1112/blms.70486

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