Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves

Alexandr Buryak; Abner Hernandez Rodriguez

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arXiv · 2610.01841

Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves

Alexandr Buryak·Abner Hernandez Rodriguez

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Abstract

In an earlier paper of P. Rossi and the first author, a construction of a wide class of quantum hierarchies was presented, with the input data given by an arbitrary cohomological field theory. A crucial role in the construction is played by the double ramification (DR) cycles on the moduli spaces of stable curves. As a special case, one gets a quantization of the hierarchy of the Intermediate Long Wave (ILW) equation. The ILW equation has two famous limits: the Korteweg--de Vries equation and the Benjamin--Ono (BO) equation, and for the latter one a quantum hierarchy was constructed by Nazarov and Sklyanin. In our paper, we propose a conjecture describing a relation between a limit of the quantum ILW hierarchy and the Nazarov--Sklyanin hierarchy and present various checks to support it.

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Alexandr Buryak, Abner Hernandez Rodriguez. 2026-10-01. Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves. https://arxiv.org/abs/2610.01841

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