Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves
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.
Related
- Moduli spaces of logarithmic connections associated with difference Painlevé equations of type E(1)n
- Generalized Frobenius Structures on Hurwitz Spaces, Their Open Extensions and Associated Principal Hierarchies
- Stability conditions and moduli spaces on projective families
- Cetraro lectures on integrable systems and moduli spaces of curves
- Birational maps of moduli spaces of stable sheaves on a K3 surface induced by Fourier-Mukai transforms
BibTeX
@misc{buryak2026quantum,
title = {{Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves}},
author = {Alexandr Buryak and Abner Hernandez Rodriguez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01841},
eprint = {2610.01841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01841},
}
RIS
TY - UNPB
TI - Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves
AU - Alexandr Buryak
AU - Abner Hernandez Rodriguez
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01841
UR - https://arxiv.org/abs/2610.01841
AB - 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.
ER -