Towards Three-Dimensional Bethe Ansatz
M. Bellon, S. Boukraa, J-M. Maillard, C-M. Viallet
TL;DR
This paper introduces a new set of equations called the 'pre-Bethe-Ansatz' for three-dimensional vertex models, revealing complex algebraic structures and special parameter subvarieties that could advance understanding of integrable systems.
Contribution
It presents a novel algebraic framework for 3D vertex models, highlighting high-genus curves and their simplifications, expanding the mathematical tools for studying integrability.
Findings
Identification of algebraic curves of high genus
Discovery of simplified cases of these curves
Description of special parameter subvarieties
Abstract
We introduce a ``pre-Bethe-Ansatz'' system of equations for three dimensional vertex models. We bring to the light various algebraic curves of high genus and discuss some situations where these curves simplify. As a result we describe remarkable subvarieties of the space of parameters.
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