Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
High Energy Physics - Theory
2008-11-26 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant -matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic tool is a chain of Backlund transformations for the Hirota equation connecting quantum transfer matrices. This approach also provides a systematic way to derive the complete set of generalized Baxter equations for super spin chains.
Keywords
Cite
@article{arxiv.hep-th/0703147,
title = {Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics},
author = {Vladimir Kazakov and Alexander Sorin and Anton Zabrodin},
journal= {arXiv preprint arXiv:hep-th/0703147},
year = {2008}
}
Comments
Minor changes: misprints fixed, references added