Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics

Details Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics

2007-03-15

arxiv.org/abs/hep-th/0703147v2

Nucl.Phys.B790:345-413,2008

Physics

High Energy Physics

High Energy Physics - Theory

Minor changes: misprints fixed, references added

Scientific paper

10.1016/j.nuclphysb.2007.06.025

We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant $R$-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.

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