Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras

Details Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras

2006-12-29

arxiv.org/abs/hep-th/0612298v2

Nucl.Phys.B772:249-289,2007

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, 4 figures. v2: typos corrected, extra numerical results included

Scientific paper

10.1016/j.nuclphysb.2007.02.029

The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observed.

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