Quasi-Exactly Solvable Deformations of Gaudin Models and ``Quasi-Gaudin Algebras''

Details Quasi-Exactly Solvable Deformations of Gaudin Models and ``Quasi-Gaudin Algebras'' Quasi-Exactly Solvable Deformations of Gaudin Models and ``Quasi-Gaudin Algebras''

1997-06-14

arxiv.org/abs/hep-th/9706113v1

Mod.Phys.Lett. A13 (1998) 281-292

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1142/S0217732398000346

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic Bethe ansatz solution only for some limited parts of the spectrum. An underlying algebra responsible for both the phenomena of complete integrability and quasi-exact solvability is constructed. We call it "quasi-Gaudin algebra" and demonstrate that it is a special non-Lie-algebraic deformation of the ordinary Gaudin algebra.

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