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

Dorey, Patrick; Dunning, Clare; Masoero, Davide; Suzuki, Junji; Tateo, Roberto


Clare Dunning

Davide Masoero

Junji Suzuki

Roberto Tateo


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.


Dorey, P., Dunning, C., Masoero, D., Suzuki, J., & Tateo, R. (2007). Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras. Nuclear Physics B, 772(3), 249-289.

Journal Article Type Article
Publication Date Jun 1, 2007
Deposit Date Jul 19, 2007
Journal Nuclear Physics B
Print ISSN 0550-3213
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 772
Issue 3
Pages 249-289
Keywords Conformal field theory, Bethe ansatz, Pseudo-differential equations, Spectral problems.
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