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

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

Abstract

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.

Citation

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. https://doi.org/10.1016/j.nuclphysb.2007.02.029

• 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
• DOI: https://doi.org/10.1016/j.nuclphysb.2007.02.029
• Keywords: Conformal field theory, Bethe ansatz, Pseudo-differential equations, Spectral problems.
• Publisher URL: http://arxiv.org/abs/hep-th/0612298