Generalized sℓ (2) Gaudin algebra and corresponding Knizhnik–Zamolodchikov equation

Salom, I.  (Institute of Physics, University of Belgrade, P.O. Box 57, Belgrade, 11080, Serbia) ; Manojlović, N.  (Grupo de Física Matemática da Universidade de Lisboa, Campo Grande, Edifício C6, Lisboa, PT-1749-016, Portugal) (Departamento de Matemática, F.C.T., Universidade do Algarve, Campus de Gambelas, Faro, PT-8005-139, Portugal) ; Cirilo António, N. (Center for Functional Analysis, Linear Structures and Applications, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, 1049-001, Portugal)

28 December 2018

Abstract: The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the corresponding Knizhnik–Zamolodchikov equations for the non-periodic sℓ(2) Gaudin model, as well as deriving the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, we provide a closed form expression also for the scalar products of the off-shell Bethe vectors. Finally, we provide explicit closed form of the off-shell Bethe vectors, together with a proof of implementation of the algebraic Bethe ansatz in full generality.

Published in: Nuclear Physics B 939 (2019) 358-371
Published by: Elsevier
DOI: 10.1016/j.nuclphysb.2018.12.025
License: CC-BY-3.0

Back to search

Download fulltextXML Download fulltextPDF Download fulltextPDF (PDFA)