Quantum integrability of the Alday-Arutyunov-Frolov model

Abstract

We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. We then show that the quantum integrability of the AAF model follows from this constraint. In the process, we also correct some missed points in earlier works.

40 pages; Replaced with published version. Appendix and comments added

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• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
• On extension of the Yang-Baxter equation and the fermionic $R$-operator
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