Quantum integrability of the Alday-Arutyunov-Frolov model

2011/06/30 by A. Melikyan, A. Pinzul, Victor O. Rivelles +3 · 15 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Geometry #Mathematical physics #Mathematics #Matrix (chemical analysis) #Order (exchange) #Physics #Pure mathematics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering #Scattering amplitude #Theoretical physics #hep-th

paper · pdf · doi:10.1007/jhep09(2011)092

published in Journal of High Energy Physics 2011(9) (Springer Nature) · 40 pages; Replaced with published version. Appendix and comments added

openalex publication_date 2011/09/01 · arxiv created 2011/09/22 · arxiv updated 2011/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• On S-matrix factorization of the Landau-Lifshitz model
• Integrable Hamiltonian for Classical Strings on AdS5 × S5
• Direct calculation of the S matrix in the massive thirring model
• The dilatation operator of N=4 super Yang–Mills theory and integrability
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
• The Large-N Limit of Superconformal Field Theories and Supergravity
• The large N limit of superconformal field theories and supergravity