Abstract
Abstract
Integrability of $$\mathcal{N}$$ = 1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials $$W\left(x\right)=\frac{2}{x}$$, $$W\left(x\right)=\frac{2}{{\text{sin}}x}$$, and $$W\left(x\right)=\frac{2}{{\text{sinh}}x}$$ is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.
Publisher
Springer Science and Business Media LLC
Reference18 articles.
1. M.B. Green, J.H. Schwarz and E. Witten, Superstring theory. Volume 1: introduction, Cambridge University Press, Cambridge, U.K. (1988) [INSPIRE].
2. G.W. Gibbons and P.K. Townsend, Black holes and Calogero models, Phys. Lett. B 454 (1999) 187 [hep-th/9812034] [INSPIRE].
3. I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: or a walk through superspace, IOP, Bristol, U.K. (1998) [INSPIRE].
4. A. Galajinsky, Integrability of N = 1 supersymmetric Ruijsenaars-Schneider three-body system, JHEP 11 (2023) 008 [arXiv:2309.13891] [INSPIRE].
5. S.N.M. Ruijsenaars and H. Schneider, A new class of integrable systems and its relation to solitons, Annals Phys. 170 (1986) 370 [INSPIRE].