Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems

• Main Authors: Sergey Fedoruk, Evgeny Ivanov, Olaf Lechtenfeld, Stepan Sidorov
• Format: Article
• Language: English
• Published: SpringerOpen 2018-04-01
• Series: Journal of High Energy Physics
• Subjects: Extended Supersymmetry; Field Theories in Lower Dimensions; Matrix Models; Superspaces
• Online Access: http://link.springer.com/article/10.1007/JHEP04(2018)043

Abstract SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an N=4 $$ \mathcal{N}=4 $$ supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra su^2|1 $$ \widehat{su}\left(2\Big|1\right) $$. The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.