$\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model

Abstract

The $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model obtained in arXiv:1902.08023 by gauging the $\mathcal{N}=2$ superfield matrix system is studied. Classical and quantum $\mathcal{N}=2$ supersymmetry generators are found. The difference in the structure of classical and quantum supercharges is established. It is shown that, unlike classical supercharges, quantum supersymmetry generators can be limited to an invariant sub-sector that does not contain off-diagonal fermion operators. The Lax pair for supersymmetric generalization of the hyperbolic Calogero-Sutherland system is constructed.

1+16 pages; v3: references and some clarifications added, typos corrected

References in corpus (15)

• Physics and Mathematics of Calogero particles
• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• Calogero models and nonlocal conformal transformations
• N=4 mechanics, WDVV equations and roots
• Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the (4,4,0) ones
• On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
• $\mathcal{N}$-extended supersymmetric Calogero models
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Gauged spinning models with deformed supersymmetry
• Supersymmetric many-body Euler-Calogero-Moser model
• Extended supersymmetric Calogero model
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models

Cited by in corpus (5)

• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• Spinning particles on 2-sphere in accord with the Bianchi classification
• New $\mathcal{N}=2$ superspace Calogero models
• Relativistic generalization of the rational Calogero model