$\mathcal{N}$-extended supersymmetric Calogero models

Abstract

We propose a new $\mathcal{N}$-extended supersymmetric $su(n)$ spin-Calogero model. Employing a generalized Hamiltonian reduction adopted to the supersymmetric case, we explicitly construct a novel rational $n$-particle Calogero model with an arbitrary even number of supersymmetries. It features $\mathcal{N}{n}^2$ rather than $\mathcal{N}n$ fermionic coordinates and increasingly high fermionic powers in the supercharges and the Hamiltonian.

1+6 pages

References in corpus (8)

• Physics and Mathematics of Calogero particles
• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• N=4 supersymmetric 3-particles Calogero model
• Goldfish geodesics and Hamiltonian reduction of matrix dynamics
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Gauged spinning models with deformed supersymmetry
• Ruijsenaars-Schneider three-body models with N=2 supersymmetry

Cited by in corpus (18)

• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Supersymmetric many-body Euler-Calogero-Moser model
• Extended supersymmetric Calogero model
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models
• Spinning extensions of $D(2,1;\alpha )$ superconformal mechanics
• Remarks on N=1 supersymmetric extension of the Euler top
• Supersymmetric V-systems
• Superfield approach to higher derivative N=1 superconformal mechanics
• Spinning particles on 2-sphere in accord with the Bianchi classification
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• On $OSp(N|2)$ superconformal mechanics
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• New $\mathcal{N}=2$ superspace Calogero models
• Supersymmetric Calogero models from superfield gauging
• Integrability of supersymmetric Calogero-Moser models