Extended supersymmetric Calogero model

Abstract

We present a surprising redefinition of matrix fermions which brings the supercharges of the $\mathcal{N}$-extended supersymmetric $A_{n-1}$ Calogero model introduced in [1] to the standard form maximally cubic in the fermions. The complexity of the model is transferred to a non-canonical and nonlinear conjugation property of the fermions. Employing the new cubic supercharges, we apply a supersymmetric generalization of a "folding" procedure for $A_{2n-1}\oplus A_1$ to explicitly construct the supercharges and Hamiltonian for arbitrary even-$\mathcal{N}$ supersymmetric extensions of the $B_n$, $C_n$ and $D_n$ rational Calogero models. We demonstrate that all considered models possess a dynamical $osp(\mathcal{N}|2)$ superconformal symmetry.

arXiv comment1+7 pages; v2: more precise citations, one ref. added, version appearing in PLB

References in corpus (21)

• Physics and Mathematics of Calogero particles
• Black Holes and Calogero Models
• Supersymmetric Calogero models by gauging
• Hidden Algebras of the (super) Calogero and Sutherland models
• Superconformal mechanics
• (Super)conformal many-body quantum mechanics with extended supersymmetry
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• New D(2,1;alpha) Mechanics with Spin Variables
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• N=4 mechanics, WDVV equations and roots
• New insight into WDVV equation
• Many-particle mechanics with D(2,1;alpha) superconformal symmetry
• N=4 supersymmetric 3-particles Calogero model
• Generalized Calogero models through reductions by discrete symmetries
• Many-Body Superconformal Systems from Hamiltonian Reductions
• N=4 superconformal n-particle mechanics via superspace
• $\mathcal{N}$-extended supersymmetric Calogero models
• Multidimensional Calogero systems from matrix models
• On the geometry of V-systems
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• New Super Calogero Models and OSp(4|2) Superconformal Mechanics

Cited by in corpus (9)

• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models
• Superfield approach to higher derivative N=1 superconformal mechanics
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• Supersymmetric Calogero models from superfield gauging
• New $\mathcal{N}=2$ superspace Calogero models
• Integrability of supersymmetric Calogero-Moser models