Abstract
We explicitly construct a supersymmetric so(n) spin-Calogero model with an arbitrary even number N of supersymmetries. It features 12Nn(n+1) rather than Nn fermionic coordinates and a very simple structure of the supercharges and the Hamiltonian. The latter, together with additional conserved currents, form an osp(N|2) superalgebra. We provide a superspace description for the simplest case, namely N=2 supersymmetry. The reduction to an N-extended supersymmetric goldfish model is also discussed.
Highlights
In recent years notable progress was achieved in the supersymmetrization of the bosonic matrix models [1,2,3,4,5,6]
N bosonic coordinates xi which stem from the diagonal part of a real symmetric matrix
N n fermions ψia and ψi a, which combine with the xi to n supermultiplets
Summary
In recent years notable progress was achieved in the supersymmetrization of the bosonic matrix models [1,2,3,4,5,6]. The key feature of a supersymmetric extension of one-dimensional models within the Hamiltonian approach is the appearance of additional fermionic matrix degrees of freedom accompanying the standard N n fermions customarily required for an N -extended supersymmetric system with n bosonic coordinates. We implemented this feature to construct a supersymmetric extension of Hermitian matrix models which admits an arbitrary number of supersymmetries [6]. We will perform the supersymmetric version of the reduction (1.8), ending up with an N -extended supersymmetric goldfish model
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