N=4 supersymmetric 3-particles Calogero model

Details N=4 supersymmetric 3-particles Calogero model N=4 supersymmetric 3-particles Calogero model

2008-05-22

arxiv.org/abs/0805.3480v1

Nucl.Phys.B805:24-39,2008

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-w

Scientific paper

10.1016/j.nuclphysb.2008.06.024

We constructed the most general N=4 superconformal 3-particles systems with translation invariance. In the basis with decoupled center of mass the supercharges and Hamiltonian possess one arbitrary function which defines all potential terms. We have shown that with the proper choice of this function one may describe the standard, $A_2$ Calogero model as well as $BC_2, B_2,C_2$ and $D_2$ Calogero models with N=4 superconformal symmetry. The main property of all these systems is that even with the coupling constant equal to zero they still contain nontrivial interactions in the fermionic sector. In other words, there are infinitely many non equivalent N=4 supersymmetric extensions of the free action depending on one arbitrary function. We also considered quantization and explicitly showed how the supercharges and Hamiltonian are modified.

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