N=4 supersymmetric 3-particles Calogero model

TL;DR

This paper constructs the most general N=4 superconformal three-particle systems with translation invariance, unifying several Calogero models and revealing nontrivial fermionic interactions even at zero coupling.

Contribution

It introduces a broad class of N=4 superconformal three-particle models characterized by an arbitrary function, encompassing various Calogero models and highlighting persistent fermionic interactions.

Findings

Unified description of multiple Calogero models within N=4 superconformal framework

Existence of nontrivial fermionic interactions at zero coupling

Explicit quantization and modification of supercharges and Hamiltonian

Abstract

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.