# Extended supersymmetric Calogero model

## TL;DR

This paper redefines matrix fermions in supersymmetric Calogero models, simplifying supercharges to a cubic form and constructing extended models with superconformal symmetry.

## Contribution

Introduces a new fermion redefinition that simplifies supercharges and extends supersymmetric Calogero models to arbitrary even-N with superconformal symmetry.

## Key findings

- Supercharges are cubic in fermions with nonlinear conjugation.
- Constructed extended models for B, C, D types with superconformal symmetry.
- All models exhibit dynamical osp(N|2) superconformal symmetry.

## Abstract

We present a surprising redefinition of matrix fermions which brings the supercharges of the $\cal N$-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-$\cal N$ supersymmetric extensions of the $B_n$, $C_n$ and $D_n$ rational Calogero models. We demonstrate that all considered models possess a dynamical $osp({\cal N}|2)$ superconformal symmetry.