N=4 superconformal Calogero models

TL;DR

This paper develops new N=4 superconformal quantum many-body models on the real line, extending Calogero models with novel potentials and interactions, including three- and four-particle systems based on root systems G_2 and F_4.

Contribution

It introduces a method using conformal automorphisms to generate superconformal models from decoupled particles, and finds new models with non-decoupling center-of-mass motion.

Findings

Derived unique G_2-type Hamiltonian with three-body interactions

Analyzed N=4 superconformal models for root systems A_1 + G_2 and F_4

Discovered new models beyond Wyllard's solutions with extended center-of-mass interactions

Abstract

We continue the research initiated in hep-th/0607215 and apply our method of conformal automorphisms to generate various N=4 superconformal quantum many-body systems on the real line from a set of decoupled particles extended by fermionic degrees of freedom. The su(1,1|2) invariant models are governed by two scalar potentials obeying a system of nonlinear partial differential equations which generalizes the Witten-Dijkgraaf-Verlinde-Verlinde equations. As an application, the N=4 superconformal extension of the three-particle (A-type) Calogero model generates a unique G_2-type Hamiltonian featuring three-body interactions. We fully analyze the N=4 superconformal three- and four-particle models based on the root systems of A_1 + G_2 and F_4, respectively. Beyond Wyllard's solutions we find a list of new models, whose translational non-invariance of the center-of-mass motion fails to decouple and extends even to the relative particle motion.