N=4 superconformal Calogero models
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.
Cite
@article{arxiv.0708.1075,
title = {N=4 superconformal Calogero models},
author = {Anton Galajinsky and Olaf Lechtenfeld and Kirill Polovnikov},
journal= {arXiv preprint arXiv:0708.1075},
year = {2008}
}
Comments
1+21 pages; v2: slight changes in section 4, new subsection 5.3 with additional results (a full list of n=3 and n=4 models), acknowledgments and one reference added, JHEP version