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.

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

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• Extended supersymmetric Calogero model
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• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
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