= 4 superconformal Calogero models

We continue the research initiated in hep-th/0607215 and apply our method of conformal automorphisms to generate various = 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 = 4 superconformal extension of the three-particle (A-type) Calogero model generates a unique G₂-type Hamiltonian featuring three-body interactions. We fully analyze the = 4 superconformal three- and four-particle models based on the root systems of A₁⊕G₂ and F₄, 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.