2007/08/31 by Anton Galajinsky, Olaf Lechtenfeld, Kirill Polovnikov 路 2 citations
Mathematics 路 Physics and Astronomy 路 #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th
paper 路 pdf 路 doi:10.1088/1126-6708/2007/11/008
published as JHEP0711:008,2007 路 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
arxiv created 2007/11/01 路 openalex publication_date 2007/11/06 路 arxiv updated 2009/12/01 路 openalex created_date 2016/06/24 路 openalex updated_date 2026/07/28
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 G2-type Hamiltonian featuring three-body interactions. We fully analyze the N=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.