N = 4 superconformal Calogero models

Anton Galajinsky, Kirill Victorovich Polovnikov, Olaf Lechtenfeld

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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 G 2-type Hamiltonian featuring three-body interactions. We fully analyze the = 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.

Original languageEnglish
Article number008
JournalJournal of High Energy Physics
Issue number11
Publication statusPublished - 1 Nov 2007


  • Conformal and W Symmetry
  • Extended Supersymmetry/Integrable Equations in Physics

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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