N=4 mechanics, WDVV equations and roots

Anton Galajinsky, Olaf Lechtenfeld, Kirill Victorovich Polovnikov

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


= 4 superconformal multi-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial differential equations linear in U and generalizing the Witten-Dijkgraaf- Verlinde-Verlinde (WDVV) equation for F. Putting U≡0 yields a class of models (with zero central charge) which are encoded by the finite Coxeter root systems. We extend these WDVV solutions F in two ways: the A n system is deformed n-parametrically to the edge set of a general orthocentric n-simplex, and the BCF-type systems form one-parameter families. A classification strategy is proposed. A nonzero central charge requires turning on U in a given F background, which we show is outside the reach of the standard root-system ansatz for indecomposable systems of more than three particles. In the three-body case, however, this ansatz can be generalized to establish a series of nontrivial models based on the dihedral groups I 2(p), which are permutation symmetric if 3 divides p. We explicitly present their full prepotentials.

Original languageEnglish
Article number113
JournalJournal of High Energy Physics
Issue number3
Publication statusPublished - 2009


  • Conformal and W symmetry
  • Extended supersymmetry
  • Ntegrable equations in physics

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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