= 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.
- Conformal and W symmetry
- Extended supersymmetry
- Ntegrable equations in physics
ASJC Scopus subject areas
- Nuclear and High Energy Physics