### Abstract

= 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 language | English |
---|---|

Article number | 113 |

Journal | Journal of High Energy Physics |

Volume | 2009 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2009*(3), [113]. https://doi.org/10.1088/1126-6708/2009/03/113

**N=4 mechanics, WDVV equations and roots.** / Galajinsky, Anton; Lechtenfeld, Olaf; Polovnikov, Kirill Victorovich.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2009, no. 3, 113. https://doi.org/10.1088/1126-6708/2009/03/113

}

TY - JOUR

T1 - N=4 mechanics, WDVV equations and roots

AU - Galajinsky, Anton

AU - Lechtenfeld, Olaf

AU - Polovnikov, Kirill Victorovich

PY - 2009

Y1 - 2009

N2 - = 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.

AB - = 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.

KW - Conformal and W symmetry

KW - Extended supersymmetry

KW - Ntegrable equations in physics

UR - http://www.scopus.com/inward/record.url?scp=67650249290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650249290&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2009/03/113

DO - 10.1088/1126-6708/2009/03/113

M3 - Article

AN - SCOPUS:67650249290

VL - 2009

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 113

ER -