### Abstract

Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1, 1|2) in mechanics. Remarking that SU(1, 1|2) is a particular member of a chain of supergroups SU(1, 1|n) parametrized by an integer n, here we begin a systematic study of SU(1, 1|n) multi-particle mechanics. A representation of the superconformal algebra su(1, 1|n) is constructed on the phase space spanned by m copies of the (1, 2n, 2n−1) supermultiplet. We show that the dynamics is governed by two prepotentials V and F, and the Witten-Dijkgraaf-Verlinde-Verlinde equation for F shows up as a consequence of a more general fourth-order equation. All solutions to the latter in terms of root systems reveal decoupled models only. An extension of the dynamical content of the (1, 2n, 2n−1) supermultiplet by angular variables in a way similar to the SU(1, 1|2) case is problematic.

Original language | English |
---|---|

Article number | 114 |

Journal | Journal of High Energy Physics |

Volume | 2016 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1 Sep 2016 |

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### Keywords

- Conformal and W Symmetry
- Extended Supersymmetry

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2016*(9), [114]. https://doi.org/10.1007/JHEP09(2016)114

**Superconformal SU(1, 1|n) mechanics.** / Galajinsky, Anton; Lechtenfeld, Olaf.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2016, no. 9, 114. https://doi.org/10.1007/JHEP09(2016)114

}

TY - JOUR

T1 - Superconformal SU(1, 1|n) mechanics

AU - Galajinsky, Anton

AU - Lechtenfeld, Olaf

PY - 2016/9/1

Y1 - 2016/9/1

N2 - Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1, 1|2) in mechanics. Remarking that SU(1, 1|2) is a particular member of a chain of supergroups SU(1, 1|n) parametrized by an integer n, here we begin a systematic study of SU(1, 1|n) multi-particle mechanics. A representation of the superconformal algebra su(1, 1|n) is constructed on the phase space spanned by m copies of the (1, 2n, 2n−1) supermultiplet. We show that the dynamics is governed by two prepotentials V and F, and the Witten-Dijkgraaf-Verlinde-Verlinde equation for F shows up as a consequence of a more general fourth-order equation. All solutions to the latter in terms of root systems reveal decoupled models only. An extension of the dynamical content of the (1, 2n, 2n−1) supermultiplet by angular variables in a way similar to the SU(1, 1|2) case is problematic.

AB - Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1, 1|2) in mechanics. Remarking that SU(1, 1|2) is a particular member of a chain of supergroups SU(1, 1|n) parametrized by an integer n, here we begin a systematic study of SU(1, 1|n) multi-particle mechanics. A representation of the superconformal algebra su(1, 1|n) is constructed on the phase space spanned by m copies of the (1, 2n, 2n−1) supermultiplet. We show that the dynamics is governed by two prepotentials V and F, and the Witten-Dijkgraaf-Verlinde-Verlinde equation for F shows up as a consequence of a more general fourth-order equation. All solutions to the latter in terms of root systems reveal decoupled models only. An extension of the dynamical content of the (1, 2n, 2n−1) supermultiplet by angular variables in a way similar to the SU(1, 1|2) case is problematic.

KW - Conformal and W Symmetry

KW - Extended Supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=84988531464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988531464&partnerID=8YFLogxK

U2 - 10.1007/JHEP09(2016)114

DO - 10.1007/JHEP09(2016)114

M3 - Article

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 114

ER -