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
Superconformal SU(1, 1|n) mechanics. / Galajinsky, Anton; Lechtenfeld, Olaf.
In: Journal of High Energy Physics, Vol. 2016, No. 9, 114, 01.09.2016.Research output: Contribution to journal › Article
}
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 -