N=4 mechanics, WDVV equations and roots
| dc.creator | Galajinsky, Anton | |
| dc.creator | Lechtenfeld, Olaf | |
| dc.creator | Polovnikov, Kirill | |
| dc.date | 2008-02-29 | |
| dc.date | 2009-02-04 | |
| dc.date.accessioned | 2026-07-07T12:56:37Z | |
| dc.date.available | 2026-07-07T12:56:37Z | |
| dc.description | N=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 of 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. | |
| dc.description | 1+25 pages; v2: major revision (more general analysis, new solutions, additional references); v3: improvements in sects.5,8,9, refs. added | |
| dc.identifier | https://arxiv.org/abs/0802.4386 | |
| dc.identifier | http://arxiv.org/abs/0802.4386 | |
| dc.identifier | JHEP 0903:113,2009 | |
| dc.identifier | doi:10.1088/1126-6708/2009/03/113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224643 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | N=4 mechanics, WDVV equations and roots | |
| dc.type | text |