Details
| Original language | English |
|---|---|
| Article number | 113 |
| Journal | Journal of high energy physics |
| Volume | 2009 |
| Issue number | 3 |
| Publication status | Published - 2009 |
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.
Keywords
- Conformal and W symmetry, Extended supersymmetry, Ntegrable equations in physics
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of high energy physics, Vol. 2009, No. 3, 113, 2009.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - N=4 mechanics, WDVV equations and roots
AU - Galajinsky, Anton
AU - Lechtenfeld, Olaf
AU - Polovnikov, Kirill
N1 - Copyright: Copyright 2012 Elsevier B.V., All rights reserved.
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
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 -