Details
| Original language | English |
|---|---|
| Pages (from-to) | 185-204 |
| Number of pages | 20 |
| Journal | Communications in Mathematical Physics |
| Volume | 300 |
| Issue number | 1 |
| Publication status | Published - 2010 |
Abstract
We consider Lie(G)-valued G-invariant connections on bundles over spaces, where G/H, ℝ × G/H and ℝ2 × G/H, G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds ℝ × G/H and ℝ2 × G/H carry G2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on ℝ × G/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G2-structures on ℝ × G/H. It is shown that both G2-instanton equations can be obtained from a single Spin(7)-instanton equation on ℝ × G/H.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Communications in Mathematical Physics, Vol. 300, No. 1, 2010, p. 185-204.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Yang-Mills Flows on Nearly Kähler Manifolds and G2-Instantons
AU - Harland, Derek
AU - Ivanova, Tatiana A.
AU - Lechtenfeld, Olaf
AU - Popov, Alexander D.
N1 - Copyright: Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010
Y1 - 2010
N2 - We consider Lie(G)-valued G-invariant connections on bundles over spaces, where G/H, ℝ × G/H and ℝ2 × G/H, G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds ℝ × G/H and ℝ2 × G/H carry G2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on ℝ × G/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G2-structures on ℝ × G/H. It is shown that both G2-instanton equations can be obtained from a single Spin(7)-instanton equation on ℝ × G/H.
AB - We consider Lie(G)-valued G-invariant connections on bundles over spaces, where G/H, ℝ × G/H and ℝ2 × G/H, G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds ℝ × G/H and ℝ2 × G/H carry G2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on ℝ × G/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G2-structures on ℝ × G/H. It is shown that both G2-instanton equations can be obtained from a single Spin(7)-instanton equation on ℝ × G/H.
UR - http://www.scopus.com/inward/record.url?scp=77957113905&partnerID=8YFLogxK
U2 - 10.48550/arXiv.0909.2730
DO - 10.48550/arXiv.0909.2730
M3 - Article
AN - SCOPUS:77957113905
VL - 300
SP - 185
EP - 204
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -