TY - JOUR
T1 - Yang-Mills instantons and dyons on group manifolds
AU - Ivanova, Tatiana A.
AU - Lechtenfeld, Olaf
N1 - Funding Information:
The authors are grateful to A.D. Popov for fruitful discussions and useful comments. T.A.I. acknowledges the Heisenberg–Landau program and the Russian Foundation for Basic Research (grant 06-01-00627-a) for partial support and the Institut für Theoretische Physik der Leibniz Universität Hannover for its hospitality. The work of O.L. is partially supported by the Deutsche Forschungsgemeinschaft.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/12/4
Y1 - 2008/12/4
N2 - We consider Euclidean SU (N) Yang-Mills theory on the space G × R, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint G-action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G = SU (2) ≅ S3, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on G × R to Minkowski and construct finite-energy dyon-type Yang-Mills solutions. The special case of G = SU (2) × SU (2) may be used in heterotic flux compactifications.
AB - We consider Euclidean SU (N) Yang-Mills theory on the space G × R, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint G-action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G = SU (2) ≅ S3, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on G × R to Minkowski and construct finite-energy dyon-type Yang-Mills solutions. The special case of G = SU (2) × SU (2) may be used in heterotic flux compactifications.
UR - http://www.scopus.com/inward/record.url?scp=55749100829&partnerID=8YFLogxK
U2 - 10.1016/j.physletb.2008.10.027
DO - 10.1016/j.physletb.2008.10.027
M3 - Article
AN - SCOPUS:55749100829
SN - 0370-2693
VL - 670
SP - 91
EP - 94
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
IS - 1
ER -