Abstract
The Yang-Mills theories in d=7 and d=8 with the arbitrary gauge group G are considered. Generalized self-duality-type relations for gauge fields are reduced to systems of nonlinear differential equations on functions of one variable (Ward equations). Ward equations may be reduced to equations which follow from Yang-Baxter equations. This permits us to obtain new classes of explicit solutions of the Yang-Mills equations in d=7 and d=8.
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References
Corrigan, E., Devchand, C., Fairlie, D. B., and Nuyts, J., Nuclear Phys. B214, 452 (1983).
Ward, R. S., Nuclear Phys. B236, 381 (1984).
Fairlie, D. B. and Nuyts, J., J. Phys. A. 17, 2867 (1984); J. Math. Phys. 25, 2025 (1984); Nuyts, J., Lecture Notes in Phys. 201, 306 (1984); Devchand, C. and Fairlie, D. B., Phys. Lett. 141B, 73 (1984); Brihaye, Y., Devchand, C., and Nuyts, J., J. Phys. Rev. D32, 990 (1985).
Fubini, S. and Nicolai, H., Phys. Lett. 155B, 369 (1985).
Dündarer, R., Gürsey, F., and Tze, C.-H., J. Math. Phys. 25, 1496 (1984).
Ward, R. S., Phys. Lett. 112A, 3 (1985).
Rouhani, S., Phys. Lett. 104A, 7 (1984).
Kulish, P. P. and Sklyanin, E. K., Trudy LOMI, 95, 129 (1980) (in Russian).
Belavin, A. A. and Drinfeld, V. G., Funct. Anal. Appl. 16, 159 (1982).
Faddeev, L. D. and Takhtajan, L. A., Hamiltonian Methods in the Theory of Solitons, Springer, Berlin, 1987.
Semikhatov, A. M., Group Theoretical Methods in Physics, Vol. 1 (M. A. Markov (ed.)), Moscow, 1986, p. 156.
Bourbaki, N., Groupes et algèbres de Lie, Chapitre IV–VI, Hermann, Paris, 1968.
Belavin, A. A., Funct. Anal. Appl. 14, 18 (1980).
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Ivanova, T.A., Popov, A.D. Self-dual Yang-Mills fields in d=7,8, octonions and ward equations. Lett Math Phys 24, 85–92 (1992). https://doi.org/10.1007/BF00402672
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DOI: https://doi.org/10.1007/BF00402672