Abstract
The (anti)self-duality equations for gauge fields in dimensiond=4 and the generalization of these equations ford>4 are considered. The results on solutions of the (anti)self-duality equations ind≥4 are reviewed. Some new classes of solutions of Yang-Mills equations ind≥4 for arbitrary gauge fields are described.
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References
A. Actor,Rev. Mod. Phys.,51, 461 (1979); A. I. Leznov and M. V. Savel'ev,Fiz. Elem. Chastits At. Yadra,11, 40 (1980).
R. Rajaraman,Solitons and Instantons, North-Holland, Amsterdam (1984).
M. K. Prasad, in:Geometrical Ideas in Physics [Russian translation], Mir, Moscow (1983), p. 64.
M. B. Green, J. H. Schwarz, and E. Witen,Superstring Theory, Vols. 1 and 2, C.U.P., Cambridge (1987).
A. Strominger,Nucl. Phys. B,343, 167 (1990); A. Dabholkar, G. Gibbons, J. A. Harvey, and R. F. Ruiz,Nucl. Phys. B,340, 33 (1990); C. G. Callan, J. A. Harvey, and A. Strominger,Nucl. Phys. B,359, 611 (1991); M. J. Duff and J. X. Lu,Nucl. Phys. B,354, 129, 141 (1991);357, 534 (1991).
J. A. Harvey and A. Strominger,Phys. Rev. Lett.,66, 549 (1991).
A. S. Schwarz,Commun. Math. Phys.,56, 79 (1977); D. B. Fairlie,Phys. Lett. B,82, 97 (1979); N. S. Manton,Nucl. Phys. B,158, 141 (1980); P. Forgacs and N. S. Manton,Commun. Math. Phys. 72, 15 (1980); G. Chapline and N. S. Manton,Nucl. Phys. B,184, 391 (1981); A. S. Schwarz and Yu. S. Tyupkin,Nucl. Phys. B,187, 321 (1981).
E. Corrigan, C. Devchand, D. B. Fairlie, and J. Nuyts,Nucl. Phys. B,214, 452 (1983).
R. S. Ward,Ncul. Phys. B,236, 381 (1984).
D. B. Fairlie and J. Nuyts,J. Phys. A.,17, 2867 (1984); J. Nuyts,Lect. Notes Phys.,201, 306 (1984); C. Devchand and D. B. Fairlie,Phys. Lett. B,141, 73 (1984).
S. Fubini and H. Nicolai,Phys. Lett. B,155, 369 (1985).
A. M. Semikhatov, in:Group-Theoretical Methods in Physics.Proc. of the Third International Seminar, Vol. 1 [in Russian], Nauka, Moscow (1986), p. 156.
E. Corrigan, P. Goddard, and A. Kent,Commun. Math. Phys.,100, 1 (1985).
A. D. Popov,Europhys. Lett.,17, 23 (1992); T. A. Ivanova,Usp. Mat. Nauk,47, 191 (1992); T. A. Ivanova and A. D. Popov,Lett. Math. Phys.,24, 85 (1992).
A. D. Popov,Pis'ma Zh. Eksp. Teor. Fiz.,55, 261 (1992); A. D. Popov,Mod. Phys. Lett. A,7, 2077 (1992).
T. A. Ivanova,Usp. Mat. Nauk,46, 149 (1991);Vestn. Mosk. Univ. Mat. Mekh., Ser. 1, No. 3, 10 (1992);Mat. Zametki,52, 43 (1992).
T. A. Ivanova and A. D. Popov,Lett. Math. Phys.,23, 29 (1991).
A. D. Popov,Pis'ma Zh. Eksp. Teor. Fiz.,54, 71 (1991).
A. D. Popov,Teor. Mat. Fiz.,89, 402 (1991).
L. Berard-Bergery and T. Ochiani, in:Global Riemann. Geom. Symp., New York (1984), p. 52.
Yu. i. Manin,Gauge Fields and Complex Geometry [in Russian], Nauka, Moscow (1984).
M. J. Ablowitz, D. J. Costa, and K. Tenenblat,Stud. Appl. Math.,77, 37 (1987).
M. M. Capria and S. M. Salamon,Nonlinearity,1, 517 (1988); T. Nitta,Tôhoku Math. J.,40, 425 (1988); J.F. Clazebrook,Rep. Math. Phys.,25, No. 2, 141; A. Galperin, E. Ivanov, V. Ogievetsky, and E. Sokatchev,Ann. Phys. (N. Y.),185, 1 (1988); K. Galicki and Y. S. Poon,J. Math. Phys.,32, 1263 (1991).
S. Salamon,Invent. Math.,67, 143 (1982);Ann. Sci. Ec. Norm. Sup.,19, 31 (1986); N. R. O'Brien and J. H. Rawnsley,Ann. Glob. Anal. Geom.,3, 29 (1985).
R. J. Baston and M. G. Eastwood,The Penrose Transform: Its Interaction with Representation Theory, Clarendon Press, Oxford (1989).
D. H. Tchrakian,J. Math. Phys.,21, 166 (1980);Phys. Lett. B,150, 360 (1985);155, 255 (1985); O. Lechtenfeld, W. Nahm, and D. H. Tchrakian,Phys. Lett. B,162, 143 (1985); A. Chakrabarti, T. H. Sherry, and D. H. Tchrakian,Phys. Lett. B,162, 340 (1985); G. M. O'Brien and D. H. Tchrakian,Lett. Math. Phys.,11, 133 (1986);J. Math. Phys.,29, 1242 (1988); D. O'Se and D. H. Tchrakian,Lett. Math. Phys.,13, 211 (1987); Y. Yang,Lett. Math. Phys.,19, 257, 285 (1990); D. H. Tchrakian and A. Chakrabarti,J. Math. Phys.,32, 2532 (1991).
B. Grossman, T. W. Kephart, and J. D. Stasheff, Commun. Math. Phys.,96, 431 (1984); Y. Brihaye, C. Devchand, and J. Nuyts,Phys. Rev. D,32, 990 (1985).
C. Sacliogly,Nucl. Phys. B,277, 487 (1986); K. Fujii,Lett. Math. Phys.,12, 363 (1986).
F. A. Bais and P. Batenburg,Nucl. Phys.B,269, 363 (1986); P. Batenburg and R. H. Rietdijk,Nucl. Phys. B,313, 393 (1989).
S. Kobayashi and K. Nomizu,Foundations of Differential Geometry, Vol. 2, Interscience, New York (1963).
B. De Wit and H. Nicolai,Nucl. Phys. B,231, 506 (1984); A. R. Dündarer, F. Gürsey, and C.-H. Tze,J. Math. Phys.,25, 1496 (1984); A. R. Dündarer and F. Gürsey,J. Math. Phys.,32, 1176 (1991).
S. Rouhani,Phys. Lett. A,104, 7 (1984).
R. S. Ward,Phys. Lett. A,112, 3 (1985).
W. Nahm,Lect. Notes Phys.,180, 456 (1984);201, 189 (1984).
N. J. Hitchin,Commun. Math. Phys.,89, 145 (1983); S. K. Donaldson,Commun. Math. Phys.,96, 387 (1984); J. Hartubise,Commun. Math. Phys.,100 191 (1989);120, 613 (1989); J. Hartubise and M. K. Murray,Commun. Math. Phys.,133, 487 (1990).
M. Atiyah and N. Hitchin,The Geometry and Dynamics of Magnetic Monopoles, Princeton (1988).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii,The Theory of Solitons. The Inverse Scatting Method [in Russian], Nauka, Moscow (1980); M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Maths. Vol.4), Philadelphia (1981).
A. N. Leznov and M. V. Saveliev,Commun. Math. Phys.,74, 111 (1980); N. Ganoulis, P. Goddard, and D. Olive,Nucl. Phys. B,205, 601 (1982); A. Charkrabarti,Nucl. Phys. B.,248, 209 (1984).
A. M. Perelomov,Integrable Systems of Classical Mechanics and Lie Algebras [in Russian], Nauka, Moscow (1990); A. N. Leznov and M. V. Savel'ev,Group Methods of Integration of Nonlinear Dynamical Systems [in Russian], Nauka, Moscow (1985).
S. Chakravarty, M. J. Ablowitz, and P. A. Clarkson,Phys. Rev. Lett.,65, 1085, 2086E (1990).
H. Pedersen and Y. S. Poon,Commun. Math. Phys.,117, 569 (1988); K. Galicki and Y. S. Poon,J. Math. Phys.,32, 1263 (1991).
N. J. Hitchin, A. Karlhede, U. Lindström, and M. Roček,Commun. Math. Phys.,108, 535 (1987); A. Karlhede, U. Lindström, and M. Roček,commun. Math. Phys.,108, 529 (1987); U. Lindström and M. Roček,Commun. Math. Phys.,115, 21 (1988).
A. D. Popov,Mod. Phys. Lett. A,5, 2057 (1990); A. D. Popov and A. G. Sergeev, Communication JINR E2-92-261, Dubna (1992).
R. S. Ward,Phys. Lett. B,234, 81 (1990).
R. S. Ward,Philos. Trans. R. Soc. London, Ser. A,315, 451 (1985); N. J. Hitchin,Proc. London Math. Soc.,55, 59 (1987); A. D. Popov,Yad. Fiz.,51, 883 (1990).
A. D. Popov,Pis'ma Zh. Eksp. Teor. Fiz.,54, 128 (1991).
E. Kovacs and S.-Y., Lo,Phys. Rev. D.,19, 3649 (1979); S. Chakravarty and E. T. Newman,J. Math. Phys.,28, 334 (1987); J. Villarroel.J. Math. Phys.,28, 2610 (1987); L. Hajiivanov and D. Stoyanov,Lett. Math. Phys.,13 93 (1987).
H. J. Vega,Commun. Math. Phys.,116, 659 (1988).
T. T. Wu and C. N. Yang,Phys. Rev. D,12, 3843 (1975);13, 3233 (1976).
I. Ya. Aref'eva and I. V. Volovich,Usp. Fiz. Nauk,146, 655 (1985); D. P. Sorokin and V. I. Tkach,Fiz. Elem. Chastits At. Yadra,18, 1035 (1987); Yu. S. Vladimirov and A. D. Popov, in:Classical Field Theory and The Theory of Gravitation, Vol. 1 [in Russian], VINITI, Moscow (1991), p. 5.
A. D. Popov,Europhys. Lett.,19, 465 (1992).
Additional information
Moscow State University; Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 2, pp. 316–342, February, 1993.
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Ivanova, T.A., Popov, A.D. (Anti)self-dual gauge fields in dimensiond≥4. Theor Math Phys 94, 225–242 (1993). https://doi.org/10.1007/BF01019334
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DOI: https://doi.org/10.1007/BF01019334