Self-dual MacDowell-Mansouri gravity coupled to self-dual Yang-Mills fields

G. Y. Chee

doi:10.1103/PhysRevD.62.064014

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Self-dual MacDowell-Mansouri gravity coupled to self-dual Yang-Mills fields

G. Y. Chee^*

China Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing, 100080, China
Physics Department, Liaoning Normal University, Dalian, 116029, China

^*Email address: gyq@mail.dlptt. ln.cn

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Phys. Rev. D 62, 064014 – Published 9 August, 2000

DOI: https://doi.org/10.1103/PhysRevD.62.064014

Abstract

A unified action for self-dual MacDowell-Mansouri gravity and Yang-Mills fields is proposed. The dual operation acting on the curvature and the self-dual and anti-self-dual decomposition are performed with respect to spacetime indices rather than internal indices, which makes the action simpler than the one given by Nieto and Socorro. In the new action the (anti-)self-dual Yang-Mills curvature couples only to the (anti-)self-dual curvature of the spacetime and then the self-dual and the anti-self-dual parts of the action are separated completely.

References (19)

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[c1] R. S. Ward, Nucl. Phys. B236, 381 (1984).

[c2] L. J. Mason and G. A. Sparling, Phys. Lett. A 137, 29 (1989).

[c3] R. S. Ward and R. O. Wells, Twistor Geometry and Field Theory (Cambridge University Press, Cambridge, England, 1990).

[c4] L. J. Mason and N. M. J. Woodhous, Integrability, Self-Duality, and Twistor Theory (Clarendon, Oxford, 1996).

[c5] J. Plebanski, J. Math. Phys. 16, 2395 (1975).

[c6] R. Penrose, Gen. Relativ. Gravit. 7, 31 (1976).

[c7] L. J. Mason and E. T. Newman, Commun. Math. Phys. 121, 659 (1989).

[c8] A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986); Phys. Rev. D 36, 1587 (1987).

[c9] S. W. MacDowell and F. Masouri, Phys. Rev. Lett. 38, 739 (1977).

[c10] J. A. Nieto, O. Obregon, and J. Socorro, Phys. Rev. D 50, R3583 (1994).

[c11] J. A. Nieto, J. Socorro, and O. Obregon, Phys. Rev. Lett. 76, 3482 (1996).

[c12] H. Garcia-Compean, O. Obregon, J. F. Plebanski, and C. Ramirez, Phys. Rev. D 57, 7501 (1998).

[c13] H. Garcia-Compean, O. Obregon, and C. Ramirez, Phys. Rev. D 58, 104012 (1998).

[c14] H. Garcia-Compean, J. A. Nieto, O. Obregon, and C. Ramirez, Phys. Rev. D 59, 124003 (1999).

[c15] J. A. Nieto and J. Socorro, Phys. Rev. D 59, 041501 (1999).

[c16] R. Penrose and W. Rindler, Spinors and Spacetime (Cambridge University Press, Cambridge, England, 1984).

[c17] G. Y. Chee, Phys. Rev. D 54, 6552 (1996).

[c18] G. Y. Chee, Gen. Relativ. Gravit. 30, 1735 (1998).

[c19] R. Gambini and L. Herrera, J. Math. Phys. 21, 1449 (1980).

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Self-dual MacDowell-Mansouri gravity coupled to self-dual Yang-Mills fields

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