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

Physics

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Fundamental Problems And General Formalism, Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity

Scientific paper

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.

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