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arXiv · hep-th/0002144

Finite energy/action solutions of $p_1$ Yang-Mills equations on $p_2$ Schwarzschild and deSitter backgrounds for dimension $d \ge 4$

Y. Brihaye·A. Chakrabarti·D. H. Tchrakian
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Abstract

Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by $p_1$, and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by $p_2$. In this paper, we study the classical equations of the $p_1 = 1,2$ YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter,anti-deSitter) of the $p_2=1,2,3$ EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of non-self-dual YM fields. When $p_1=p_2$ self-dual solutions exist in addition. Their action is equal to the Chern-Pontryagin charge and can be compared with that of the non-self-dual solutions.

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Y. Brihaye, A. Chakrabarti, D. H. Tchrakian. 2000-05-19. Finite energy/action solutions of $p_1$ Yang-Mills equations on $p_2$ Schwarzschild and deSitter backgrounds for dimension $d \ge 4$. https://doi.org/10.1063/1.533421

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