Selfdual and non - selfdual solutions for gauge fields in Schwarzschild and deSitter backgrounds for dimension d ≥ 4
نویسنده
چکیده
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 p1, and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by p2. In this paper, we study the classical equations of the p1 = 1, 2 YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter, anti-deSitter) of the p2 = 1, 2, 3 EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of non-self-dual YM fields. When p1 = p2 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.
منابع مشابه
Nonselfdual Solutions for Gauge Fields in Schwarzschild and Desitter Backgrounds for Dimension D ≥ 4
A particularly simple class of nonselfdual solutions are obtained for gauge fields in Schwarzschild and deSitter backgrounds. For Lorentz signature these have finite energy and finite action for Euclidean signature. In each case one obtains either real or a pair of complex conjugate solutions. The actions are easily computed for any dimension d. Numerical values are given for d = 4, 6, 7, 8, 9,...
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