Monopole and dyon solutions in AdS space

Abstract

We consider monopole and dyon classical solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We discuss both singular and regular solutions to the second order equations of motion showing that singular Wu-Yang like dyons can be found, the resulting metric being of the Reissner-Nordstrom type (with cosmological constant). Concerning regular solutions, we analyze the conditions under which they can be constructed discussing, for vanishing coupling constant, the main distinctive features related to the anti-de Sitter asymptotic condition; in particular, we find in this case that the v.e.v. of the Higgs scalar, | H (∞)| , should be quantized in units of the natural mass scale 1/e r 0 (related to the cosmological constant) according to | H (∞)| 2 =m(m+1)(e r 0 ) −2 , with m ∈ Z .