Monopole and Dyon Solutions in AdS space

TL;DR

This paper explores monopole and dyon solutions in Einstein-Yang-Mills-Higgs theory within anti-de Sitter space, revealing conditions for regular solutions and quantization of the Higgs vacuum expectation value.

Contribution

It provides new insights into the existence and properties of monopole and dyon solutions in AdS space, including quantization conditions for the Higgs field.

Findings

Singular dyons resemble Reissner-Nordström black holes.

Regular solutions require Higgs VEV quantization in AdS.

Distinct features emerge at zero coupling constant.

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-N\"ordstrom 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, $|\vec H(\infty)|$, should be quantized in units of the natural mass scale $1/e r_0$ (related to the cosmological constant) according to $|\vec H(\infty)|^2 = m(m+1) (e r_0 )^{-2}$, with $m \in Z$.