Monopoles in AdS

Abstract

Applications to holographic theories have led to some recent interest in magnetic monopoles in four-dimensional Anti-de Sitter spacetime. This paper is concerned with a study of these monopoles, using both analytic and numerical methods. An approximation is introduced in which the fields of a charge N monopole are explicitly given in terms of a degree N rational map. Within this approximation, it is shown that the minimal energy monopole of charge N has the same symmetry as the minimal energy Skyrmion with baryon number N in Minkowski spacetime. Beyond charge two the minimal energy monopole has only a discrete symmetry, which is often Platonic. The rational map approximation provides an upper bound on the monopole energy and may be viewed as a smooth non-abelian refinement of the magnetic bag approximation, to which it reverts under some additional approximations. The analytic results are supported by numerical solutions obtained from simulations of the non-abelian field theory. A similar analysis is performed on the monopole wall that emerges in the large N limit, to reveal a hexagonal lattice as the minimal energy architecture.