Monopoles in AdS

TL;DR

This paper studies magnetic monopoles in four-dimensional Anti-de Sitter spacetime using analytic and numerical methods, revealing their symmetry properties, energy bounds, and lattice structures relevant to holographic theories.

Contribution

It introduces a rational map approximation for monopoles, connecting their symmetry and energy properties to those of Skyrmions, and analyzes monopole walls in the large N limit.

Findings

Minimal energy monopoles share symmetries with Skyrmions.

Rational map approximation bounds monopole energy and refines magnetic bag models.

Monopole walls form hexagonal lattices in the large N limit.

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.