Gravitating $\sigma$ Model Solitons

Abstract

We study axially symmetric static solitons of O(3) nonlinear $\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\tilde n$ados-Teitelboim-Zanelli black holes without non-Abelian scalar hair.