Gravitating $\sigma$ Model Solitons

TL;DR

This paper investigates axially symmetric static solitons in a nonlinear sigma model coupled to (2+1)-dimensional anti-de Sitter gravity, revealing the existence of nontopological solitons and their relation to charged BTZ black holes.

Contribution

It presents new solutions of sigma model solitons in AdS gravity, including nontopological solitons with half-integer winding and their connection to charged BTZ black holes.

Findings

Regular topological lumps cannot form black holes.

Nontopological solitons with half-integer winding exist.

Spacetimes involve charged BTZ black holes without scalar hair.

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.