A note on the non-existence of $\sigma$-model solitons in the 2+1 dimensional AdS gravity

TL;DR

This paper proves that static solitons in the 2+1 dimensional O(3) sigma model cannot exist when a negative cosmological constant is present, highlighting limitations of soliton solutions in AdS gravity.

Contribution

It establishes the non-existence of gravitating static solitons in the 2+1 dimensional O(3) sigma model with negative cosmological constant.

Findings

No static soliton solutions in AdS gravity for the model.

Clarifies constraints on soliton existence in lower-dimensional AdS spacetimes.

Contributes to understanding of soliton behavior in curved backgrounds.

Abstract

We show that the gravitating static soliton in the 2+1 dimensional O(3) $\sigma$ model does not exist in the presence of a negative cosmological constant.