Dilute Instanton Gas of an O(3) Skyrme Model

TL;DR

This paper investigates how the Skyrme term influences instantons in a 1+1 dimensional O(3) sigma model, providing explicit calculations of instanton effects and semiclassical quantization.

Contribution

It presents an explicit analysis of instantons in a Skyrmed O(3) sigma model, including fluctuation determinants and vacuum energy shifts, in a scale-breaking setting.

Findings

Instantons are self-dual and explicitly evaluable.

Fluctuation actions reduce to scalar form, enabling determinant calculations.

The study demonstrates semiclassical quantization in a Skyrme-modified model.

Abstract

The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are self-dual and can be evaluated explicitly. They are also localised to an absolute scale, and their fluctuation action can be reduced to a scalar subsystem. This permits the explicit calculation of the fluctuation determinant and the shift in vacuum energy due to instantons. The model also illustrates the semiclassical quantisation of a Skyrmed field theory.