Topological solitons in the supersymmetric Skyrme model

TL;DR

This paper explores supersymmetric extensions of the Skyrme model, constructing various Euclidean solitons across different dimensions, including instantons, Skyrmions, and vortex-instantons, revealing their non-BPS nature and supersymmetry breaking.

Contribution

It introduces a supersymmetric Skyrme model and systematically constructs Euclidean solitons in multiple dimensions via Scherk-Schwarz reduction, highlighting novel non-BPS solutions.

Findings

Constructed Euclidean instantons in 4D supersymmetric Skyrme model.

Derived 3D Skyrmion-instantons through dimensional reduction.

Obtained finite-action 2D vortex-instantons with broken supersymmetry.

Abstract

A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.