BPS Skyrmions of Generalized Skyrme Model In Higher Dimensions

TL;DR

This paper explores higher-dimensional Skyrme models, identifying BPS submodels and their properties, including topological degrees and self-duality conditions, extending the understanding of Skyrmions beyond three dimensions.

Contribution

It introduces a generalized ansatz for higher-dimensional Skyrme models and characterizes the BPS submodels, revealing their existence and properties in higher dimensions.

Findings

Two BPS submodels identified: BPS Skyrme and scale-invariant.

BPS Skyrmions with B≥1 exist in the first submodel.

The scale-invariant model exhibits stronger self-duality conditions.

Abstract

In this work we consider the higher dimensional Skyrme model, with spatial dimension $d > 3$, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, \(B\geq 1\), a modified generalized hedgehog ansatz is used where we assign an integer \(n_i\) for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-invariant model. The properties of the higher dimensional version of both submodels are studied and it is found that the BPS Skyrmions with \(B\geq1\) exist in the first submodel but there is only \(B=1\) BPS Skyrmion in the second submodel. We also study the higher dimensional version of self-duality conditions in terms of strain tensor eigenvalues and find that, in general, the scale-invariant model has a stronger self-duality condition than the BPS Skyrme model.