# Exact self-duality in a modified Skyrme model

## TL;DR

This paper introduces a modified Skyrme model with a non-constant coupling matrix that admits exact self-dual solutions, maintaining conformal invariance and providing explicit Skyrmion solutions with unity topological charge.

## Contribution

It presents a novel modification of the Skyrme model that supports exact self-dual solutions through a variable coupling matrix, enhancing understanding of topological solitons.

## Key findings

- Supports exact self-dual Skyrmions with unity topological charge
- Maintains conformal invariance in three dimensions
- Breaks some internal symmetries of the original model

## Abstract

We propose a modification of the Skyrme model that supports a self-dual sector possessing exact non-trivial finite energy solutions. The action of such a theory possesses the usual quadratic and quartic terms in field derivatives, but the couplings of the components of the Maurer-Cartan form of the Skyrme model is made by a non-constant symmetric matrix, instead of the usual Killing form of the SU(2) Lie algebra. The introduction of such a matrix make the self-duality equations conformally invariant in three space dimensions, even though it may break the global internal symmetries of the original Skyrme model. For the case where that matrix is proportional to the identity we show that the theory possesses exact self-dual Skyrmions of unity topological charges.