Rational Skyrmions

TL;DR

This paper introduces a new explicit rational function method for constructing Skyrmions using ADHM data, providing more accurate and computationally straightforward approximations compared to traditional methods.

Contribution

The authors develop a novel rational function approach to approximate Skyrmions directly from ADHM data, avoiding differential equations required in previous methods.

Findings

Energy of baryon number one Skyrmion is within 1% of the true solution.

Constructed baryon number two Skyrmions include an axially symmetric configuration.

Method simplifies Skyrmion approximation by using explicit algebraic formulas.

Abstract

A new method is introduced to construct approximations to Skyrmions that are explicit rational functions of the spatial Cartesian coordinates. The scheme uses ADHM data of a Yang-Mills instanton to produce a Skyrmion with a baryon number that is equal to the instanton number. The formula for the Skyrmion involves only the evaluation of the ADHM data, in contrast to the Atiyah-Manton construction that requires the solution of a differential equation that can only be solved explicitly in the case of a spherically symmetric Skyrmion. Examples with baryon numbers one and two are studied in detail. The energy of the rational Skyrmion with baryon number one is lower than that of the Atiyah-Manton Skyrmion, which is already within one percent of the energy of the true numerically computed Skyrmion. A family of baryon number two Skyrmions is presented, which includes an axially symmetric Skyrmion that smoothly transforms to a pair of well-separated single Skyrmions as the parameter is varied.