A consistent two-skyrmion configuration space from instantons

Abstract

To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the relative size of the Skyrme and meson fields. We study the N = 1 and N = 2 systems in detail. Two interacting skyrmions can excite the meson field through scattering, suggesting that the meson and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.

ADHM skyrmions

“…. This phenomenon is known to exist in the 1 + 1 sector [20], but this is the first time it has been observed for higher charges.…”

“…Inspired by the holographic model of Sakai-Sugimoto [19], Sutcliffe showed that the standard Skyrme model is the first term in an infinite series of Skyrme models coupled to towers of vector mesons. Recently, it was conjectured that the full moduli space of instantons can be understood as low energy modes of a skyrmion, provided at least one vector meson is included in the Skyrme theory [20].…”

A model for gauged skyrmions with low binding energies

“…On top of its phenomenological successes, a beautiful advantage of Sutcliffe's model is how it explains the accuracy of the Atiyah-Manton approximation [28] of Skyrme fields from Yang-Mills instantons; the holonomy of instantons on R 4 well-approximate skyrmions, and Sutcliffe's model provides a solid theoretical framework for controlling how good the approximation is. This relationship with instantons also allows for a consistent configuration space on which to study low-energy interactions of skyrmions [29,30].…”

A model for gauged skyrmions with low binding energies

“…On top of its phenomenological successes, a beautiful advantage of Sutcliffe's model is how it explains the accuracy of the Atiyah-Manton approximation [28] of Skyrme fields from Yang-Mills instantons; the holonomy of instantons on R 4 well-approximate skyrmions, and Sutcliffe's model provides a solid theoretical framework for controlling how good the approximation is. This relationship with instantons also allows for a consistent configuration space on which to study low-energy interactions of skyrmions [29,30].…”