Atiyah-Manton Construction of Skyrmions in Eight Dimensions

Understand

We show that the eight-dimensional instanton solution, which satisfies the self-duality equation $F \wedge F = *_8 F \wedge F$, realizes the static Skyrmion configuration in eight dimensions through the Atiyah-Manton construction.

• The relevant energy functional of the Skyrme field is obtained by the formalism developed by Sutcliffe.
• By comparing the Skyrmion olution associated with the extreme of the energy, with the Atiyah-Manton solution constructed by the instantons, we find that they agree with high accuracy.
• This is a higher-dimensional analogue of the Atiyah-Manton construction of Skyrmions in four dimensions.