Skyrmions, instantons and holography

TL;DR

This paper extends the connection between instantons and Skyrmions by proving that instanton holonomies solve a BPS Skyrme model coupled with vector mesons, improving nuclear binding energy predictions and relating to holographic string theory models.

Contribution

It demonstrates that instanton holonomies exactly solve a BPS Skyrme model with vector mesons and explores the effects of truncating vector mesons on Skyrmion properties.

Findings

Instanton holonomies produce exact solutions to a BPS Skyrme model.

Including only the first vector meson improves the Skyrme model's accuracy.

Truncation closer to BPS systems better reproduces nuclear binding energies.

Abstract

Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by proving that instanton holonomies produce exact solutions of a BPS Skyrme model, in which the Skyrme field is coupled to a tower of vector mesons. Neglecting any (or indeed all) of the vector mesons breaks the scale invariance and removes the BPS property of the Skyrmions. However, it is shown that a truncation of the BPS Skyrme theory, in which only the first vector meson is included, already moves the Skyrme model significantly closer to the BPS system. A theory that is close to a BPS system is required to reproduce the experimental data on binding energies of nuclei. A zero-mode quantization of the Skyrmion is performed in the truncated BPS theory and the results are compared to the physical properties of the nucleon. The approach is an analogue in five-dimensional Minkowski spacetime of a recent holographic construction of a Skyrme model by Sakai and Sugimoto, based on a string theory derivation of a Yang-Mills-Chern-Simons theory in a curved five-dimensional spacetime.