From the Sakai-Sugimoto Model to the Generalized Skyrme Model

TL;DR

This paper derives a generalized Skyrme model from the Sakai-Sugimoto model, highlighting the role of a sextic term and its connection to the BPS Skyrme model in the small 't Hooft coupling limit.

Contribution

It introduces a novel derivation of the generalized Skyrme model including a sextic term from the Sakai-Sugimoto model, linking holographic QCD to Skyrmion physics.

Findings

The sextic term arises from integrating out the $ ho$ meson and tower states.

In the small 't Hooft coupling limit, the Skyrmion is well described by the derived model.

Adding a pion mass term yields the BPS Skyrme model.

Abstract

We derive the generalized Skyrme model as a low-energy effective model of the Sakai-Sugimoto model. The novelty with the past is the presence of the sextic term equal to the topological charge squared. This term appears when the $\omega$ meson, and the tower of states on top of it, are integrated out. We claim that, in the small 't Hooft coupling limit, the instanton is well described by a Skyrmion arising from the low energy effective Lagrangian of the Sakai-Sugimoto model. The sextic term plays a dominant role in this limit. Moreover, when a pion mass term is added we recover the BPS Skyrme model in the small 't Hooft coupling limit.