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.
Highlights
The Sakai-Sugimoto (SS) model is a top-down holographic model of QCD [1,2]
We find that a new term is generated by this procedure: a sextic term in a number of derivatives which correspond to the topological charge squared
We claim that in the small ’t Hooft coupling limit, the instanton becomes very large and eventually can be studied by considering only the generalized Skyrme effective obtained by integrating out all the massive vector meson
Summary
The Sakai-Sugimoto (SS) model is a top-down holographic model of QCD [1,2]. The model, among all the holographic attempts, is one of the closest example to QCD and being a top-down model, it has very few parameters to adjust. We claim that in the small ’t Hooft coupling limit, the instanton becomes very large and eventually can be studied by considering only the generalized Skyrme effective obtained by integrating out all the massive vector meson. In this limit, the instanton really turns out to be a Skyrmion. We find the ’t Hooft coupling interpolates between two distinct BPS models for baryons: small self-dual instantons for large λ and large BPS Skyrmions for small λ This is a generalization of what happens in lower dimensions with the baby-Skyrme model [12].
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