Nucleus from string theory

In generic holographic QCD, we find that baryons are bound to form a nucleus, and that its radius obeys the empirically-known mass-number ($A$) dependence $r\propto A^{1/3}$ for large $A$. Our result is robust, since we use only a generic property of D-brane actions in string theory. We also show that nucleons are bound completely in a finite volume. Furthermore, employing a concrete holographic model (derived by Hashimoto, Iizuka, and Yi, describing a multibaryon system in the Sakai-Sugimoto model), the nuclear radius is evaluated as $\mathcal{O}(1)\times A^{1/3}[\mathrm{fm}]$, which is consistent with experiments.

Figure 1

Gravity dual of QCD-like confining gauge theories with $A$ baryons. The horizontal directions are our 3-dimensional space, and the vertical direction is the holographic direction. This 10-dimensional spacetime is curved, and the bottom is capped by a smooth compact manifold, which is the IR end. The baryon vertices ($A$ red balls) sit on the $N_f$ flavor D-branes. The degrees of freedom of the baryons are open strings attached to the baryon vertices.

Figure 2

The nuclear density distribution $\rho (r)$ obtained in the large $D$ limit, (10). At the core of the nucleus $r\sim 0$, the distribution is homogeneous. For $r>r_0$, the density is exactly zero, meaning the complete finiteness of nuclei. A graphical image is drawn in the next figure.

Figure 3

The density distribution of the nucleus. Darker color means smaller density. Ignoring the surface defect, we find a homogeneous density distribution.