Nuclear Force from String Theory

We compute the nuclear force in a holographic model of QCD on the basis of a D4-D8 brane configuration in type IIA string theory. The repulsive core of nucleons is important in nuclear physics, but its origin has not been well understood in strongly coupled QCD. We find that the string theory via gauge/string duality deduces this repulsive core at a short distance between nucleons. Since baryons in the model are realized as solitons given by Yang-Mills instanton configuration on flavor D8-branes, ADHM construction of two instantons probes well the nucleon interaction at short scale, which provides the nuclear force quantitatively. We obtain a central force, as well as a tensor force, which is strongly repulsive as suggested in experiments and lattice results. In particular, the nucleon-nucleon potential V(r) (as a function of the distance) scales as r(-2), which is peculiar to the holographic model. We compare our results with the one-boson exchange model using the nucleon-nucleon-meson coupling obtained in our previous paper [K. Hashimoto, T. Sakai and S. Sugimoto, Prog. Theor. Phys. 120 (2008) 1093, arXiv:0806.3122].