Holographic Deuteron and Nucleon-Nucleon Potential

We compute the potential between a pair of nucleons in the D4-D8 holographic QCD. In the large ’t Hooft coupling limit, λ ≫ 1, the hadronic size of the baryon is small ∼ 1/ √ λMKK , and their interaction with mesons are well approximated by a set of dimension four and five operators. The nucleon-nucleon potential emerges from one-boson exchange picture involving massless pseudo-scalars and an infinite tower of spin one mesons. We find in particular that ρ meson exchanges are dominated by a dimension five derivative coupling of tensor type, whereas for ω mesons and axial mesons, such tensor couplings are completely absent. The potential is universally repulsive ∼ 1/r2 at short distance, and has the usual long-distance attractive behavior ∼ −1/r3 along a isosinglet and spin triplet channel. Both the large Nc form and the finite Nc form are given. In the former, a shallow classical minimum of depth ∼ 0.1MKKNc/λ forms at around rMKK ≃ 5.5.