Nucleon-nucleon potential in holographic QCD

Abstract

We derive the nucleon-nucleon potential in the D4-D8 model of holographic QCD. The nucleon-nucleon potential emerges from one-boson exchange picture with massless pseudo-scalars and an infinite tower of spin one mesons. We observe in particular that the tensor coupling of the ρ meson with nucleon comes out naturally larger than the vector coupling, whereas for ω mesons and axial mesons, such tensor couplings are completely absent. The potential is universally repulsive ∼ 1 / r 2 at short distance, and has the usual long-distance attractive behavior ∼ − 1 / r 3 along a isospin singlet and spin triplet channel. Both the large N c form and the finite N c form are given. In the former, a shallow classical minimum of depth ∼ 0.1 M K K N c / λ forms at about r M K K ≃ 5.5 . We discuss shallow bound states of nucleons with the holographic potential.