We provide a calculation of $N$-body ($N\ge 3$) nucleon interactions at short distances in holographic QCD. In the Sakai-Sugimoto model of large-$N_c$ massless QCD, $N$ baryons are described by $N$ Yang-Mills instantons in 5 spacetime dimensions. We compute a classical short-distance interaction Hamiltonian for $N$ ’t Hooft instantons. This corresponds to $N$ baryons sharing identical classical spins and isospins. We find that genuine $N$-body nuclear forces turn out to vanish for $N\ge 3$, at leading order. This suggests that classical $N$-body forces are always suppressed compared with 2-body forces.

• Received 17 November 2009

DOI:https://doi.org/10.1103/PhysRevD.81.106003