Searching for an attractive force in holographic nuclear physics

We are looking for a holographic explanation of nuclear forces, especially the attractive forces. Recently, the repulsive hard core of a nucleon-nucleon potential was obtained in the Sakai-Sugimoto model, and we show that a generalized version of that model - with an asymmetric configuration of the flavor D8 branes - also has an attractive potential. While the repulsive potential stems from the Chern-Simons interactions of the U(2) flavor gauge fields in 5D, the attractive potential is due to a coupling of the gauge fields to a scalar field describing fluctuations of the flavor branes' geometry. At intermediate distances r between baryons - smaller than R_KK = O(1)/M_ωmeson but larger than the radius ρ ̃ R _KK/√λ'_tHooft of the instanton at the core of a baryon - both the attractive and the repulsive potentials behave as 1/r ², but the attractive potential is weaker: Depending on the geometry of the flavor D8 branes, the ratio C_a/r = -V^attr(r)/V ^rep(r) ranges from 0 to 1 9 . The 5D scalar fields also affect the isovector tensor and spin-spin forces, and the overall effect is similar to the isoscalar central forces, V (r) → (1 - C_a/r) × V (r). At longer ranges r > O(R_KK), we find that the attractive potential decays faster than the repulsive potential, so the net potential is always repulsive. This unrealistic behavior may be peculiar to the Sakai-Sugimoto-like models, or it could be a general problem of the N_c → ∞ limit inherent in holography.