Searching for an attractive force in holographic nuclear physics

Abstract

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 _{ω meson} but larger than the radius $\rho \sim {{{{R_{\text{KK}}}}} \left/ {{\sqrt {{{\lambda_{{\text{'t Hooft}}}}}} }} \right.}$ 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 $\frac{1}{9}$. 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.