Matrix model and holographic baryons in the D0-D4 background

We study the spectrum and short-distance two-body force of holographic baryons by the matrix model, which is derived from the Sakai-Sugimoto model in the D0-D4 background (D0-D4/D8 system). The matrix model is derived by using the standard technique in string theory, and it can describe multibaryon systems. We rederive the action of the matrix model from open string theory on the baryon vertex, which is embedded in the D0-D4/D8 system. The matrix model offers a more systematic approach to the dynamics of the baryons at short distances. In our system, we find that the matrix model describes stable baryonic states only if $\zeta =U_{Q_0}^3/U_{KK}^3<2$, where $U_{Q_0}^3$ is related to the number density of smeared D0-branes. This result in our paper is exactly the same as some previous results studied in this system, presented in [W. Cai, C. Wu, and Z. Xiao, Phys. Rev. D 90, 106001 (2014)]. We also compute the baryon spectrum ($k=1$ case) and short-distance two-body force of baryons ($k=2$ case). The baryon spectrum is modified and could be able to fit the experimental data if we choose a suitable value for $\zeta$. And the short-distance two-body force of baryons is also modified by the appearance of smeared D0-branes from the original Sakai-Sugimoto model. If $\zeta >2$, we find that the baryon spectrum will be totally complex and an attractive force will appear in the short-distance interaction of baryons, which may consistently correspond to the existence of unstable baryonic states.