Holographic three flavor baryon in the Witten-Sakai-Sugimoto model with the D0-D4 background

Abstract: With the construction of the Witten-Sakai-Sugimoto model in the D0-D4 background, we systematically investigate the holographic baryon spectrum in the case of three flavors. The background geometry in this model is holographically dual to $U\left(N_{c}\right)$ Yang-Mills theory in large $N_{c}$ limit involving an excited state with a nonzero $\theta$ angle or glue condensate $\left\langle \mathrm{Tr}\mathcal{F}\wedge\mathcal{F}\right\rangle =8\pi^{2}N_{c}\tilde{\kappa}$, which is proportional to the charge density of the smeared D0-branes through a parameter $b$ or $\tilde{\kappa}$. The classical solution of baryon in this model can be modified by embedding the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton and we carry out the quantization of the collective modes with this solution. Then we extend the analysis to include the heavy flavor and find that the heavy meson is always bound in the form of the zero mode of the flavor instanton in strong coupling limit. The mass spectrum of heavy-light baryons in the situation with single- and double-heavy baryon is derived by solving the eigen equation of the quantized collective Hamiltonian. Afterwards we obtain that the constraint of stable baryon states has to be $1<b<3$ and the difference in the baryon spectrum becomes smaller as the D0 charge increases. It indicates that quarks or mesons can not form stable baryons if the $\theta$ angle or glue condensate is sufficiently large. Our work is an extension of the previous study of this model and also agrees with those conclusions.