  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.
