Holographic heavy baryons in the Witten-Sakai-Sugimoto model with the D0-D4 background

Abstract

We extend the holographic analysis of the light-baryon spectrum by Cai et al. [Phys. Rev. D 90, 106001 (2014)] to the case involving the heavy flavors. With the construction of the Witten-Sakai-Sugimoto model in the D0-D4 background, we use the mechanism proposed by Liu and Zahed by including two light-flavor and one heavy-flavor brane, to describe the heavy-light baryons as heavy mesons bound to a flavor instanton. The background geometry of this model corresponds to an excited state in the dual field theory with a nonzero glue condensate $⟨\mathrm{Tr}\mathcal{F}\ensuremath{\wedge}\mathcal{F}⟩=8{\ensuremath{\pi}}^{2}{N}_{c}\stackrel{\texttildelow{}}{\ensuremath{\kappa}}$ (or equivalently a nonzero $\ensuremath{\theta}$ angle), which is proportional to the number density of the D0-brane charge. In the strong-coupling limit, this model shows that the heavy meson is always bound in the form of the zero mode of the flavor instanton in the fundamental representation. We systematically study the quantization of the effective Lagrangian of heavy-light baryons by employing the soliton picture, and derive the mass spectrum of heavy-light baryons in the situation with single- and double-heavy baryons. We find that the difference in the mass spectrum becomes smaller if the density of the D0-brane charge increases, and the stability constraint of the heavy-light baryons is $1<b<3$. This indicates that a baryon cannot stably exist for a sufficiently large D0 charge density, which is in agreement with the conclusions in the previous study of this model.