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

TL;DR

This paper extends the holographic Witten-Sakai-Sugimoto model to include heavy flavors, analyzing heavy-light baryons as bound states of heavy mesons and flavor instantons, and studies how the D0-brane charge density affects their stability and mass spectrum.

Contribution

It introduces a novel holographic approach to heavy-light baryons in the D0-D4 background, revealing the impact of D0-brane charge density on baryon stability and spectrum.

Findings

Heavy mesons are bound as zero modes of flavor instantons.

Mass spectrum differences decrease with increasing D0-brane charge density.

Baryons become unstable when D0 charge density exceeds a certain threshold.

Abstract

We extend the holographic analysis of light-baryon spectrum in \cite{key-50} 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 in \cite{key-59,key-60,key-61} by including two light and one heavy flavor branes, 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 nonzero glue condensate $\left\langle \mathrm{Tr}\mathcal{F}\wedge\mathcal{F}\right\rangle =8\pi^{2}N_{c}\tilde{\kappa}$, or equivalently a $\theta$ angle, which is proportional to the number density of the D0-brane charge. At strongly coupled 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 for 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 baryon. We find the difference in the mass spectrum becomes smaller if the density of D0-brane charge increases and the constraint of stable states of the heavy-light baryons is $1<b<3$. It indicates that baryon can not stably exist for sufficiently large density of D0 charge which is in agreement with the conclusions in the previous study of this model.