Holographic Baryons as Quantum Hall Droplets

TL;DR

Using the WSS holographic model with $N_f=1$, the paper demonstrates a first-principle construction of baryons as holographic Hall droplets realized by charged D6-branes ending on flavor D8-branes. The D6 worldvolume hosts a $U(1)_N$ Chern-Simons theory, enabling a boundary edge mode interpretation and a relation between baryon number, charge, and angular momentum, $q_s = N n_B$ and $J = \frac{N}{2} n_B^2$ (for the relevant sector). The authors compute the baryon mass and radius in the confined and deconfined phases, study related defects (punctured domain walls, sandwich vortons) and map out metastability and decay channels, yielding phase-diagram–like insights. The work provides a concrete holographic realization of baryons as Hall droplets, links to edge physics, and suggests extensions to multi-flavor Hall droplets and possible connections to real QCD and beyond-Standard-Model sectors.

Abstract

We provide a first-principle construction of baryons as quantum Hall droplets in single-flavor holographic QCD. The baryons are described as charged D6-branes with a circular boundary on a flavor D8-brane in the Type IIA backgrounds dual to the confining and non-confining phases. The holographic description allows us to calculate precisely their properties, such as mass and size. We also consider other objects with baryonic charge, such as vortons, domain walls with holes, and "sandwich vortons", and discuss the relative (meta)stability of all these configurations.

Figures (30)

• Figure 1: Schematic picture of the chirally broken (left) and chirally symmetric (right) phases in the deconfined phase of the Witten-Sakai-Sugimoto model. The $x_4$-direction is compactified on a circle with radius $1/M_{KK}$, and $u$ is the holographic coordinate with $u =\infty$ being the boundary where the dual field theory lives. If the asymptotic distance $L$ between the flavor branes is sufficiently small, a deconfined, chirally broken phase (left figure) becomes possible. In this phase, the connected flavor branes are embedded non-trivially in the background according to a definite function $x_4(u)$.
• Figure 6: Cylinder configuration (a) and its one-point compactification $\mathbb{PT}$ (b). The boundary is indicated in blue.
• Figure 7: Projection of the revolution plot of $a_\psi$ (left panel) and $\hat{a}_\psi$ (right panel). This solution is computed for $\lambda = 100$ and $b=0.4$ in the confined phase.
• Figure 8: Numerical solution of $\rho$ (times $M_{KK}$) for $b=0.1$ and $\lambda=100$ as a function of the rescaled holographic coordinate $\hat{u}=u/u_J \in [0.92,1]$, describing a stable baryon with baryon number $n_B=1$. The profile's derivative at $\hat{u} = 1$ is zero, indicating the (meta)stability of this embedding, while it goes to $\infty$ at $\hat{u}=u_E/u_J$, consistently with the smoothness of the manifold.
• Figure 9: Numerical solutions for $u_J^{-1}\tilde{a}_t$ (left panel) and $(u_J L)^{-1}\tilde{a}_\psi$ (right panel) as a function of the rescaled holographic coordinate $\hat{u}$ for $b=0.1$ and $\lambda=100$.