Baryon as a Quantum Hall Droplet and the Quark-Hadron Duality

We show that the recent proposal to describe the $N_f=1$ baryon in the large number of the color limit as a quantum Hall droplet can be understood as a chiral bag in a ($1+2$)-dimensional strip using the Cheshire Cat principle. For a small bag radius, the bag reduces to a vortex line which is the smile of the cat with flowing gapless quarks all spinning in the same direction. The disk enclosed by the smile is described by a topological field theory due to the Callan-Harvey anomaly outflow. The chiral bag naturally carries the unit baryon number and spin $\frac{1}{2}{N}_c$. The generalization to arbitrary $N_f$ is discussed.

Figure 1

($1+2$)-dimensional chiral bag surrounding a QH droplet. The bag is an annulus of width $2R$ clouded by an ${\eta }^{\prime }$ with a monodromy of $2\pi$. In the limit of the zero bag radius, the chiral bag reduces to a vortex string with unit baryon number.

Figure 2

($1+2$)-dimensional chiral bag as an infinite strip in the $y$ direction (out of the page) with periodic boundary condition and U(1) chiral boundary condition along the $x$ direction.