Abstract
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 1/2N_{c}. The generalization to arbitrary N_{f} is discussed.
Highlights
Introduction.—In the large number of the color limit, ’t Hooft suggested that QCD is dominated by planar diagrams, with infinitely many weakly interacting mesons and glueballs [1]
Chiral solitons made solely of nonlinearly interacting pions are a prototype of these solitons, an idea put forth decades ago by Skyrme [3] well before the advent of QCD
Komargodski [5] pointed at the peculiar character of the QCD baryons for Nf 1⁄4 1, where the chiral effective theory is dominated by the axial U(1) anomaly for the η0 meson, and where the soliton construction no longer applies since, for instance, the standard topological charge cannot be identified
Summary
Komargodski [5] pointed at the peculiar character of the QCD baryons for Nf 1⁄4 1, where the chiral effective theory is dominated by the axial U(1) anomaly for the η0 meson, and where the soliton construction no longer applies since, for instance, the standard topological charge cannot be identified. He noted that the effective theory has a conserved topological current Jαβγ 1⁄4 εαβγλ∂λη0=2π. When the bag radius is shrunk to zero, only the smile of the cat is left with
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