# Baryon as a Quantum Hall Droplet and the Cheshire Cat Principle

## TL;DR

This paper connects the description of baryons as quantum Hall droplets to the chiral bag model using the Cheshire cat principle, revealing a topological and vortex line interpretation with consistent baryon number and spin.

## Contribution

It demonstrates that the quantum Hall droplet model of baryons can be understood as a chiral bag in 1+2 dimensions, unifying two conceptual frameworks.

## Key findings

- Baryons as quantum Hall droplets can be modeled as chiral bags.
- The small bag radius limit corresponds to a vortex line with flowing quarks.
- The topological field theory describes the enclosed disc, ensuring baryon number and spin are consistent.

## Abstract

We show that the recent proposal to describe the $N_f=1$ baryon in the large number of 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 disc enclosed by the smile is described by a topological field theory due to the Callan-Harvey anomaly out-flow. The chiral bag carries naturally unit baryon number and spin $\frac 12 N_c$. The generalization to arbitrary $N_f$ is discussed.