Baryons as Quantum Hall Droplets

TL;DR

This paper models baryons as quantum Hall droplets in large N QCD, providing a novel approach that matches phenomenological properties and offers insights into baryon structure beyond Skyrmion models.

Contribution

It introduces a new model of baryons as quantum Hall droplets, especially for one-flavor QCD, using a 2+1D meta-stable configuration of the η' particle.

Findings

Mass, size, spin, and isospin match phenomenological expectations.

Baryon number corresponds to magnetic symmetry on the quantum Hall sheet.

Chiral excitations carry baryon number and resemble fractional quantum Hall electrons.

Abstract

We revisit the problem of baryons in the large N limit of Quantum Chromodynamics. A special case in which the theory of Skyrmions is inapplicable is one-flavor QCD, where there are no light pions to construct the baryon from. More generally, the description of baryons made out of predominantly one flavor within the Skyrmion model is unsatisfactory. We propose a model for such baryons, where the baryons are interpreted as quantum Hall droplets. An important element in our construction is an extended, 2+1 dimensional, meta-stable configuration of the $\eta'$ particle. Baryon number is identified with a magnetic symmetry on the 2+1 dimensional sheet. If the sheet has a boundary, there are finite energy chiral excitations which carry baryon number. These chiral excitations are analogous to the electron in the fractional quantum Hall effect. Studying the chiral vertex operators we are able to determine the spin, isospin, and certain excitations of the droplet. In addition, balancing the tension of the droplet against the energy stored at the boundary we estimate the size and mass of the baryons. The mass, size, spin, isospin, and excitations that we find agree with phenomenological expectations.