Quark Confinement and the Fractional Quantum Hall Effect

TL;DR

This paper draws an analogy between quark confinement in baryons and the fractional quantum Hall effect, suggesting that quark confinement is a correlation effect and predicting an energy gap in the system.

Contribution

It introduces a novel topological analogy between baryons and FQHE, confirming quark confinement as a correlation phenomenon and deriving a Hamiltonian predicting an energy gap.

Findings

Quark systems exhibit a filling factor of 1/3, similar to FQHE.

The topology of baryons resembles that of FQHE systems.

An energy gap is predicted for heavy three-quark systems.

Abstract

Working in the physics of Wilson factor and Aharonov-Bohm effect, we find in the fluxtube-quark system the topology of a baryon consisting three heavy flavor quarks resembles that of the fractional quantum Hall effect (FQHE) in condensed matter. This similarity yields the result that the constituent quarks of baryon have the "filling factor" 1/3, thus the previous conjecture that quark confinement is a correlation effect was confirmed. Moreover, by deriving a Hamiltonian of the system analogous to that of FQHE, we predict an energy gap for the ground state of a heavy three-quark system.