Topological Discrete Algebra, Ground State Degeneracy, and Quark Confinement in QCD

TL;DR

This paper introduces a hidden discrete symmetry algebra in QCD that depends on space topology, providing a gauge-invariant way to distinguish confinement from deconfinement phases and revealing new quantum numbers related to fractional quantum Hall effects.

Contribution

It presents a novel discrete symmetry algebra in QCD based on permutation groups, linking topology to quark confinement and deconfinement phases.

Findings

Ground state degeneracy depends on space topology.

Discrete symmetry distinguishes confinement and deconfinement.

New quantum numbers related to fractional quantum Hall effect in deconfinement phase.

Abstract

Based on the permutation group formalism, we present a discrete symmetry algebra in QCD. The discrete algebra is hidden symmetry in QCD, which is manifest only on a space-manifold with non-trivial topology. Quark confinement in the presence of the dynamical quarks is discussed in terms of the discrete symmetry algebra. It is shown that the quark deconfinement phase has the ground state degeneracy depending on the topology of the space, which gives a gauge-invariant distinction between the confinement and deconfinement phases. We also point out that new quantum numbers relating to the fractional quantum Hall effect exist in the deconfinement phase.