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

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.

arXiv comment11 pages, 1 figure

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• Gapless Topological Order, Gravity, and Black Holes
• Robust Topological Degeneracy of Classical Theories
• Multiplicity, probabilities, and canonical sectors for the cold QCD matter
• Roberge-Weiss periodicity, canonical sector and modified Polyakov-loop
• Persistent homology analysis of deconfinement transition in effective Polyakov-line model
• Information theoretical view of QCD effective model with heavy quarks