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Topological discrete algebra, ground-state degeneracy, and quark confinement in QCD

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 nontrivial topology. Quark confinement in the presence of dynamical quarks is discussed in terms of the discrete symmetry algebra. It is shown that the quark deconfinement phase has 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.