Monopole condensation and Polyakov loop in finite-temperature pure QCD

We study the relation between the abelian monopole condensation and the deconfinement phase transition of the finite-temperature pure QCD. The expectation value of the monopole contribution to the Polyakov loop becomes zero when a long monopole loop is distributed uniformly in the configuration of the confinement phase. On the other hand, it becomes non-zero when the long monopole loop disappears in the deconfinement phase. We also discuss the relation between the monopole behaviors and the usual interpretation of the spontaneous breaking of Z(N) symmetry in finite-temperature SU(N) QCD. It is found that the boundary condition of the space direction is important to understand tile Z(N) symmetry in terms of the monopoles.