# Monopole Condensation and Polyakov Loop in Finite-Temperature Pure QCD

## TL;DR

This paper investigates how monopole condensation relates to the deconfinement transition in finite-temperature pure QCD, linking monopole behavior to Polyakov loop expectation values and Z(N) symmetry breaking.

## Contribution

It provides new insights into the connection between monopole dynamics and the deconfinement phase transition in pure QCD, emphasizing the role of boundary conditions.

## Key findings

- Monopole contribution to Polyakov loop vanishes in confinement phase.
- Long monopole loops disappear in deconfinement phase.
- Boundary conditions influence Z(N) symmetry interpretation.

## Abstract

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 the Z(N) symmetry in terms of the monopoles.