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arXiv · 1701.05280

Monopole and Polyakov loop

Aiichi Iwazaki
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Abstract

We propose a new order parameter of a $Z_N$ symmetry in SU(N) gauge theories in $4$ dimensional Minkowski space-time, assuming spatial periodic boundary conditions. It is given by $Tr(P\exp(i\int_c A_{\mu}dx^{\mu}))$ where the spatial path $c$ is taken, for example, along $x_1$ axis. The parameter vanishes when the $Z_N$ symmetry is preserved. We calculate the contribution of QCD monopoles to the order parameter and show that when the monopoles condense $\langle\Phi\rangle\neq 0$, it vanishes, while it does not vanish when they do not condense. These calculations are performed using a monopole field $\Phi$ canonically quantized in a model of dual superconductor.

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Aiichi Iwazaki. 2017-01-19. Monopole and Polyakov loop. https://doi.org/10.1103/physrevd.95.094026

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