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On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge theory

Maximal Abelian gauge fixing and subsequent Abelian projection of SU(2) lattice gauge theory defines closed trajectories of magnetic monopoles. These trajectories can be interpreted in terms of an effective scalar field theory of the MAG monopoles using the worldline representation of the functional determinants. Employing the monopole worldlines detected in the numerical simulation, we show that a scalar bound state exists. The screening mass $m$ of this state properly scales towards the continuum limit. We find m ~ 1.3 $GeV when the string tension sigma = 440 MeV is used as reference scale.