Dirac strings and monopoles in the continuum limit of SU(2) lattice gauge theory

Magnetic monopoles are known to emerge as leading non-perturbative fluctuat ions in the lattice version of non-Abelian gauge theories in some gauges. I n terms of the Dirac quantization condition, these monopoles have magnetic charge \Q(M)\ = 2. Also, magnetic monopoles with \Q(M)\ = 1 can be introduc ed on the lattice via the 't Hooft loop operator. We consider the \Q(M)\ I = 1,2 monopoles in the continuum limit of the lattice gauge theories. To su bstitute for the Dirac strings which cost no action on the lattice, we allo w for singular gauge potentials which are absent in the standard continuum version. Once the Dirac strings are allowed, it turns possible to find a so lution with zero action for a monopole-antimonopole pair. This implies equi valence of the standard and modified continuum versions in perturbation the ory. To imitate the nonperturbative vacuum, we introduce then a nonsingular background. The modified continuum version of the gluodynamics allows in t his case for monopoles with finite non-vanishing action. Using similar tech niques, we construct the 't Hooft loop operator in the continuum and predic t its behavior at small and large distances both at zero and high temperatu res. (C) 2001 Elsevier Science B.V. All rights reserved.