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66 fm. The numerical value applies to d"4. S. 4 fm, quite close to l , on the 3% level. Qualitative agreement has also been reported by Teper [214] from simulations of S;(2), S;(3), S;(4) and S;(5) gauge theories in three dimensions. The bosonic string picture for r< "a¸ predicts a behaviour similar to Eq. 29) for the O "nite-temperature potential, calculated from Polyakov line correlators [215], 1 ! 2) ( )" ! #2 . 30) The Polyakov line is de"ned as [Eq. 31) where T denotes time ordering of the argument.

4, in lattice units [166]. The "gure demonstrates that at the level of  precision achieved, deviations from the continuous "t curve are statistically signi"cant for r44a. erence. 3. ects (FSE) arises. ected by the infra-red cut-o!. S. Bali / Physics Reports 343 (2001) 1}136 43 Fig. 3. 4. decon"nement phase transition, any asymptotic string tension will disappear. The other source of FSE on Wilson loops is related to un-wanted interactions of source and anti-source around the periodic boundaries that will become negligible as ¸ aPR: by unwrapping the spatial torus onto N an in"nite hyper-cubic lattice of cells with spatial periods, ¸ a, it becomes obvious that each charge N at position r is accompanied by an in"nite set of mirror charges at rn "r#n¸ a, n integer.

Ectively one-dimensional, #ux tube or Abrikosov}Nielsen}Olesen (ANO) vortex [196}199]. As a consequence, this yields a constant energy density per unit length and a static potential that is linearly rising as a function of the distance. One can study the spectrum of such a vibrating string in simple models [200,190,47]. Of course, the string action is not a priori known. 2) free bosonic "elds associated to the transverse degrees of freedom of the string. S. 2)  <(r)" r 1! " r! 26) while for a fermionic string [202] one would expect the coe$cient of the correction term to the linear behaviour to be only one quarter as big as the Nambu}Goto one above.

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