We investigate the implications of Nambu-Goto (NG), Luscher-Weisz (LW) and Polyakov-Kleinert (PK) string actions for the Casimir energy of the QCD flux-tube at one and two loop order at finite temperature. We perform our numerical study on the 4-dim pure SU(3) Yang-Mills lattice gauge theory at finite temperature $beta=6.0$. The static quark-antiquark potential is calculated using link-integrated Polyakov loop correlators. At a high temperature-close to the critical point- We find that the rigidity and self-interactions effects of the QCD string to become detectable. The remarkable feature of this model is that it retrieves a correct dependency of the renormalized string tension on the temperature. Good fit to static potential data at source separations $R ge 0.5$ fm is obtained when including additional two-boundary terms of (LW) action. On the other-hand, at a lower temperature-near the QCD plateau- We detect signatures of two boundary terms of the Luscher-Weisz (LW) string action. The (LW) string with boundary action is yielding a static potential which is in a good agreement with the lattice data, however, for color source separation as short as $R=0.3$ fm.
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