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We present the complete next-to-next-to-leading-order calculation of thecorrelation function of two Polyakov loops for temperatures smaller than theinverse distance between the loops and larger than the Coulomb potential. Wediscuss the relationship of this correlator with the singlet and octetpotentials which we obtain in an Effective Field Theory framework based onfinite-temperature potential Non-Relativistic QCD, showing that the Polyakovloop correlator can be re-expressed, at the leading order in a multipoleexpansion, as a sum of singlet and octet contributions. We also revisit thecalculation of the expectation value of the Polyakov loop atnext-to-next-to-leading order.

The Polyakov loop correlator at NNLO and singlet and octet correlators