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The Polyakov loop correlator at NNLO and singlet and octet correlators

We present the complete next-to-next-to-leading-order calculation of the correlation function of two Polyakov loops for temperatures smaller than the inverse distance between the loops and larger than the Coulomb potential. We discuss the relationship of this correlator with the singlet and octet potentials which we obtain in an Effective Field Theory framework based on finite-temperature potential Non-Relativistic QCD, showing that the Polyakov loop correlator can be re-expressed, at the leading order in a multipole expansion, as a sum of singlet and octet contributions. We also revisit the calculation of the expectation value of the Polyakov loop at next-to-next-to-leading order.