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In this paper we re-derive the effective Nambu-Goto theory result for thePolyakov loop correlator, starting from the free bosonic string and using acovariant quantization. The boundary conditions are those of an open stringattached to two D0-branes at spatial distance R, in a target space with compacteuclidean time. The one-loop free energy contains topologically distinctsectors corresponding to multiple covers of the cylinder in target spacebordered by the Polyakov loops. The sector that winds once reproduces exactlythe Nambu-Goto partition function. In our approach, the world-sheet dualitybetween the open and closed channel is most evident and allows for an explicitinterpretation of the free energy in terms of tree level exchange of closedstrings between boundary states. Our treatment is fully consistent only ind=26; extension to generic d may be justified for large R, and is supported byMontecarlo data. At shorter scales, consistency and Montecarlo data seem tosuggest the necessity of taking into account the Liouville mode of Polyakov'sformulation.Comment: 17 pages, 4 figures, minor corrections, a few references added,  version accepted for publication in JHE

Polyakov loop correlators from D0-brane interactions in bosonic string theory