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

In this paper we re-derive the efiective Nambu-Goto theory result for the Polyakov loop correlator, starting from the free bosonic string and using a covariant quan- tization. The boundary conditions are those of an open string attached to two D0-branes at spatial distance R, in a target space with compact euclidean time. The one-loop free energy contains topologically distinct sectors corresponding to multiple covers of the cylin- der in target space bordered by the Polyakov loops. The sector that winds once reproduces exactly the Nambu-Goto partition function. In our approach, the world-sheet duality be- tween the open and closed channel is most evident and allows for an explicit interpretation of the free energy in terms of tree level exchange of closed strings between boundary states. Our treatment is fully consistent only in d = 26; extension to generic d may be justifled for large R, and is supported by Montecarlo data. At shorter scales, consistency and Mon- tecarlo data seem to suggest the necessity of taking into account the Liouville mode of Polyakov’s formulation.