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

TL;DR

The paper shows that the Nambu-Goto effective string description of Polyakov-loop correlators can be derived from a covariant quantization of the bosonic string with open-string boundary conditions on two D0-branes at finite temperature. By computing the open-string one-loop free energy, performing a modular transformation, and interpreting the result in the closed-string channel via boundary states, the authors demonstrate that the winding sector with unit wrapping reproduces the NG partition function, while higher-winding sectors correspond to massive closed-string exchanges. The analysis is consistent in d=26 and aligns with Monte Carlo data for large R and generic d, while highlighting potential Liouville-mode effects at shorter distances. The work provides a photon-clear string-theoretic interpretation of the Polyakov-loop correlator and a framework for exploring string interactions and other observables in gauge theories. It also emphasizes the open/closed duality and boundary-state formalism as powerful tools in connecting gauge observables to string dynamics.

Abstract

In this paper we re-derive the effective Nambu-Goto theory result for the Polyakov loop correlator, starting from the free bosonic string and using a covariant quantization. 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 cylinder 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 between 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 justified for large R, and is supported by Montecarlo data. At shorter scales, consistency and Montecarlo data seem to suggest the necessity of taking into account the Liouville mode of Polyakov's formulation.