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

TL;DR

This paper derives the Polyakov loop correlator from bosonic string theory, connecting open string boundary conditions to Nambu-Goto results and exploring implications for string interactions and lattice data.

Contribution

It provides a covariant quantization derivation of Polyakov loop correlators from bosonic strings, clarifying open-closed string duality and extending results to different spacetime dimensions.

Findings

Reproduces Nambu-Goto partition function from open string sector

Shows world-sheet duality explicitly in the derivation

Supports extension to non-critical dimensions with Monte Carlo data

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.