QCD string from D0 branes

TL;DR

This paper presents high-precision simulations of the 3d gauge Ising model, comparing interquark potentials with effective string theories, confirming Nambu-Goto predictions at large distances, and exploring deviations at shorter scales.

Contribution

It provides a detailed comparison between Monte Carlo data and effective string models, including a covariant derivation of the Nambu-Goto result with insights into the Liouville mode effects.

Findings

Nambu-Goto predictions match Monte Carlo data at large distances

Free string model is definitively excluded by the data

Deviations at shorter distances suggest Liouville mode contributions

Abstract

We report the results of a set of high precision simulations performed in the 3d gauge Ising model. We evaluated the interquark potential and the first few energy levels and compared them with the predictions obtained with the effective Nambu-Goto string and with the free bosonic string. The data are precise enough to unambiguously distinguish between the free string predictions and those obtained using the N-G effective string. At large distances we find a remarkable agreement between Monte Carlo data and N-G predictions for the first excited energy level, while the free string picture is definitely excluded. As the interquark distance is decreased (and/or the finite temperature becomes higher) the Monte Carlo results show larger and larger deviations both from the N-G and from the free string predictions. In order to better understand this behaviour we re-derived the effective Nambu-Goto theory result for the Polyakov loop correlator using a covariant quantization. We chose as boundary conditions those of an open string attached to two D0-branes at spatial distance $R$, in a target space with compact euclidean time. Obviously our treatment is fully consistent only in $d=26$. The extension to generic $d$ requires taking into account the Liouville mode of Polyakov's formulation. The analogy with the standard light cone calculation suggests that the contribution due to the Liouville field can be neglected for large $R$. At shorter scales, the Liouville mode cannot be neglected and its contribution to the interquark potential might be the source of the discrepancies with respect to the effective N-G results that we observe in our Monte Carlo simulations.