Can holography reproduce the QCD Wilson line?

TL;DR

This paper investigates whether classical holographic models can accurately reproduce lattice QCD Wilson line results across all distances, focusing on short-distance behavior and potential matching.

Contribution

It analyzes various holographic models and renormalization schemes to determine conditions for reproducing lattice Wilson line results, including short-distance Coulombic behavior.

Findings

Holographic models can include a constant term in the potential after renormalization.

All examined models admit a constant term consistent with lattice results.

The short-distance Coulombic potential can be achieved under specific gravitational background conditions.

Abstract

Recently a remarkable agreement was found between lattice simulations of long Wilson lines and behavior of the Nambu Goto string in flat space-time. However, the latter fails to fit the short distance behavior since it admits a tachyonic mode for a string shorter than a critical length. In this paper we examine the question of whether a classical holographic Wilson line can reproduce the lattice results for Wilson lines of any length. We determine the condition on the the gravitational background to admit a Coulombic potential at short distances. We analyze the system using three different renormalization schemes. We perform an explicit best fit comparison of the lattice results with the holographic models based on near extremal D3 and D4 branes, non-critical near extremal AdS6 model and the Klebanov Strassler model. We find that all the holographic models examined admit after renormalization a constant term in the potential. We argue that the curves of the lattice simulation also have such a constant term and we discuss its physical interpretation.