Short distance behaviour of the effective string

TL;DR

This study investigates the short-distance behavior of the effective string in a (2+1)D Z_2 gauge model, testing Nambu-Goto predictions and comparing with other gauge theories, revealing deviations at low temperatures and small distances.

Contribution

It provides high-precision measurements of the Polyakov loop correlator at short distances, challenging the Nambu-Goto model predictions and extending boundary term results to finite temperature.

Findings

Numerical results deviate from Nambu-Goto two-loop predictions at low temperatures and small distances.

Comparison with SU(2) and SU(3) models shows similar deviations, indicating a possible universal feature.

Generalization of boundary term effects to finite temperature enhances understanding of interquark potentials.

Abstract

We study the Polyakov loop correlator in the (2+1) dimensional Z_2 gauge model. An algorithm that we have presented recently, allows us to reach high precision results for a large range of distances and temperatures, giving us the opportunity to test predictions of the effective Nambu-Goto string model. Here we focus on the regime of low temperatures and small distances. In contrast to the high temperature, large distance regime, we find that our numerical results are not well described by the two loop-prediction of the Nambu-Goto model. In addition we compare our data with those for the SU(2) and SU(3) gauge models in (2+1) dimensions obtained by other authors. We generalize the result of L\"uscher and Weisz for a boundary term in the interquark potential to the finite temperature case.