Effective string picture for confinement at finite temperature: theoretical predictions and high precision numerical results

TL;DR

This paper combines theoretical predictions from the effective string model with high-precision lattice simulations to analyze the interquark potential at finite temperature, focusing on the L"uscher term and boundary effects.

Contribution

It provides analytical calculations of subleading corrections in the effective string model and compares these with detailed lattice simulation results.

Findings

The L"uscher term accurately describes the short-distance potential.

Boundary terms can significantly affect the potential predictions.

Numerical results support the effective string model at finite temperature.

Abstract

The effective string picture of confinement is used to derive theoretical predictions for the interquark potential at finite temperature. At short distances, the leading string correction to the linear confining potential between a heavy quark-antiquark pair is the "L\"uscher term''. We assume a Nambu--Goto effective string action, and work out subleading contributions in an analytical way. We discuss the contribution given by a possible ``boundary term'' in the effective action, comparing these predictions with results from simulations of lattice $Z_2$ gauge theory in three dimensions, obtained with an algorithm which exploits the duality of the $Z_2$ gauge model with the Ising spin model.