Abstract

In this review, after a general introduction to the Effective String Theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

Highlights

  • The natural context in which we can see the Effective String Theory (EST) at work is in the confining phase of Lattice Gauge Theories (LGT) where EST is expected to describe the large distance behaviour of the confining flux tube joining a quark antiquark pair

  • In this review we focused in particular on the behaviour of the interquark potential and of the flux tube width

  • In this review we introduced the EST, following the seminal papers of Lüscher and collaborators, as a tool to describe the behaviour of Wilson loops in LGT beyond the roughening transition

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Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. We shall see below that this is not by chance and that it is instead a direct consequence of the peculiar nature of the EST and of the strong constraining power of Lorentz invariance in this context This explains the impressive universality of the infrared regime of confining gauge theories (with only a mild dependence on the number of space–time dimensions, exactly as predicted by the Nambu–Goto model), which show essentially the same behaviour for the interquark potential, the deconfinement temperature and the glueball spectrum. In particular an important reason of interest of this limit is that, in LGTs with a second order deconfinement transition, several non trivial results on EST can be obtained using renormalization group arguments of the type discussed in [13] This approach, which allows to map a (d + 1) dimensional LGT into a suitably chosen d dimensional spin model, will be one of the main focus of the present review.

A Brief Summary of LGTs
Finite Temperature LGTs
The Finite Temperature Interquark Potential
Center Symmetry and the Polyakov Loop
The Svetitsky–Yaffe Conjecture
EST Versus LGT
Effective String Description of the Interquark Potential
The Nambu–Goto Action
The Nambu–Goto Action at Finite Temperature
Beyond Nambu–Goto
Comparison with Monte Carlo Simulations
LGT Observables
EST Predictions Versus Monte Carlo Results for Different LGTs
Width of the Confining Flux Tube at High Temperature
Definition of the Flux Tube Thickness
Dimensional Reduction and the Svetitsky–Yaffe Approach
Open Issues and Concluding Remarks

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