Effective String Theory of three-dimensional SU(N) gauge theories beyond the Nambu--Got\=o approximation

TL;DR

This paper investigates the effective string description of confining flux tubes in 3D SU(N) gauge theories, extracting corrections beyond the Nambu-Goto approximation through high-precision lattice simulations and analytical bounds.

Contribution

It provides the first extraction of correction terms to the effective string action in 3D SU(N) theories from lattice data, extending understanding beyond the Nambu-Goto model.

Findings

Corrections to the Nambu-Goto action are compatible with analytical bounds.

Results for N=3 and N=6 support the large-N limit approach.

Polyakov loop correlators match conformal perturbation predictions for SU(3).

Abstract

We study the effective bosonic string that describes confining flux tubes in three-dimensional SU(N) Yang--Mills theories. Although the low-energy properties are universal and well described by the Nambu--Got\=o action, the subtle dependence on the gauge group is embedded in a series of corrections, which remain undetermined, appearing in the expansion around the limit of an infinitely long string. We extract the first two of these corrections from a set of high-precision Monte Carlo simulations of Polyakov loop correlators at finite temperatures close to the deconfinement transition. We present and compare the results of new lattice simulations for theories with N=3 and N=6 color charges, along with an improved estimate for the N=2 case, discussing the approach to the large-N limit. We show that our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. Additionally, we present a new test of the Svetitsky--Yaffe conjecture for the SU(3) theory in three dimensions, showing that our results for the correlator of Polyakov loops perfectly agree with the predictions obtained using a conformal perturbation approach to the two-dimensional three-state Potts model