Spectrum of the open QCD flux tube in d=2+1 and its effective string description

TL;DR

This paper investigates the behavior of the flux tube in 2+1 dimensional lattice gauge theories, comparing effective string theory predictions with high-precision data to understand confinement and boundary effects.

Contribution

It provides high-accuracy measurements of the flux tube energy in 3D SU(2) and SU(3) gauge theories and tests effective string theory predictions at next-to-leading order.

Findings

Good agreement with Nambu-Goto predictions at order R^{-3}

Identification of boundary term coefficients in the effective action

Confirmation of corrections appearing at order R^{-4}

Abstract

Simulations in lattice gauge theory suggest that the formation of a flux tube between quark and antiquark leads to quark confinement. It is conjectured that the infrared behaviour of the flux tube is governed by an effective string theory and simulations show good agreement between lattice data and its predictions. To next-to leading order ($R^{-3}$) in the inverse $q\bar{q}$ separation $R$ the effective string theory is equivalent to Nambu-Goto string theory. For the open flux tube in three dimensions corrections appear at order $R^{-4}$. We compare these predictions to high-accuracy measurements of the groundstate energy of the flux tube in 3d SU(2) and SU(3) gauge theory and extract the coefficient of the leading order boundary term in the effective action.