The Width of the Color Flux Tube at 2-Loop Order

TL;DR

This paper calculates the width of the color flux tube in Yang-Mills theory at 2-loop order, revealing a logarithmic divergence at zero temperature and a linear divergence at low temperatures, enhancing understanding of flux tube fluctuations.

Contribution

It provides a systematic 2-loop calculation of the flux tube width using effective field theory, including boundary conditions and temperature effects, which was not previously done.

Findings

At zero temperature, the width diverges logarithmically with quark separation.

At low non-zero temperature, the width diverges linearly with separation.

The calculation incorporates boundary conditions and temperature effects on flux tube fluctuations.

Abstract

The color flux tube connecting a static quark-anti-quark pair in Yang-Mills theory supports massless transverse fluctuations, which are the Goldstone bosons of spontaneously broken translation invariance. Just as in chiral perturbation theory, the dynamics of these Goldstone bosons is described by a systematic low-energy effective field theory. We use the effective theory to calculate the width of the fluctuating string at the 2-loop level, using both cylindrical and toroidal boundary conditions. At zero temperature, the string width diverges logarithmically with the quark-anti-quark distance r. On the other hand, at low but non-zero temperature T = 1/\beta, for r >> \beta, the string width diverges linearly.