Revisiting the flux tube spectrum of 3d SU(2) lattice gauge theory

TL;DR

This study measures the flux tube spectrum in 3D SU(2) gauge theory, comparing it with effective string theory predictions, and finds both qualitative agreement and some deviations at small separations.

Contribution

It provides high-precision measurements of the flux tube spectrum in 3D SU(2) gauge theory and tests effective string theory predictions including boundary effects.

Findings

Qualitative agreement with Nambu-Goto string theory at large separations.

Observation of boundary term effects causing splitting of the second excited state.

Slight deviations from effective string theory predictions for the first excited state on fine lattices.

Abstract

We perform a high precision measurement of the spectrum of the QCD flux tube in three-dimensional $\SU(2)$ gauge theory at multiple lattice spacings. We compare the results at large $q\bar{q}$ separations $R$ to the spectrum predicted by the effective string theory, including the leading order boundary term with a non-universal coefficient. We find qualitative agreement with the predictions from the leading order Nambu-Goto string theory down to small values of $R$, while, at the same time, observing the predicted splitting of the second excited state due to the boundary term. On fine lattices and at large $R$ we observe slight deviations from the EST predictions for the first excited state.