Spectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N=2,3)

Understand

We perform a high precision measurement of the static $q\bar{q}$ potential in three-dimensional SU($N$) gauge theory with $N=2,3$ and compare the results to the potential obtained from the effective string theory.

• In particular, we show that the exponent of the leading order correction in $1/R$ is 4, as predicted, and obtain accurate results for the continuum limits of the string tension and the non-universal boundary coefficient $\bar{b}_2$, including an extensive analysis of all types of systematic uncertainties.
• We find that the magnitude of $\bar{b}_2$ decreases with increasing $N$, leading to the possibility of a vanishing $\bar{b}_2$ in the large $N$ limit.
• In the standard form of the effective string theory possible massive modes and the presence of a rigidity term are usually not considered, even though they might give a contribution to the energy levels.