String tensions of SU(N) gauge theories in 2+1 dimensions

TL;DR

This study computes the string tensions in SU(N) gauge theories in 2+1 dimensions with high precision, comparing results to theoretical models and identifying small but significant discrepancies that persist even at large N.

Contribution

The paper provides highly accurate calculations of string spectra for multiple N values and analyzes corrections to theoretical predictions, revealing persistent discrepancies at large N.

Findings

Nambu-Goto approximation is accurate down to short lengths

Corrections to the Luscher term are identified and compared to theories

Continuum limit string tensions differ slightly from some theoretical predictions

Abstract

We calculate the energy spectrum of closed strings in SU(N) gauge theories with N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control all systematic errors, and this allows us to perform a precise comparison with different theoretical predictions. When we study the dependence of the string mass on its length L we find that the Nambu-Goto prediction is a very good approximation down to relatively short lengths, where the Luscher term alone is insufficient. We then isolate the corrections to the Luscher term, and compare them to recent theoretical predictions, which indeed seem to be mildly preferred by the data. When we take these corrections into account and extract string tensions from the string masses, we find that their continuum limit is lower by 2%-1% from the predictions of Karabli, Kim, and Nair. The discrepancy decreases with N, but when we extrapolate our results to N=oo we still find a discrepancy of 0.88% which is a 4.5 sigma effect.