A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions

TL;DR

This paper uses lattice techniques to precisely calculate the string tensions in SU(N) gauge theories in 2+1 dimensions, testing an analytic prediction and finding it accurate but not exact, especially at large N.

Contribution

The study provides a highly accurate lattice-based calculation of string tensions in SU(N) gauge theories, critically testing the Karabali-Kim-Nair prediction across various N.

Findings

Prediction is within 3% for all N

Discrepancy decreases as N increases

Remaining ~1% discrepancy at N=∞ is statistically significant

Abstract

We use lattice techniques to calculate the continuum string tensions of SU(N) gauge theories in 2+1 dimensions. We attempt to control all systematic errors at a level that allows us to perform a precise test of the analytic prediction of Karabali, Kim and Nair. We find that their prediction is within 3% of our values for all N and that the discrepancy decreases with increasing N. When we extrapolate our results to N=oo we find that there remains a discrepancy of ~ 1%, which is a convincing ~6 sigma effect. Thus, while the Karabali-Nair analysis is remarkably accurate at N=oo, it is not exact.