k-string tensions in SU(N) gauge theories

TL;DR

This paper investigates the spectrum of confining strings in four-dimensional SU(N) gauge theories, providing lattice computations of string tensions for SU(6) and comparing results to theoretical formulas.

Contribution

It presents the first lattice calculation of multiple string tensions in SU(6) gauge theory and tests their ratios against the sine formula, revealing deviations from Casimir scaling.

Findings

Results support the sine formula for string tension ratios.

Deviations from Casimir scaling are observed.

Uncertainty in measurements is approximately 2-4%.

Abstract

In the context of four-dimensional SU(N) gauge theories, we study the spectrum of the confining strings. We compute, for the SU(6) gauge theory formulated on a lattice, the three independent string tensions sigma_k related to sources with Z_N charge k=1,2,3, using Monte Carlo simulations. Our results, whose uncertainty is approximately 2% for k=2 and 4% for k=3, are consistent with the sine formula sigma_k/sigma = sin(k pi/N) / \sin(pi/N) for the ratio between sigma_k and the standard string tension sigma, and show deviations from the Casimir scaling. The sine formula is known to emerge in supersymmetric SU(N) gauge theories and in M-theory. We comment on an analogous behavior exhibited by two-dimensional SU(N)xSU(N) chiral models.