K-string tensions in SU(N) gauge theories

Abstract

In the context of four-dimensional SU(AO 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 σk related to sources with ZN 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 σk/σ=sin(kπ/N)/sin(π/N) for the ratio between σk and the standard string tension σ, 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) × SU(N) chiral models. © 2001 The American Physical Society.