The k=2 string tension in four-dimensional SU(N) gauge theories

Abstract We calculate the k =2 string tension in SU (4) and SU (5) gauge theories in 3+1 dimensions, and compare it to the k =1 fundamental string tension. We find, from the continuum extrapolation of our lattice calculations, that σ k =2 / σ f =1.40±0.08 in the SU (4) gauge theory, and that σ k =2 / σ f =1.56±0.10 in SU (5). We remark upon the way this might constrain the dynamics of confinement and the intriguing implications it might have for the mass spectrum of SU ( N ) gauge theories. We also note that these results agree closely with the MQCD-inspired conjecture that the SU ( N ) string tension varies as σ k ∝ sin( πk / N ).