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

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 σk=2/σf=1.40±0.08 in the SU(4) gauge theory, and that σk=2/σf=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 σk∝ sin(πk/N).