Universality ofk-string tensions from holography and the lattice

We consider large Wilson loops with quarks in higher representations in SU(N)Yang-Mills theories. We consider representations with common N-ality and checkwhether the expectation value of the Wilson loop depends on the specificrepresentation or only on the N-ality. In the framework of AdS/CFT we show that = dim R exp -sigma_k A, namely that the string tension depends only onthe N-ality k but the pre-exponent factor is representation dependent. Thelattice strong coupling expansion yields an identical result at infinite N, butshows a representation dependence of the string tension at finite N, a resultwhich we interpret as an artifact. In order to confirm the representationindependence of the string tension we re-analyse results of lattice simulationsinvolving operators with common N-ality in pure SU(N) Yang-Mills theory. Wefind that the picture of the representation-independence of the string tensionis confirmed by the spectrum of excited states in the stringy sector, while thelowest-lying states seem to depend on the representation. We argue that thisunexpected result is due to the insufficient distance of the static sources forthe asymptotic behaviour to be visible and give an estimate of the distanceabove which a truly representation-independent spectrum should be observed.Comment: Refs. added, discussion in sect. 3 improved, other minor changes; to appear in JHE