Universality of k-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 -ality and check whether the expectation value of the Wilson loop depends on the specific representation or only on the -ality. In the framework of AdS/CFT we show that ⟨W_R⟩ = dim R exp (−σ_k), namely that the string tension depends only on the -ality k but the pre-exponent factor is representation dependent. The lattice strong coupling expansion yields an identical result at infinite N, but shows a representation dependence of the string tension at finite N, a result which we interpret as an artifact. In order to confirm the representation independence of the string tension we re-analyse results of lattice simulations involving operators with common -ality in pure SU(N) Yang-Mills theory. We find that the picture of the representation-independence of the string tension is confirmed by the spectrum of excited states in the stringy sector, while the lowest-lying states seem to depend on the representation. We argue that this unexpected result is due to the insufficient distance of the static sources for the asymptotic behaviour to be visible and give an estimate of the distance above which a truly representation-independent spectrum should be observed.