Universality of k-string Tensions from Holography and the Lattice

TL;DR

This paper investigates whether the string tension in SU(N) Yang-Mills theories depends solely on N-ality or also on the specific representation, using holography, lattice expansions, and simulations, and finds evidence supporting N-ality dependence for the spectrum of excited states.

Contribution

It demonstrates that the string tension depends only on N-ality in the large N limit through holography and lattice analysis, and clarifies the representation dependence observed in low-lying states.

Findings

String tension depends only on N-ality at large N.

Representation dependence appears in the lowest-lying states.

Excited states show N-ality dependence, confirming the universality of string tension.

Abstract

We consider large Wilson loops with quarks in higher representations in SU(N) Yang-Mills theories. We consider representations with common N-ality and check whether the expectation value of the Wilson loop depends on the specific representation or only on the N-ality. In the framework of AdS/CFT we show that <W_R> = dim R exp -sigma_k A, namely that the string tension depends only on the N-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 N-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.