Spectrum of k-string tensions in SU(N) gauge theories

Nonabelian gauge theories are the building blocks of the field-theoretical description of fundamental interactions. It is therefore essential to achieve a deep understanding of their physical content and a better quantitative knowledge of their testable predictions. It is widely believed that nonabelian gauge theories admit a reinterpretation in terms of effective strings; describing their properties is an issue of the utmost importance. In particular one would like to understand if these strings belong to some wider group of objects (“universality class”) whose properties may eventually be studied by different approaches and techniques. The study of the string tensions between static charges in representations higher than the fundamental one and for different values of N may shed new light on the nature of the confining strings, helping to identify the most appropriate models of the QCD vacuum and to select among the various confinement hypotheses. A static source carrying charge k with respect to the center ZN is confined by a k-string with string tension σk (σ1 ≡ σ is the string tension related to the fundamental representation). The k string is the lightest state propagating in the k-charged channel, and is related to the antisymmetric representation of rank k. If σk < k σ, then a string with charge k is stable against decay to k strings of charge one. Charge conjugation implies σk = σN−k. Therefore SU(3) has only one independent string tension determining the large distance behavior of the potential for k 6= 0. One must consider larger values of N to look for distinct k-strings. In particular for N ≥ 4 one may consider the ratio R(k,N) ≡ σk/σ. (1)