Non-Abelian Strings and the Luscher Term

Abstract

We calculate the Luscher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian subgroup. The Luscher term is determined by the number of light degrees of freedom on the string wordsheet. Unlike the standard π/12 we get Nπ/12 for non-Abelian strings in the U(N) gauge theories. Thus, the Luscher coefficient acquires a dependence on the rank of the gauge group. In the models with non-Abelian strings discussed in the literature there are two distinct scales: the string tension ξ(the string thickness \sim ξ^{-1/2}) and the dynamical scale of strong interactions Λ. At weak coupling ξ\ggΛ^2. The Luscher term for non-Abelian strings experiences a jump: at ξ^{-1/2}\ll L\ll Λ^{-1} it is Nπ/12 while at at L\gg Λ^{-1} the orientational moduli are frozen out and the Luscher coefficient approaches its "Luscher" value π/12. We raise the question of possible extra (i.e. non-translational) light moduli on the worldsheet of QCD strings at large N.