Non-Abelian strings and the Luescher term

We calculate the Luescher 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 Luescher term is determined by the number of light degrees of freedom on the string world sheet. Unlike the standard π/12 we get Nπ/12 for non-Abelian strings in the U(N) gauge theories. Thus, the Luescher 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 ∼ξ-1/2) and the dynamical scale of strong interactions Λ. At weak coupling ξ>>Λ2. The Luescher term for non-Abelian strings experiences a jump: at ξ-1/2<>Λ-1 the orientational moduli are frozen out and the Luescher coefficient approaches its ''Luescher'' value π/12. We raise the question of possible extra (i.e. nontranslational) light moduli on the world sheet of QCD strings at large N.