Non-Abelian strings and the Luscher term

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 world sheet. Unlike the standard pi/12 we get N pi/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 xi ( the string thickness similar to xi(-1/2)) and the dynamical scale of strong interactions boolean AND. At weak coupling xi >>boolean AND(2). The Luscher term for non-Abelian strings experiences a jump: at xi(-1/2) << L << boolean AND(-1) it is N pi/12 while at L >>boolean AND(-1) the orientational moduli are frozen out and the Luscher coefficient approaches its Luscher'' value pi/12. We raise the question of possible extra ( i.e. nontranslational) light moduli on the world sheet of QCD strings at large N.