It has been noticed that the k -string observables can be expressed in terms of the fundamental string ones. We identify a sufficient condition for a generic gravity dual background which when satisfied the mapping can be done. The condition is naturally related to a preserved quantity under the T-dualities acting on the Dp-brane describing the high representation Wilson loops. We also find the explicit relation between the observables of the heavy k -quark and the single quark states. As an application to our generic study and motivated by the fact that the anisotropic theories satisfy our condition, we compute the width of the k -string in these theories to find that the logarithmic broadening is still present, but the total result is affected by the anisotropy of the space.
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