Quantum broadening of k-strings in gauge theories

We study the thickness of the confining flux tube generated by a pair of sources in higher representations of the gauge group. Using a simple geometric picture we argue that the area of the cross-section of the flux tube, as measured by a Wilson loop probe, grows logarithmically with source separation, as a consequence of the quantum fluctuations of the underlying k-string. The slope of the logarithm turns out to be universal, i.e. it is the same for all the representations and all the gauge theories. We check these predictions in a 3D Z_4 lattice gauge model by comparing the broadening of the 1-string and the 2-string.