  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.
