  Simple scaling properties of correlation functions of a confining gauge
theory in d-dimensions lead to the conclusion that k-string dynamics is
described, in the infrared limit, by a two-dimensional conformal field theory
with conformal anomaly c=(d-2)T_k/T_1, where T_k is the k-string tension. This
result applies to any gauge theory with stable k-strings. We check it in a 3D
Z_4 gauge model at finite temperature, where a string effect directly related
to c can be clearly identified.
