  We develop a field-theoretic representation for the configurations of an
interface between two ordered phases of a q-state Potts model in two
dimensions, in the solid-on-solid approximation. The model resembles the field
theory of directed percolation and may be analysed using similar
renormalisation group methods. In the one-loop approximation these reveal a
simple mechanism for the emergence of a critical value q_c, such that for q<q_c
the interface becomes a fractal with a vanishing interfacial tension at the
critical point, while for q>q_c the interfacial width diverges at a finite
value of the tension, indicating a first-order transition. The value of the
Widom exponent for q<q_c within this approximation is in fair agreement with
known exact values. Some comments are made on the case of quenched randomness.
We also show that the q-> minus infinity limit of our model corresponds to
directed percolation and that the values for the exponents in the one-loop
approximation are in reasonable agreement with accepted values.
