End-to-end distance on contour loops of random Gaussian surfaces

A self-consistent field theory that describes a part of a contour loop of a random Gaussian surface as a trajectory interacting with itself is constructed. The exponent nu characterizing the end-to-end distance is obtained by a Flory argument. The result is compared with different previous derivations and is found to agree with that of Kondev and Henley over most of the range of the roughening exponent of the random surface.