  It is established that the distribution of the zero energy eigenfunctions of
(2 + 1)-dimensional Dirac electrons in a random gauge potential is described by
the Liouville model. This model has a line of critical points parameterized by
the strength of disorder and the scaling dimensions of the inverse
participation ratios coincide with the dimensions obtained in the conventional
localization theory. From this fact we conclude that the renormalization group
trajectory of the latter theory lies in the vicinity of the line of critical
points of the Liouville model.
