  In this work we put forward an effective Gaussian free field description of
critical wavefunctions at the transition between plateaus of the integer
quantum Hall effect. To this end, we expound our earlier proposal that powers
of critical wave intensities prepared via point contacts behave as pure scaling
fields obeying an Abelian operator product expansion. Our arguments employ the
framework of conformal field theory and, in particular, lead to a
multifractality spectrum which is parabolic. We also derive a number of old and
new identities that hold exactly at the lattice level and hinge on the
correspondence between the Chalker-Coddington network model and a
supersymmetric vertex model.
