  We prove that the Laessig-Wiese (LW) field theory for the freezing transition
of the secondary structure of random RNA is renormalizable to all orders in
perturbation theory. The proof relies on a formulation of the model in terms of
random walks and on the use of the multilocal operator product expansion.
Renormalizability allows us to work in the simpler scheme of open polymers, and
to obtain the critical exponents at 2-loop order. It also allows to prove some
exact exponent identities, conjectured in LW.
