  Folding of RNA is subject to a competition between entropy, relevant at high
temperatures, and the random, or random looking, sequence, determining the low-
temperature phase. It is known from numerical simulations that for random as
well as biological sequences, high- and low-temperature phases are different,
e.g. the exponent rho describing the pairing probability between two bases is
rho = 3/2 in the high-temperature phase, and approximatively 4/3 in the
low-temperature (glass) phase. Here, we present, for random sequences, a field
theory of the phase transition separating high- and low-temperature phases. We
establish the existence of the latter by showing that the underlying theory is
renormalizable to all orders in perturbation theory. We test this result via an
explicit 2-loop calculation, which yields rho approximatively 1.36 at the
transition, as well as diverse other critical exponents, including the response
to an applied external force (denaturation transition).
