  We develop a theoretical description of the critical zipping dynamics of a
self-folding polymer. We use tension propagation theory and the formalism of
the generalized Langevin equation applied to a polymer that contains two
complementary parts which can bind to each other. At the critical temperature,
the (un)zipping is unbiased and the two strands open and close as a zipper. The
number of closed base pairs $n(t)$ displays a subdiffusive motion characterized
by a variance growing as $\langle \Delta n^2(t) \rangle \sim t^\alpha$ with
$\alpha < 1$ at long times. Our theory provides an estimate of both the
asymptotic anomalous exponent $\alpha$ and of the subleading correction term,
which are both in excellent agreement with numerical simulations. The results
indicate that the tension propagation theory captures the relevant features of
the dynamics and shed some new insights on related polymer problems
characterized by anomalous dynamical behavior.
