  In this work, we analyze the excitonic gap generation in the strong-coupling
regime of thin films of three-dimensional time-reversal-invariant topological
insulators. We start by writing down the effective gauge theory in
2+1-dimensions from the projection of the 3+1-dimensional quantum
electrodynamics. Within this method, we obtain a short-range interaction, which
has the form of a Thirring-like term, and a long-range one. The interaction
between the two surface states of the material induces an excitonic gap. By
using the large-$N$ approximation in the strong-coupling limit, we find that
there is a dynamical mass generation for the excitonic states that preserves
time-reversal symmetry and is related to the dynamical chiral-symmetry breaking
of our model. This symmetry breaking occurs only for values of the
fermion-flavor number smaller than $N_{c}\approx 11.8$. Our results show that
the inclusion of the full dynamical interaction strongly modifies the critical
number of flavors for the occurrence of exciton condensation, and therefore,
cannot be neglected.
