  The continuous quantum phase transition between noninteracting, time-reversal
symmetric topological and trivial insulators in three dimensions is described
by the massless Dirac fermion. We address the stability of this quantum
critical point against short range electronic interactions by using
renormalization group analysis and mean field theory. For sufficiently weak
interactions, we show that the nature of the direct transition remains
unchanged. Beyond a critical strength of interactions we find that either (i)
there is a direct first order transition between two time reversal symmetric
insulators or (ii) the direct transition is eliminated by an intervening time
reversal and inversion odd "axionic" insulator. We also demonstrate the
existence of an interaction driven first order quantum phase transition between
topological and trivial gapped states in lower dimensions.
