  The Breit-Wheeler pair production process in $2+1$ dimensional spacetime is
investigated. In the perturbative regime, non-vanishing rates at the energy
threshold are found when odd numbers of photons take part on the reaction. This
behaviour is understood as a direct consequence of the reduced dimensionality
and resembles a corresponding prediction made in gapped graphene monolayers. In
the non-perturbative strong field regime the effect of the dimensionality
manifests itself in a different rate dependence on the quantum non-linearity
parameter. The consequence of this deviation is discussed briefly in line with
the applicability of perturbation theory. We argue that, in addition to large
values of the quantum non-linearity parameter, the superrenormalisable
character of quantum electrodynamics in $2+1$ dimensional spacetime might give
rise to a breakdown of perturbation theory within certain energy scales.
