  The peculiar electron dispersion in Dirac materials makes lowest-order Auger
processes prohibited or marginally prohibited by energy and momentum
conservation laws. Thus, Auger recombination (AR) in these materials is very
sensitive to many-body effects. We incorporate them at the level of the $GW$
approximation into the nonequilibrium Green's functions approach to AR and
study the role of dynamic screening, spectrum broadening and renormalization in
the case of weakly pumped undoped graphene. We find that incorrect treatment of
many-body effects can lead to an order-of-magnitude error in the recombination
rate. We show that the AR time weakly (sublinearly) depends on the background
dielectric constant, which limits the possibility to control recombination by
the choice of substrate. However, the AR time can be considerably prolonged by
placing graphene under a metal gate or by introducing a bandgap. With carrier
cooling taken into account, our results comply with experiments on photoexcited
graphene.
