  In this paper we show that wormholes in (2+1) dimensions cannot be sourced by
Casimir energy. Recently, it has been shown that in (3+1) dimensions this is
possible by the direct computation of the correct shape and redshift functions.
We show that in (2+1) dimensions the same is not true since the event horizon
is inevitable. We do the analysis for massive and massless fermions, as well as
for scalar fields, and find that a possibility to circumvent this trouble is to
introduce a cosmological constant, immerse the sheet in (3+1) dimensional
manifold and apply a perpendicular uniform and weak magnetic field. We finally
discuss the possibility of observing the condensed matter analogous of the
wormhole in the graphene sheet.
