  Extra dimensions (ED) have been used as attempts to explain several phenomena
in particle physics over the years. In this paper we investigate the role of an
abelian gauge field as mediator of the interaction between dark matter (DM) and
Standard Model (SM) particles, in a model with two flat and transverse ED
compactified on the chiral square. DM is confined in a thin brane, localized at
the origin of the chiral square, while the SM is localized in a finite width
brane, lying in the opposite corner of the square. A brane-localized kinetic
term is present in the DM brane, while in the fat brane it is not allowed. In
this model the kinetic mixing is not required because we assume that the SM
particles couple to the mediator through their $B-L$ charges, while DM couples
to it via a dark charge. Assuming a complex scalar field as DM candidate it is
possible to obtain the observed DM relic abundance and avoid direct detection
constraints for some parameter choices.
