  We discuss domain walls and vacuum energy density (cosmological constant) in
N=1 gluodynamics and in non-supersymmetric large N orientifold field theories
which have been recently shown to be planar equivalent (in the boson sector) to
N=1 gluodynamics. A relation between the vanishing force between two parallel
walls and vanishing cosmological constant is pointed out. This relation may
explain why the cosmological constant vanishes in the orientifold field theory
at leading order although the hadronic spectrum of this theory does not contain
fermions in the limit N-->infinity. The cancellation is among even and odd
parity bosonic contributions, due to NS-NS and R-R cancellations in the annulus
amplitude of the underlying string theory. We use the open-closed string
channel duality to describe interaction between the domain walls which is
interpreted as the exchange of composite ``dilatons'' and ``axions'' coupled to
the walls. Finally, we study some planar equivalent pairs in which both
theories in the parent-daughter pair are non-supersymmetric.
