  We consider 'orbifold' and 'orientifold' field theories from the dual closed
string theory side. We argue that a necessary condition for planar equivalence
to hold is the absence of a closed string tachyonic mode in the dual
non-supersymmetric string. We analyze several gauge theories on R3xS1. In the
specific case of U(N) theories with symmetric/anti-symmetric fermions
('orientifold field theories') the relevant closed string theory is
tachyon-free at large compactification radius (due to winding modes), but it
develops a tachyonic mode below a critical radius. Our finding is with
agreement with field theory expectations of a phase transition from a C-parity
violating phase to a C-parity preserving phase as the compactification radius
increases. In the case of U(N)xU(N) theories with bi-fundamental matter
('orbifold field theories') a tachyon is always present in the string spectrum,
at any compactification radius. We conclude that on R4 planar equivalence holds
for 'orientfiold field theories', but fails for 'orbifold field theories'
daughters of N=4 SYM and suggest the same for daughters of N=1 SYM. We also
discuss examples of SO/Sp gauge theories with symmetric/anti-symmetric
fermions. In this case planar equivalence holds at any compactification radius
-in agreement with the absence of tachyons in the string dual.
