Non-Perturbative Planar Equivalence and the Absence of Closed String Tachyons

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 R × S. 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) × U(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 R 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.