A note on C-parity conservation and the validity of orientifold planar equivalence

We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like-but otherwise generic-representations of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang-Mills theory and orientifold field theory on R⁴, since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.