Effective Lagrangians for orientifold theories

We construct effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two nonsupersymmetric theories which are orientifold daughters of supersymmetric gluodynamics (containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group). Since the parent and daughter theories are planar equivalent, at [Formula Presented] the effective Lagrangians in the orientifold theories basically coincide with the bosonic part of the VY Lagrangian. We depart from the supersymmetric limit in two ways. First, we consider finite (albeit large) values of N. Then [Formula Presented] effects break supersymmetry. We suggest seemingly the simplest modification of the VY Lagrangian which incorporates these [Formula Presented] effects, leading to a nonvanishing vacuum energy density. We analyze the spectrum of the finite-[Formula Presented] nonsupersymmetric daughters. For [Formula Presented] the two-index antisymmetric representation (one flavor) is equivalent to one-flavor QCD. We show that in this case the scalar quark-antiquark state is heavier than the corresponding pseudoscalar state, “[Formula Presented]” Second, we add a small fermion mass term. The fermion mass term breaks supersymmetry explicitly. The vacuum degeneracy is lifted. The parity doublets split. We evaluate the splitting. Finally, we include the [Formula Presented] angle and study its implications.