Predictions for QCD from Supersymmetry

TL;DR

This paper constructs effective Lagrangians for non-supersymmetric orientifold theories derived from supersymmetric models, analyzing their spectra, vacuum energy, and effects of finite N, fermion mass, and theta-angle.

Contribution

It proposes a minimal modification of the Veneziano-Yankielowicz Lagrangian to incorporate 1/N effects and studies the resulting spectrum and vacuum structure at finite N.

Findings

Scalar state is heavier than pseudoscalar in N=3 case.

Vacuum energy density becomes non-zero due to 1/N effects.

Fermion mass lifts vacuum degeneracy and splits parity doublets.

Abstract

We review the construction of the effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two non-supersymmetric theories containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group (orientifold theories). Since these theories are planar equivalent, at N\to\infty to super Yang-Mill their effective Lagrangians coincides with the bosonic part of the VY Lagrangian. We depart from the supersymmetric limit in two ways. First, we consider finite but still large values of N. Then 1/N effects break supersymmetry. We suggest a minimal modification of the VY Lagrangian which incorporates these 1/N effects, leading to a non-vanishing vacuum energy density. We then analyze the spectrum at finite N. For N=3 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, ``eta^prime''. 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 \theta-angle and study its implications.