Effective Lagrangians for Orientifold Theories

TL;DR

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

Contribution

It constructs and analyzes effective Lagrangians for orientifold theories, extending Veneziano-Yankielowicz models beyond supersymmetry and finite N effects.

Findings

Scalar state heavier than pseudoscalar in N=3 case

Finite N effects induce non-zero vacuum energy

Fermion mass lifts vacuum degeneracy and splits parity doublets

Abstract

We construct effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two non-supersymmetric 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 N\to\infty 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 1/N effects break supersymmetry. We suggest seemingly the simplest modification of the VY Lagrangian which incorporates these 1/N effects, leading to a non-vanishing vacuum energy density. We analyze the spectrum of the finite-N non-supersymmetric daughters. 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' ''. 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.