The Phases of Non-supersymmetric Gauge Theories: the $SO(N_c)$ Case Study

Abstract

We investigate the IR phases of non-supersymmetric (non-SUSY) $SO(N_c)$ gauge theories with $N_F$ fermions in the vector representation obtained by perturbing the SUSY theory with anomaly mediated SUSY breaking (AMSB). We find that of the wide variety of phases appearing in the SUSY theory only two survive: for $N_F<\frac{3}{2} (N_c-2)$ the theory confines, breaking the $SU(N_F)$ global symmetry to $SO(N_F)$, while for $\frac{3}{2} (N_c-2)<N_F<3(N_c-2)$ the theory flows to a (super)-conformal fixed point. The abelian Coulomb and free magnetic phases do not survive and collapse to the confining phase. We also investigate the behavior of loop operators in order to provide a clear distinction between the confining and screened phases. With the choice of $Spin(N_c)$ for the global structure of the gauge group, we find that the electric Wilson loop indeed obeys an area law, providing one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory. We identify monopole condensation as the dynamics underlying confinement. These monopoles arise naturally for $N_F=N_c-2$. The case with smaller number of flavors can be obtained by integrating out flavors, and we confirm numerically that the monopole condensate persists in the presence of AMSB and mass perturbations.