Phases of Confining SU(5) Chiral Gauge Theory with Three Generations

We explore the possible low energy phases of the confining non-supersymmetric $SU(5)$ chiral gauge theory with three generations of fermions in the $(10+\bar{5})$ representations. This theory has the same fermion and gauge matter content as the simplest Georgi-Glashow grand unified theory of the Standard Model and has an $SU(3)\times SU(3)\times U(1)$ global symmetry. Using 't Hooft anomaly matching, most attractive channel, and soft SUSY breaking approaches, we outline a number of possible consistent low energy vacua including one with a remnant $SO(3)\times U(1)$ symmetry that is analogous to the one-generation model. For the soft SUSY breaking approach, we find that as one extrapolates to large SUSY breaking to recover the original theory, a phase transition is possible. We show that such a phase transition is guaranteed if SUSY breaking is communicated via anomaly mediation.