2-index chiral gauge theories

We undertake a systematic study of the $4$-dimensional $SU(N)$ $2$-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the $2$-index symmetric and anti-symmetric representations, with no fundamentals, and they do not admit a large-$N$ limit. We employ a combination of perturbative and nonperturbative methods, enabling us to constrain their infrared (IR) phases. Specifically, we leverage the 't Hooft anomalies associated with continuous and discrete groups to eliminate a few scenarios. In some cases, the anomalies rule out the possibility of fermion composites. In other cases, the interplay between the continuous and discrete anomalies leads to multiple higher-order condensates, which inevitably form to match the anomalies. Further, we pinpoint the most probable symmetry-breaking patterns by searching for condensates that match the full set of anomalies resulting in the smallest number of IR degrees of freedom. Higher-loop $β$-function analysis suggests that a few theories may flow to a conformal fixed point.