On the Proof of Chiral Symmetry Breaking through Anomaly Matching in QCD-like Theories: An Exemplification

Our recent works revisit the proof of chiral symmetry breaking in the confining phase of four-dimensional QCD-like theories, i.e. $SU(N_c)$ gauge theories with $N_f$ flavors of vectorlike quarks in the fundamental representation. The analysis relies on the structure of 't Hooft anomaly matching and persistent mass conditions for theories with same $N_c$ and different $N_f$. In this paper, we work out concrete examples with $N_c=3$ and $N_c=5$ to support and elucidate the results in the companion papers. Within the same examples, we also test some claims made in earlier works.