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We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU($N$) gauge group and an anomaly-free set of $n_{S_k}$ copies of chiral fermions transforming as the symmetric rank-$k$ tensor representation, $S_k$, and $n_{\bar A_\ell}$ copies of fermions transforming according to the conjugate antisymmetric rank-$\ell$ tensor representation, $\bar A_\ell$, of this group with $k, \ \ell \ge 2$.
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Clearly, our study of S k A ¯ ℓ S_{k}\bar{A}_{\ell} chiral gauge theories is equivalent to the study of the set with fermions in the conjugate representations S ¯ k \bar{S}_{k} and A ℓ A_{\ell}
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In the extended Standard Model that includes SM-singlet right-handed neutrinos, there can be bare Majorana mass terms for these
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