• beyond the Standard Model Physics
• composite Higgs
• Pati-Salam symmetry
• strongly interacting theories

In this thesis we review the previous classification of UV fermionic completions of Composite Higgs (CH) theories.

In the first four chapters we review Composite Higgs models and the possible symmetries that can characterize a fermionic completion of such a theory.

In chapter 5,6, and partly in 7 we present our results.
Our models are characterized by new fermions interacting via a new strong gauge interaction G_{HC}.
We focus on sectors based on the Pati-Salam group, in which the color and B-L are unified in the leptocolor SU(4)_{LC}. In particular, we require that in our models the leptocolor group spontaneously breaks to SU(3)_c x U(1)_{B-L}. In this way, Pati-Salam scalar leptoquarks appear in the spectrum.
We proceed to fully classify non-chiral CH theories satisfying this additional request.

We then study chiral dynamics, that were less studied in the previous classification of CH models. Among the others, we find some viable chiral models that satisfy our requirements.

Of course, the dynamics presented satisfy only a set of necessary conditions, and not all of them are phenomenologically viable models.
This work is intended to be only as the first step toward a more complete understanding of possible strongly interacting sectors of CH theories.