Vacuum alignment in a composite 2HDM

We study in detail the vacuum structure of a composite two Higgs doublet model based on a minimal underlying theory with 3 Dirac fermions in pseudo-real representations of the condensing gauge interactions, leading to the SU(6)/Sp(6) symmetry breaking pattern. We find that, independently on the source of top mass, the most general CP-conserving vacuum is characterised by three non-vanishing angles. A special case occurs if the Yukawas are aligned, leading to a single angle. In the latter case, a Dark Matter candidate arises, protected by a global U(1) symmetry.