Techni-Composite Higgs models with (a)symmetric dark matter candidates

We propose a novel class of composite models that feature both a technicolor and a composite Higgs vacuum limit, resulting in an asymmetric dark matter candidate. These Techni-Composite Higgs models are based on an extended left-right electroweak symmetry with a pseudo-Nambu Goldstone boson Higgs and stable dark matter candidates charged under a global $\mathrm{U}(1)_X$ symmetry, connected to the baryon asymmetry at high temperatures via the $SU(2)_{\rm R}$ sphaleron. We consider, as explicit examples, four-dimensional gauge theories with fermions charged under a new confining gauge group $G_{\rm HC} $.