The four scalar degrees of freedom of the Standard Model, the Higgs and the longitudinal components of the Ws and Z, are amenable to different EFT descriptions. "SMEFT" wraps them up in a single Higgs doublet, whereas "HEFT" treats the Higgs and the Goldstones separately. We identify (field redefinition invariant) features of the scalar field space manifold that can only be described by the latter HEFT, and thereby identify two classes of UV completions for which HEFT is required: i) those which contain extra sources of electroweak symmetry breaking, ii) those which contain particles getting all of their mass from electroweak symmetry breaking.
