Case study in dimensional deconstruction

We test dimensional deconstruction on a model of Arkani-Hamed, Cohen, and Georgi that is predicted to have a naturally light composite Higgs boson, i.e., one whose mass M is much less than its binding scale {Λ}, and whose quartic coupling {λ} is large, so that its vacuum expectation value v~M/√λΛ also. We consider two different underlying dynamics---UV completions---at the scale {Λ} for this model. We find that the expectation from dimensional deconstruction is not realized and that low-energy details depend crucially on the UV completion. In one case, MΛ and λ1; hence, v~Λ. In the other, {λ} can be large or small, but then so is M, and v is still O(Λ).