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 $v\sim M/\sqrt{\lambda }\ll \Lambda$ 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, $M\ll \Lambda$ and $\lambda \ll 1;$ hence, $v\sim \Lambda .$ In the other, λ can be large or small, but then so is M, and $v$ is still $O\left(\Lambda \right).\mathrm{}$