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 Lambda, and whose quartic coupling lambda is large, so that its vacuum expectation value vsimilar toM/rootlambda<<Lambda also. We consider two different underlying dynamics-UV completions-at the scale Lambda 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<<Lambda and lambda<<1; hence, vsimilar toLambda. In the other, lambda can be large or small, but then so is M, and v is still O(Lambda).