A Case Study in Dimensional Deconstruction

Abstract

We test Arkani-Hamed et al.&#39;s dimensional deconstruction on a model 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 λis large, so that its vacuum expectation value v \sim M/\sqrtλ << Λalso. We consider two different underlying dynamics--UV completions--at the scale Λfor 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 << Λand λ<< 1, hence, v \sim Λ. In the other, λcan be large or small, but then so is M, and v is still O(Λ).