Case study in dimensional deconstruction

Abstract

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/√λ≪Λ 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≪Λ and λ≪1; hence, v∼Λ. In the other, λ can be large or small, but then so is M, and v is still O(Λ).