A Case Study in Dimensional Deconstruction

Abstract

We test Arkani-Hamed et al.'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).

Figures (8)

• Figure 1: The full moose for the ring model of Ref. acga, showing its UV completion. Strong gauge goups are labeled by $n_1,n_2,\dots,n_N$ and weak gauge groups by $m_1,m_2,\dots,m_N$. Fermions $\psi_{Lk}$ and $\psi_{Rk}$ transform as $(n,m,1)$ and $(n,1,m)$ of $(SU(n)_k \otimes SU(m)_k \otimes SU(m)_{k+1})$.
• Figure 2: The condensed moose for the ring model of Ref. acga, characterizing its low--energy structure with nonlinear sigma fields $U_k = \exp{(i\pi_k/f)}$ linking the weak groups $SU(m)_k$ and $SU(m)_{k+1}$.
• Figure 3: Graphical depiction of the Hamiltonian ${\cal H}_N$ in Eq. (\ref{['eq:HN']}). Fermions transform as indicated in Eq. (\ref{['eq:fermionsa']}) under the weak gauge groups $SU(m)_k$, whose bosons are identified in the figure. An $\times$ indicates a dynamical mass insertion. Strong $SU(n)$ gauge boson interactions within each fermion loop are not indicated. There are no strong gauge interactions between loops.
• Figure 4: The condensed moose for the toroidal model of Ref. acgb. The weak $SU(m)_{kl}$ group is denoted by a circle at the site $(k,l)$. The site $(k,l)$ is identified with the sites $(k+N,l)$ and ($k,l+N)$. Nonlinear sigma model link--fields $U_{kl}$ and $V_{kl}$ transform according to Eq. (\ref{['eq:UVtransform']}).
• Figure 5: The complete moose for the toroidal model of Ref acgb with a QCD--like UV completion. The weak $SU(m)_{kl}$ gauge groups are as in Fig. 4, and the strong $SU(k-{{ { 1\over { 2 } }}},l)$ and $SU(k,l-{{ { 1\over { 2 } }}})$ gauge groups are indicated by squares. Fermions transform as in Eq. (\ref{['eq:fermionsb']}).