Toward higher-spin symmetry breaking in the bulk

We present a new vacuum of the bosonic higher-spin gauge theory in $d+1$ dimensions, which has leftover symmetry of the Poincaré algebra in $d$ dimensions. Its structure is very simple: the space-time geometry is that of $AdS$, while the only nonzero field is a scalar. The scalar extends along the Poincaré radial coordinate $z$ and is shown to be linearly exact for an arbitrary mixture of its two $\mathrm{\Delta }=2$ and $\mathrm{\Delta }=d-2$ conformal branches. The obtained vacuum breaks the global higher-spin symmetry leading to a broken phase that lives in the Minkowski space-time.