Massless and massive higher spins from anti-de Sitter space waveguide

Understanding Higgs mechanism for higher-spin gauge fields is an outstanding open problem. We investigate this problem in the context of Kaluza-Klein compactification. Starting from a free massless higher-spin field in (d+2)-dimensional anti-de Sitter space and compactifying over a finite angular wedge, we obtain an infinite tower of heavy, light and massless higher-spin fields in (d+1)-dimensional anti-de Sitter space. All massive higher-spin fields are described gauge invariantly in terms of Stueckelberg fields. The spectrum depends on the boundary conditions imposed at both ends of the wedges. We observed that higher-derivative boundary condition is inevitable for spin greater than three. For some higher-derivative boundary conditions, equivalently, spectrum-dependent boundary conditions, we get a non-unitary representation of partially-massless higher-spin fields of varying depth. We present intuitive picture which higher-derivative boundary conditions yield non-unitary system in terms of boundary action. We argue that isotropic Lifshitz interfaces in O(N) Heisenberg magnet or O(N) Gross-Neveu model provides the holographic dual conformal field theory and propose experimental test of (inverse) Higgs mechanism for massive and partially massless higher-spin fields.