Massless and Massive Higher Spins from Anti-de Sitter Space Waveguide

TL;DR

This paper explores how higher-spin fields in anti-de Sitter space can acquire mass through boundary conditions in a Kaluza-Klein compactification, revealing connections to non-unitary theories and potential experimental tests.

Contribution

It introduces a novel approach to generating massive and partially-massless higher-spin fields via boundary conditions in AdS waveguides, linking to holography and experimental models.

Findings

Infinite tower of higher-spin fields obtained from compactification.

Higher-derivative boundary conditions lead to non-unitary spectra.

Proposes experimental tests related to Higgs mechanism in condensed matter models.

Abstract

Higgs mechanism to massive higher-spin gauge fields is an outstanding open problem. We investigate this issue 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 St\"ueckelberg fields. The spectrum depends on the boundary conditions imposed at both ends of the wedges. We obseved 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.