Gauge fields as composite boundary excitations

TL;DR

The paper develops a group-theoretical framework linking bulk AdS massless fields to boundary conformal currents via SO(n-1,2) representations. It shows that bulk gauge excitations correspond to boundary currents, while boundary massless states are bulk singletons, with massless representations residing at unitarity bounds; through non-decomposable representations and tensor products, it provides a dictionary between boundary composites and bulk fields, including explicit dimensional examples. The work offers a structured view of how gravity and Yang–Mills symmetries in AdS map to global boundary symmetries and outlines the role of singleton composites in constructing bulk massless spectra, with implications for AdS/CFT-type dualities and higher-dimensional gauge theories.

Abstract

We investigate representations of the conformal group that describe "massless" particles in the interior and at the boundary of anti-de Sitter space. It turns out that massless gauge excitations in anti-de Sitter are gauge "current" operators at the boundary. Conversely, massless excitations at the boundary are topological singletons in the interior. These representations lie at the threshold of two "unitary bounds" that apply to any conformally invariant field theory. Gravity and Yang-Mills gauge symmetry in anti-De Sitter is translated to global translational symmetry and continuous $R$-symmetry of the boundary superconformal field theory.