The masses of gauge fields in higher spin field theory on the bulk of $AdS_{4}$

TL;DR

The paper investigates how massless higher-spin gauge fields in $AdS_{4}$ can acquire mass through a one-loop effect mediated by a local $h^{(\ell)}h^{(\ell-2)}\sigma$ vertex. It constructs a unique two-derivative, gauge-invariant interaction and analyzes the Goldstone mode responsible for mass generation, using both longitudinal (Stückelberg) and TT/de Donder formalisms via the Lichnerowicz operator. The loop calculation yields a mass $m^{2}_{\ell}$ proportional to $g_{\ell}^{2}/N$, and matching with the boundary $O(N)$ sigma-model fixes the coupling $g_{\ell}$. This work provides a concrete bulk realization of HS symmetry breaking at one loop and deepens the holographic connection between bulk higher-spin dynamics and boundary conformal data.

Abstract

A local gauge invariant interaction Lagrangian for two gauge fields of spin $\ell$ and $\ell-2$ $(\ell>2)$ and the scalar field is defined. It gives rise to one-loop corrections to the gauge field propagator. The loop function contains the Goldstone boson propagator for gauge symmetry breaking. The proportionality factor in front of this propagator is the mass squared of the gauge boson.