CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

TL;DR

This work develops a CFT-adapted, gauge-invariant formulation for totally symmetric massless higher-spin fields in $AdS_{d+1}$ using Poincaré coordinates, organizing curvature and radial contributions with ladder operators. It provides a universal Lagrangian structure ${\cal L}=\tfrac12\langle\phi|E|\phi\rangle$ where $E=E_{(2)}+E_{(1)}+E_{(0)}$, and identifies a Stueckelberg-like gauge symmetry realized through ladder operators $e_1,\bar e_1$, with a gauge-invariant mass operator ${\cal M}^2$ commuting with these ladders. The paper derives a modified de Donder gauge that yields a gauge-fixed operator ${\cal E}_{total}=(1-\tfrac14\alpha^2\bar\alpha^2)(\Box-{\cal M}^2)$, leading to decoupled equations of motion solvable by Bessel functions, and discusses how this framework relates to the Stueckelberg approach in flat space. It also analyzes the realization of the conformal algebra $so(d,2)$ and demonstrates consistency with AdS/CFT, including a detailed comparison to the standard $so(d,1)$ Fronsdal formulation. Practically, the approach provides a tractable, gauge-fixed description of higher-spin dynamics in AdS and a clear mapping between bulk and boundary conformal structures.

Abstract

Using Poincare parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.