CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS

TL;DR

The paper develops a CFT-adapted, gauge-invariant formulation for massive arbitrary spin fields in AdS using the Poincaré patch, encoding mass, curvature, and radial contributions through ladder operators. It presents three representations of the Lagrangian, constructs gauge and global AdS (conformal) symmetries in a basis aligned with boundary CFT, and introduces a modified de Donder gauge that yields decoupled, Bessel-function–solvable equations. A new arbitrary-coordinate representation and a light-cone gauge Lagrangian are also provided, along with a thorough comparison to standard gauges via a Zinoviev-like higher-spin framework, demonstrating consistent AdS/CFT compatibility. Overall, the work offers a systematic, symmetry-respecting approach to massive AdS fields and clarifies how different gauge choices relate and simplify dynamics for holographic applications.

Abstract

Using Poincare parametrization of AdS space, we study massive totally symmetric arbitrary spin 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 by using Stueckelberg formulation of massive fields. We demonstrate that the mass parameter, curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS massive fields can be expressed in terms of ladder operators. Three representations for the Lagrangian are discussed. 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 the Bessel function. New simple representation for gauge invariant Lagrangian of massive (A)dS field in arbitrary coordinates is obtained. Light-cone gauge Lagrangian of massive AdS field is also presented.