On Lagrangian formulation of Higher Spin Theories on AdS

TL;DR

This work develops a Lagrangian formulation for free bosonic Higher Spin fields in massless reducible AdS representations via an ambient-space BRST triplet formalism, embedding AdS into a flat ${\cal D}+1$ dimensional space. The authors extend the triplet construction to ambient space, derive a BRST-invariant Lagrangian for reducible AdS triplets, and illustrate the framework with a concrete vector-field example on AdS. They further discuss how massive AdS fields may be treated through auxiliary representations within the ambient-space BRST setup and outline future directions toward interactions and connections with string theory and AdS/CFT. The approach offers a new ambient-space perspective on massless and massive Higher Spin dynamics in AdS, providing groundwork for BRST-based treatments in curved backgrounds and potential links to holographic dualities.

Abstract

In this short note we present a Lagrangian formulation for free bosonic Higher Spin fields which belong to massless reducible representations of D-dimensional Anti de Sitter group using an ambient space formalism.