Ambient-space variational calculus for gauge fields on constant-curvature spacetimes

TL;DR

This paper introduces a systematic ambient-space variational calculus framework for constructing gauge field Lagrangians on constant-curvature spacetimes like AdS, unifying massive, massless, and partially massless fields.

Contribution

It develops a novel ambient-space variational calculus approach using a $d+1$ form and triplet formulation, providing a unifying, covariant action principle for various gauge fields on AdS.

Findings

Constructed ambient-space Lagrangians for gauge fields on AdS.

Unified action principle for massive, massless, and partially massless fields.

Introduced ambient-space Euler-Lagrange differential for deriving equations of motion.

Abstract

We propose a systematic generating procedure to construct free Lagrangians for massive, massless and partially massless, totally-symmetric tensor fields on $AdS_{d+1}$ starting from the BRST Lagrangian description of massless fields in the flat ambient space $\mathbb{R}^{d,2}$. A novelty is that the Lagrangian is described by a $d+1$ form on $\mathbb{R}^{d,2}$ whose pullback to $AdS_{d+1}$ gives the genuine Lagrangian defined on anti de Sitter spacetime. Our derivation uses the triplet formulation originating from the first-quantized BRST approach, where the action principle is determined by the BRST operator and the inner product of a first-quantised system. In this way we build, in a manifestly $so(2,d)$-covariant manner, a unifying action principle for the three types of fields mentioned above. In particular, our derivation justifies the form of some actions proposed earlier for massive and massless fields on AdS. We also give a general setup for ambient Lagrangians in terms of the respective jet-bundles and variational bi-complexes. In particular we introduce a suitable ambient-space Euler-Lagrange differential which allows to derive the equation of motion ambiently, i.e. without the need to explicitly derive the respective spacetime Lagrangian.