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

Abstract

We propose a systematic generating procedure to construct free Lagrangians for massive, massless and partially massless, totally-symmetric tensor fields on AdSd+1 starting from the Becchi–Rouet–Stora–Tyutin (BRST) Lagrangian description of massless fields in the flat ambient space Rd,2. A novelty is that the Lagrangian is described by a d + 1 form on Rd,2 whose pullback to AdSd+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 (anti)-de Sitter. 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 one to derive the equations of motion ambiently, i.e., without the need to explicitly derive the respective spacetime Lagrangian.