Free Field Dynamics in the Generalized AdS (Super)Space

TL;DR

The paper develops a universal, algebraic framework for free dynamics of massless fields of all spins in a generalized AdS superspace, realized through a star-product formulation of $Sp(2M)$ and its ortho-symplectic extensions. By constructing pure-gauge Cartan forms on $Sp(M)$ and employing a Fock-module description with generating functions $C(b|X)$, the authors derive covariant, $sp(2M)$-invariant equations that encode massless conformal dynamics in arbitrary even dimensions $M$, and they provide explicit solutions including light-like and plane-wave-like modes in AdS backgrounds. The work extends to supersymmetric backgrounds with $OSp(L|M)$, giving supersymmetric Cartan forms, transformation laws, and potential worldline action applications. Overall, the approach yields closed-form gauge functions and transformation laws across coordinates, enabling exact analyses of higher-spin free fields in generalized conformally flat geometries with broad implications for particle and string dynamics in M-theory contexts.

Abstract

Pure gauge representation for general vacuum background fields (Cartan forms) in the generalized $AdS$ superspace identified with $OSp(L,M)$ is found. This allows us to formulate dynamics of free massless fields in the generalized $AdS$ space-time and to find their (generalized) conformal and higher spin field transformation laws. Generic solution of the field equations is also constructed explicitly. The results are obtained with the aid of the star product realization of ortosymplectic superalgebras.