Arbitrary spin massless bosonic fields in d-dimensional anti-de Sitter space

TL;DR

This paper investigates free massless bosonic fields of arbitrary spin in even-dimensional anti-de Sitter space, deriving their equations, gauge transformations, and energy eigenvalues, with formulations in covariant and intrinsic coordinate systems.

Contribution

It introduces a comprehensive framework for describing arbitrary spin massless bosonic fields in d-dimensional AdS space, including equations, gauge conditions, and energy spectra, in both covariant and intrinsic forms.

Findings

Derived wave equations and subsidiary conditions for massless bosonic fields.

Calculated lowest energy eigenvalues for these fields.

Established relations between gauge invariance and conformal invariance definitions of masslessness.

Abstract

Arbitrary spin free massless bosonic fields propagating in even $d$ - dimensional anti-de Sitter spacetime are investigated. Free wave equations of motion, subsidiary conditions and the corresponding gauge transformations for such fields are proposed. The lowest eigenvalues of the energy operator for the massless fields and the gauge parameter fields are derived. The results are formulated in $SO(d-1,2)$ covariant form as well as in terms of intrinsic coordinates. An inter-relation of two definitions of masslessness based on gauge invariance and conformal invariance is discussed.