A unified framework for graviton, "partially massless" graviton, and photon fields in de Sitter spacetime under conformal symmetry

TL;DR

The paper develops a conformally invariant framework in de Sitter spacetime that unifies the graviton, partially massless graviton, and photon within a group-theoretical setting, employing Dirac's six-cone formalism and ambient-space projections. By analyzing dS Casimir eigenvalues and the structure of indecomposable representations, it derives CI field equations for rank-1 and rank-2 fields that reproduce the photon, partially massless graviton, and graviton under appropriate reductions and gauge constraints, while highlighting the role of global symmetry. The approach provides a unified, symmetry-driven view of massless and partially massless fields in curved backgrounds and discusses the lack of a smooth flat limit for PMG/graviton sectors, with implications for covariant quantization and cosmological physics. Overall, the work underscores the value of a global conformal framework—via Dirac's six-cone—to connect fundamental field content on dS space and to illuminate gauge and conformal properties relevant for quantum gravity in curved spacetimes.

Abstract

We develop a conformally invariant (CI) framework in $(1+3)$-dimensional de Sitter (dS) spacetime, that unifies the descriptions of graviton, ``partially massless'' graviton, and photon fields. This framework is grounded in a rigorous group-theoretical analysis in the Wigner sense and employs Dirac's six-cone formalism. Originally introduced by Dirac, the concept of conformal space and the six-cone formalism were used to derive the field equations for spinor and vector fields in $(1+3)$-dimensional Minkowski spacetime in a manifestly CI form. Our framework extends this approach to dS spacetime, unifying the treatment of massless and ``partially massless'' fields with integer spin $s>0$ under conformal symmetry. This unification enhances the understanding of fundamental aspects of gravitational theories in curved backgrounds.