Radial Dimensional Reduction: (Anti) de Sitter Theories from Flat

TL;DR

Radial dimensional reduction replaces momentum-based compactification with dilatation-based reduction, producing massive (A)dS theories from massless flat-space theories in one higher dimension. By treating AdS/dS as a hypersurface in flat space and exploiting scale invariance, the authors derive general field equations and gauge-invariant actions for arbitrary spin representations in D dimensions, via decoupled dilatation modes. They validate the approach with explicit reductions of scalar, vector, graviton, and fermion multiplets, illustrating phenomena like partial masslessness and addressing unitarity via Wick rotations. The framework offers a practical algorithm to relate flat-space and (A)dS physics and points to future work on interactions, real multiplets, and extensions to supergravity or less symmetric spaces.

Abstract

We propose a new form of dimensional reduction that constrains dilatation instead of a component of momentum. It corresponds to replacing toroidal compactification in a Cartesian coordinate with that in the logarithm of the radius. Massive theories in de Sitter or anti de Sitter space are thus produced from massless (scale invariant) theories in one higher space or time dimension. As an example, we derive free massive actions for arbitrary representations of the (anti) de Sitter group in arbitrary dimensions. (Previous general results were restricted to symmetric tensors.) We also discuss generalizations to interacting theories.