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

TL;DR

This paper introduces a novel dimensional reduction method that generates massive (anti) de Sitter theories from massless higher-dimensional theories by constraining dilatation, expanding the toolkit for constructing curved spacetime models.

Contribution

It presents a new form of dimensional reduction based on dilatation constraints, enabling derivation of massive (anti) de Sitter theories from higher-dimensional scale-invariant theories.

Findings

Derived free massive actions for arbitrary representations in (anti) de Sitter space.

Extended the method to include interacting theories.

Generalized previous results beyond symmetric tensors.

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.