Conformal actions in any dimension

TL;DR

This paper introduces a scale-invariant conformal action applicable in any dimension using biconformal gauging, revealing solutions that foliate into Ricci-flat spacetimes with a symplectic structure.

Contribution

It presents a novel class of scale-invariant polynomial actions in any dimension and solves the field equations for a minimal torsion geometry, uncovering new geometric structures.

Findings

Solutions are foliated by Ricci-flat Riemannian spacetimes.

The full space is symplectic.

Two fields on the Riemannian submanifolds determine the solution.

Abstract

Biconformal gauging of the conformal group has a scale-invariant volume form, permitting a single form of the action to be invariant in any dimension. We display several 2n-dim scale-invariant polynomial actions and a dual action. We solve the field equations for the most general action linear in the curvatures for a minimal torsion geometry. In any dimension n>2, the solution is foliated by equivalent n-dim Ricci-flat Riemannian spacetimes, and the full 2n-dim space is symplectic. Two fields defined entirely on the Riemannian submanifolds completely determine the solution: a metric, and a symmetric tensor.