Every Poincar\'e gauge theory is conformal: a compelling case for dynamical vector torsion

TL;DR

This paper demonstrates that all Poincaré gauge theories inherently possess conformal symmetry, introducing a novel scale-invariant embedding that includes a Maxwell term for vector torsion, revitalizing the role of vector torsion in gravity theories.

Contribution

The paper shows that every Poincaré gauge theory can be embedded into a conformal framework, incorporating a Maxwell term for vector torsion, thus resolving previous issues with ghost modes.

Findings

All Poincaré gauge theories are conformal.

A unique scale-invariant embedding introduces a Maxwell term for vector torsion.

The full quantum spectrum of the resulting theory is provided.

Abstract

The Poincar\'e gauge theory (PGT) of gravity provides a viable formulation of general relativity (Einstein-Cartan theory), and a popular model-building framework for modified gravity with torsion. Notoriously, however, the PGT terms which propagate vector torsion lead to strongly-coupled ghosts: the modern view is that only scalar torsion can propagate. To fix this, we revisit the concept of embedding explicit mass scales in scale-invariant theories, showing how the Klein-Gordon theory naturally leads to a slowly-rolling inflaton. We then show that the unique scale-invariant embedding of PGT leads to two new terms, one of which is the Maxwell term for vector torsion. We provide the full spectrum of quantum particles in the resulting theory. Our result means that every PGT is conformal and - after a two-decade hiatus - vector torsion is back on the menu.