Broken Weyl Gravity: Dynamical Torsion and Generalized Proca

TL;DR

This paper develops a symmetry-driven EFT for gravity with spontaneously broken Weyl invariance using the coset construction, identifying the Weyl gauge field as a Higgsed Proca mode with mass $m \\sim \,M_{ m Pl}$ and showing that gauge–gravity couplings belong to the ghost-free generalized Proca class. It further demonstrates that the Weyl field can be traded for a propagating vector torsion, yielding a healthy dynamical torsion sector while preserving Einstein gravity in the IR with controlled higher-derivative corrections. A key result is the absence of Wess–Zumino terms in $d=4$, enforced by relative Lie algebra cohomology, and the leading interactions are shown to align with generalized Proca structures, including a Stückelberg–Galileon-like longitudinal mode. The framework builds a bridge between Weyl-gauged gravity and torsionful theories, offering a symmetry-based route to ghost-free vector–tensor gravity with potential phenomenological implications in cosmology and high-energy gravity. The analysis suggests a natural suppression of certain higher-derivative operators via approximate Weyl symmetry and motivates further exploration of conformal extensions and WZ terms in related settings.

Abstract

We develop a symmetry-based construction of gravity from a phase in which Weyl invariance is spontaneously broken. Using the coset formalism, the dilaton acts as a Stuckelberg field for the gauged scale symmetry, giving the Weyl gauge field a mass of order $\mathcal{O}(M_{\rm Pl})$. The resulting gauge-gravity interactions fall within the ghost-free generalized Proca framework. We further show that the Weyl field can be exchanged for a propagating vector component of torsion, providing a natural realization of dynamical vector torsion. Our construction organizes all operators systematically, clarifies the absence of Wess-Zumino terms in $d=4$, and recovers General Relativity in the infrared with controlled higher-derivative corrections.

Figures (1)

• Figure 1: Healthy torsionful gravity with a propagating vector torsion is in one-to-one correspondence with Broken Weyl gravity. Unlike many torsionful models that are plagued by pathologies, Broken Weyl is a subset of the generalized Proca class and is ghost-free by construction.