Broken Weyl Gravity: Dynamical Torsion and Generalized Proca

2025/10/09 by Lucas Fernández Sarmiento, Sarmiento, Lucas Fernández, Rodríguez, Irvin Martínez
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2510.08778

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 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.

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Related

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• Every Poincaré gauge theory is conformal: a compelling case for dynamical vector torsion
• Weyl conformal geometry vs Weyl anomaly