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arXiv · 2510.08778

Broken Weyl Gravity: Dynamical Torsion and Generalized Proca

Lucas Fernández Sarmiento·Irvin Martínez Rodríguez
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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.

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Lucas Fernández Sarmiento, Irvin Martínez Rodríguez. 2025-10-09. Broken Weyl Gravity: Dynamical Torsion and Generalized Proca. https://arxiv.org/abs/2510.08778

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