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arXiv · 2610.40769

The running of Weyl gauged gravity: asymptotic freedom, its obstruction, and a way out

Diego Buccio·Fabrizio Chicconi·Luca Parente·Omar Zanusso
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Abstract

We compute the one-loop beta functions of quadratic gravity in Weyl conformal geometry, the gauge theory of diffeomorphisms and dilatations with a dynamical Weyl gauge boson. The divergences are extracted diagrammatically in the background field method, with a gauge fixing procedure adapted to the semidirect product structure of the gauge group. The Weyl-tensor coupling and the Weyl gauge coupling are asymptotically free, and the running of the latter is special, being independent of the other couplings and of any two-derivative matter content. The obstruction to an ultraviolet completion comes from the square of a Weyl-covariant curvature scalar, denoted $\widehat{R}{}^2$: the flow of the corresponding coupling has no fixed point in the physically interesting region and becomes trivial, the only real fixed points require a decoupled Weyl boson and a tachyonic scalar mode. This also holds when including the Standard Model with any nonminimal Higgs coupling and, more generally, for any matter with two-derivative kinetic terms. Weyl-invariant four-derivative scalars with a sufficiently large coupling to $\widehat{R}{}^2$ can remove the obstruction, producing a fixed point in the physical region that is ultraviolet attractive in all directions and has a nonvanishing Weyl gauge coupling.

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Diego Buccio, Fabrizio Chicconi, Luca Parente, Omar Zanusso. 2026-10-29. The running of Weyl gauged gravity: asymptotic freedom, its obstruction, and a way out. https://arxiv.org/abs/2610.40769

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