The running of Weyl gauged gravity: asymptotic freedom, its obstruction, and a way out
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 R̂2: 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 R̂2 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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BibTeX
@misc{buccio2026running,
title = {{The running of Weyl gauged gravity: asymptotic freedom, its obstruction, and a way out}},
author = {Diego Buccio and Fabrizio Chicconi and Luca Parente and Omar Zanusso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40769},
eprint = {2610.40769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40769},
}
RIS
TY - UNPB
TI - The running of Weyl gauged gravity: asymptotic freedom, its obstruction, and a way out
AU - Diego Buccio
AU - Fabrizio Chicconi
AU - Luca Parente
AU - Omar Zanusso
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40769
UR - https://arxiv.org/abs/2610.40769
AB - 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 R̂^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 R̂^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.
ER -