Ultraviolet Closure in Asymptotically Weyl-Invariant Gravity
Abstract
We investigate asymptotically Weyl-invariant gravity (AWIG) in the Palatini formulation, defined by an exponent n that interpolates between an Einstein-like infrared regime, where n goes to one, and a Weyl-invariant ultraviolet regime, where n goes to two. In four dimensions, we show that exact Weyl invariance within the minimal scalar Palatini f(R) sector uniquely selects the R^2 action as the ultraviolet endpoint. Interpreting the exponent as an effective curvature-dependent quantity, we constrain a phenomenological class of smooth autonomous flows compatible with the required infrared and ultraviolet endpoints. We then analyse the strict ultraviolet theory. On the regular branch R not equal to zero, and within a restricted torsionless, parity-even sector constructed purely from curvature, all admissible divergent on-shell counterterms reduce at arbitrary loop order to the original \sqrt{-g}R^2 term plus a topological Euler density. Although this conditional result does not establish full off-shell perturbative renormalizability, it provides nontrivial evidence for improved ultraviolet behaviour relative to Einstein gravity and identifies a concrete target for a future first-principles renormalization-group calculation.
Versions
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BibTeX
@misc{coumbe2026ultraviolet,
title = {{Ultraviolet Closure in Asymptotically Weyl-Invariant Gravity}},
author = {Daniel Coumbe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01047},
eprint = {2609.01047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01047},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ultraviolet Closure in Asymptotically Weyl-Invariant Gravity
AU - Daniel Coumbe
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01047
UR - https://arxiv.org/abs/2609.01047
AB - We investigate asymptotically Weyl-invariant gravity (AWIG) in the Palatini formulation, defined by an exponent n that interpolates between an Einstein-like infrared regime, where n goes to one, and a Weyl-invariant ultraviolet regime, where n goes to two. In four dimensions, we show that exact Weyl invariance within the minimal scalar Palatini f(R) sector uniquely selects the R^2 action as the ultraviolet endpoint. Interpreting the exponent as an effective curvature-dependent quantity, we constrain a phenomenological class of smooth autonomous flows compatible with the required infrared and ultraviolet endpoints. We then analyse the strict ultraviolet theory. On the regular branch R not equal to zero, and within a restricted torsionless, parity-even sector constructed purely from curvature, all admissible divergent on-shell counterterms reduce at arbitrary loop order to the original \sqrt{-g}R^2 term plus a topological Euler density. Although this conditional result does not establish full off-shell perturbative renormalizability, it provides nontrivial evidence for improved ultraviolet behaviour relative to Einstein gravity and identifies a concrete target for a future first-principles renormalization-group calculation.
ER -