Finite is not enough: Triviality bounds in nonlocal field theories
Abstract
An ultraviolet-finite theory need not be ultraviolet complete. This observation weakens the case for spacetime discreteness in quantum gravity if that case rests on removing ultraviolet divergences alone. We arrive at this observation by deriving the one-loop momentum-subtraction flow in four-dimensional ϕ4 theories with ultraviolet-suppressing form factors. The suppression freezes the running above the nonlocality scale, but the theory can hit a Landau pole before suppression sets in. We obtain a bound on the infrared coupling by requiring perturbative control at all scales. This bound varies only at the percent level across the examples we consider. We expect similar bounds in models of discrete spacetime. Thus, requiring ultraviolet completeness improves the predictivity of nonlocal theories.
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BibTeX
@misc{wagner2026finite,
title = {{Finite is not enough: Triviality bounds in nonlocal field theories}},
author = {Fabian Wagner},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07026},
eprint = {2611.07026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07026},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite is not enough: Triviality bounds in nonlocal field theories
AU - Fabian Wagner
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07026
UR - https://arxiv.org/abs/2611.07026
AB - An ultraviolet-finite theory need not be ultraviolet complete. This observation weakens the case for spacetime discreteness in quantum gravity if that case rests on removing ultraviolet divergences alone. We arrive at this observation by deriving the one-loop momentum-subtraction flow in four-dimensional ϕ^4 theories with ultraviolet-suppressing form factors. The suppression freezes the running above the nonlocality scale, but the theory can hit a Landau pole before suppression sets in. We obtain a bound on the infrared coupling by requiring perturbative control at all scales. This bound varies only at the percent level across the examples we consider. We expect similar bounds in models of discrete spacetime. Thus, requiring ultraviolet completeness improves the predictivity of nonlocal theories.
ER -