Taxonomy of Potentials in Asymptotic Limits
Abstract
In infinite-distance limits of scalar field moduli spaces in quantum gravity, particle masses, brane tensions, and scalar field potentials scale exponentially with geodesic distance. Previous work has shown that the exponential decay rates of particle masses and brane tensions admit a discrete classification. In this work, we extend this classification to the case of scalar field potentials. We find that leading contributions to the potential typically scale with tensions of codimension-1 branes as V ∼ Td−12 or codimension-0 branes as V ∼ Td, and these relations hold formally even when the associated branes are absent from the spectrum. As a result, the taxonomy rules for potentials are intimately connected to the brane taxonomy rules. More generally, potential contributions can be labeled by a collection of integers, which correspond physically to their transformation properties under Weyl rescalings and their order in the string loop expansion. This implies that the vector v⃗ = − ∇⃗ log V is lattice-valued, and indeed it lies in precisely the same lattice as the analogous vectors α⃗= − ∇⃗ log Td for codimension-0 branes of tension Td. We verify our taxonomy rules in various examples in string theory. We show that these rules imply that sums of positive potential terms satisfy the Strong Asymptotic de Sitter Conjecture, which requires |∇⃗ log V| ≥ 2/√(d−2) in asymptotic regimes of scalar field moduli space, and they imply that higher-derivative gravitational corrections are suppressed by powers of the species scale.
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BibTeX
@misc{etheredge2026taxonomy,
title = {{Taxonomy of Potentials in Asymptotic Limits}},
author = {Muldrow Etheredge and Dieter Lüst and Tom Rudelius},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03001},
eprint = {2609.03001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03001},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Taxonomy of Potentials in Asymptotic Limits
AU - Muldrow Etheredge
AU - Dieter Lüst
AU - Tom Rudelius
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03001
UR - https://arxiv.org/abs/2609.03001
AB - In infinite-distance limits of scalar field moduli spaces in quantum gravity, particle masses, brane tensions, and scalar field potentials scale exponentially with geodesic distance. Previous work has shown that the exponential decay rates of particle masses and brane tensions admit a discrete classification. In this work, we extend this classification to the case of scalar field potentials. We find that leading contributions to the potential typically scale with tensions of codimension-1 branes as V ∼ T_d−1^2 or codimension-0 branes as V ∼ T_d, and these relations hold formally even when the associated branes are absent from the spectrum. As a result, the taxonomy rules for potentials are intimately connected to the brane taxonomy rules. More generally, potential contributions can be labeled by a collection of integers, which correspond physically to their transformation properties under Weyl rescalings and their order in the string loop expansion. This implies that the vector v⃗ = − ∇⃗ log V is lattice-valued, and indeed it lies in precisely the same lattice as the analogous vectors α⃗= − ∇⃗ log T_d for codimension-0 branes of tension T_d. We verify our taxonomy rules in various examples in string theory. We show that these rules imply that sums of positive potential terms satisfy the Strong Asymptotic de Sitter Conjecture, which requires |∇⃗ log V| ≥ 2/√(d−2) in asymptotic regimes of scalar field moduli space, and they imply that higher-derivative gravitational corrections are suppressed by powers of the species scale.
ER -