Quantum Gravity Principles for 4d š¯’©=2 Supergravity Theories and Asymptotic Hodge Theory
Abstract
We study the behaviour of general four-dimensional N=2 supergravity theories near boundaries at infinity of the vector multiplet moduli space, with a focus on a clear distinction between properties that follow from supergravity alone rather than from a consistent UV completion in quantum gravity. The basis for our analysis is the appearance of a real variation of polarised Hodge structure governing the vector multiplet moduli space of N=2 supergravity, combined with very recent advances in the mathematics literature. The resulting classification of infinite distance degenerations exactly agrees, at the level of gauge couplings, with a possible interpretation of the limits as decompactification limits to five or six dimensions or as weakly coupled string limits, as expected from a quantum gravity perspective. This observation extends previous results found in the context of string compactifications on Calabi--Yau varieties and, remarkably, holds for general four-dimensional N=2 supergravity theories regardless of a UV completion. We furthermore show the existence of a KƤhler basis in which the triple couplings of the prepotential are non-negative, irrespective of a geometric origin of the supergravity theory. Finally we propose two non-trivial constraints for a four-dimensional N=2 supergravity to be compatible with quantum gravity: Integrality of the Hodge structure as a necessary condition for the completeness hypothesis and the existence of a simple normal crossing compactification of the moduli space to ensure compatibility of the weakly coupled asymptotic gravitational duality frames.
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BibTeX
@misc{kaufmann2026quantum,
title = {{Quantum Gravity Principles for 4d $\mathcalN=2$ Supergravity Theories and Asymptotic Hodge Theory}},
author = {Lukas Kaufmann and Timo Weigand},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38307},
eprint = {2609.38307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38307},
}
RIS
TY - UNPB
TI - Quantum Gravity Principles for 4d š¯’©=2 Supergravity Theories and Asymptotic Hodge Theory
AU - Lukas Kaufmann
AU - Timo Weigand
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38307
UR - https://arxiv.org/abs/2609.38307
AB - We study the behaviour of general four-dimensional N=2 supergravity theories near boundaries at infinity of the vector multiplet moduli space, with a focus on a clear distinction between properties that follow from supergravity alone rather than from a consistent UV completion in quantum gravity. The basis for our analysis is the appearance of a real variation of polarised Hodge structure governing the vector multiplet moduli space of N=2 supergravity, combined with very recent advances in the mathematics literature. The resulting classification of infinite distance degenerations exactly agrees, at the level of gauge couplings, with a possible interpretation of the limits as decompactification limits to five or six dimensions or as weakly coupled string limits, as expected from a quantum gravity perspective. This observation extends previous results found in the context of string compactifications on Calabi--Yau varieties and, remarkably, holds for general four-dimensional N=2 supergravity theories regardless of a UV completion. We furthermore show the existence of a KƤhler basis in which the triple couplings of the prepotential are non-negative, irrespective of a geometric origin of the supergravity theory. Finally we propose two non-trivial constraints for a four-dimensional N=2 supergravity to be compatible with quantum gravity: Integrality of the Hodge structure as a necessary condition for the completeness hypothesis and the existence of a simple normal crossing compactification of the moduli space to ensure compatibility of the weakly coupled asymptotic gravitational duality frames.
ER -