4维 $\mathcal{N}=2$ 超引力理论的量子引力原理与渐近Hodge理论
Quantum Gravity Principles for 4d $\mathcal{N}=2$ Supergravity Theories and Asymptotic Hodge Theory
- II. Institut für Theoretische Physik, Universität Hamburg（汉堡大学理论物理第二研究所）
- Zentrum für Mathematische Physik, Universität Hamburg（汉堡大学数学物理中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究四维N=2超引力在模空间无穷远边界的行为，基于Hodge结构变分分类退化，提出与量子引力相容的完整性及紧致化约束。
AI中文摘要：
我们研究了一般四维N=2超引力理论在矢量多重态模空间无穷远边界附近的行为，重点在于清晰区分仅由超引力本身推出的性质与由量子引力中一致的紫外完备化推出的性质。我们分析的基础是控制N=2超引力矢量多重态模空间的极化Hodge结构的实变分，结合数学文献中非常近期的进展。由此得到的无穷远退化分类，在规范耦合层面上，恰好与将极限解释为退紧致化到五维或六维，或解释为弱耦合弦极限的可能性一致，正如从量子引力视角所预期的那样。这一观察扩展了之前在Calabi-Yau流形上的弦紧致化背景下发现的结果，并且值得注意的是，它适用于一般四维N=2超引力理论，无论其紫外完备化如何。此外，我们证明了存在一个Kähler基，在该基中，prepotential的三重耦合是非负的，不论超引力理论的几何起源如何。最后，我们提出了一个四维N=2超引力与量子引力相容的两个非平凡约束：Hodge结构的完整性作为完备性假设的必要条件，以及模空间存在简单正规交叉紧致化，以确保弱耦合渐近引力对偶框架的相容性。
英文摘要：
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 Kähler 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.
