发表机构
II. Institut für Theoretische Physik, Universität Hamburg（汉堡大学理论物理第二研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立Calabi-Yau复结构模空间中边界层处于无穷Weil-Petersson距离的充要判据，证明无穷距离边界因子的交集仍为无穷距离，并验证Wang猜想。
AI 中文摘要
无穷距离极限在沼泽地纲领中扮演核心角色，但理解它们在边界因子交集处的行为是微妙的，因为这需要同时控制多个模数的极限。为解决此问题，我们建立了Calabi-Yau流形复结构模空间中任意余维边界层位于无穷Weil-Petersson距离处的充要判据。特别地，无穷距离边界因子的交集必然仍处于无穷距离。该结果适用于完整Weil-Petersson度量及任意轨迹，包括那些在saxion和axion卷绕中具有无限制层级结构的轨迹。在Type IIB弦理论紧化于Calabi-Yau三流形的情形中，我们的证明基于一个不等式，该不等式将轨迹的Weil-Petersson长度与辅助电荷矢量相关的BPS质量联系起来。若该质量趋于零而荷质比保持一致有界，则每条趋近该极限的轨迹都具有无穷长度。利用渐近Hodge理论，我们构造了满足这些条件的辅助电荷矢量，并直接从与退化相关的极限混合Hodge结构推导出该判据。更一般地，我们的结果适用于Calabi-Yau类型的极化Hodge结构变分。特别地，我们证明了Wang关于高维基上退化具有有限Weil-Petersson距离的猜想。
英文摘要
Infinite-distance limits play a central role in the Swampland program, but understanding their behaviour at intersections of boundary divisors is subtle, as it requires control over simultaneous limits of several moduli. To address this, we establish a necessary and sufficient criterion for a boundary stratum of arbitrary codimension in the complex-structure moduli space of Calabi-Yau manifolds to lie at infinite Weil-Petersson distance. In particular, intersections of infinite-distance boundary divisors necessarily remain at infinite distance. The result holds for the full Weil-Petersson metric and arbitrary trajectories, including those with unrestricted hierarchies in the saxions and axion winding. In compactifications of Type IIB string theory on Calabi-Yau threefolds, our proof is based on an inequality relating the Weil-Petersson length of a trajectory to the BPS mass associated with an auxiliary charge vector. If this mass tends to zero while the charge-to-mass ratio remains uniformly bounded, every trajectory approaching the limit has infinite length. Using asymptotic Hodge theory, we construct an auxiliary charge vector satisfying these conditions and derive the criterion directly from the limiting mixed Hodge structure associated with the degeneration. More generally, our result applies to polarized variations of Hodge structure of Calabi-Yau type. In particular, we prove Wang's conjecture on finite Weil-Petersson distance for degenerations over higher-dimensional bases.
Comments36 pages, 2 figures
