AI 中文总结
该研究开发自底向上框架，从凯勒势重建四维$\mathcal{N}=1$有效场论轻塔渐近谱，用积分缩放关系等条件组织塔缩放向量，应用于弦紧致化凯勒势可再现已知结果，还对相关多面体分类并发现其与M理论多面体关系，证明EFT弦是紫外塔结构基本构建块。
AI 中文摘要
我们开发了一个自底向上的框架，用于直接从四维$\mathcal{N}=1$有效场论的凯勒势重建轻塔的渐近谱。我们的构建使用积分缩放关系，该关系将在无穷远处变轻的塔的质量尺度与EFT弦的张力联系起来，并在解紧致化时递归应用涌现弦猜想。这些条件将塔缩放向量组织成由EFT弦向量生成的晶格，并选择全局一致的塔多面体。当应用于弦紧致化产生的凯勒势时，我们的算法精确地再现了已知的塔排列和对偶框架。然后，我们对渐近凯勒势$K\sim-\log P(s)$（其中$P(s)$是次数至多为七的齐次多项式）的允许多面体进行分类，并表明某些看似一致的凯勒势与假定的量子引力约束不兼容。对于一般多项式，通过在不同增长扇区粘贴塔排列会产生额外的限制。值得注意的是，我们重建允许的每个塔多面体都可以作为与乔伊斯$G_2$流形上的M理论相关的多面体的具体切片获得。这为一种弦普遍性形式提供了证据，其中EFT弦在EFT微扰区域中充当紫外塔结构的基本构建块。
英文摘要
We develop a bottom-up framework to reconstruct the asymptotic spectrum of light towers in four-dimensional $\mathcal{N}=1$ effective field theories directly from their Kähler potential. Our construction uses the Integral Scaling Relation, which relates the mass scales of towers becoming light at infinite distance to the tensions of EFT strings, together with the Emergent String Conjecture applied recursively upon decompactification. These conditions organize the tower scaling vectors into a lattice generated by the EFT-string vectors and select the globally consistent tower polytopes. When applied to Kähler potentials arising from string compactifications, our algorithm precisely reproduces the known arrangements of towers and duality frames. We then classify the admissible polytopes for asymptotic Kähler potentials $K\sim-\log P(s)$, with $P(s)$ a homogeneous polynomial of degree at most seven, and show that certain apparently consistent Kähler potentials are incompatible with the assumed quantum-gravity constraints. For general polynomials, additional restrictions arise from gluing the tower arrangements across different growth sectors. Remarkably, every tower polytope allowed by our reconstruction can be obtained as a concrete slice of the polytope associated with M-theory on a Joyce $G_2$-manifold. This provides evidence for a form of string universality in which EFT strings act as the fundamental building blocks of the UV tower structure in the EFT perturbative regimes.
Comments50 pages, 2 appendices, 14 figures
