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arXiv 1906.08262hep-th
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极小曲面与弱引力

Minimal Surfaces and Weak Gravity

Mehmet Demirtas, Cody Long, Liam McAllister, Mike Stillman

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25 pages
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摘要：

我们表明，弱引力猜想（WGC）意味着一个非平凡的上限的最小体积循环在某些同源类，承认没有校准的代表的体积。在Calabi-Yau三重的定向折叠$X$上的IIB型弦论的紧化中，我们考虑由全纯和反全纯圈的并集$Σ_{\cup}$表示的同调类$[Σ] \in H_4(X,\mathbb{Z})$.应用于轴子电荷$[Σ]$的WGC的瞬子形式意味着包裹$[Σ]$的最小体积代表$Σ_{\mathrm{min}}$的非BPS欧几里得D3膜的作用的上界。我们给出了一个明确的例子的orientifold $X$的超曲面的复曲面品种，和超平面$\mathcal{H} \subset H_4(X,\mathbb{Z})$，使任何$[Σ] \in H$满足WGC，最小体积服从$\mathrm{Vol}(Σ_{\mathrm{min}}) \ll \mathrm{Vol}(Σ_{\cup})$：全纯和反全纯组件重组，形成一个小得多的循环。特别地，应用于$X$的子晶格WGC意味着大的重组，无论子晶格多么稀疏。因此，包裹$Σ_{\mathrm{min}}$的非BPS瞬子比包裹$Σ_{\cup}$的单独成分的BPS瞬子的研究所预测的更重要。我们的分析取决于一种新的计算有效因子在$X$，不继承有效因子的复曲面品种。

英文摘要：

We show that the Weak Gravity Conjecture (WGC) implies a nontrivial upper bound on the volumes of the minimal-volume cycles in certain homology classes that admit no calibrated representatives. In compactification of type IIB string theory on an orientifold $X$ of a Calabi-Yau threefold, we consider a homology class $[Σ] \in H_4(X,\mathbb{Z})$ represented by a union $Σ_{\cup}$ of holomorphic and antiholomorphic cycles. The instanton form of the WGC applied to the axion charge $[Σ]$ implies an upper bound on the action of a non-BPS Euclidean D3-brane wrapping the minimal-volume representative $Σ_{\mathrm{min}}$ of $[Σ]$. We give an explicit example of an orientifold $X$ of a hypersurface in a toric variety, and a hyperplane $\mathcal{H} \subset H_4(X,\mathbb{Z})$, such that for any $[Σ] \in H$ that satisfies the WGC, the minimal volume obeys $\mathrm{Vol}(Σ_{\mathrm{min}}) \ll \mathrm{Vol}(Σ_{\cup})$: the holomorphic and antiholomorphic components recombine to form a much smaller cycle. In particular, the sub-Lattice WGC applied to $X$ implies large recombination, no matter how sparse the sublattice. Non-BPS instantons wrapping $Σ_{\mathrm{min}}$ are then more important than would be predicted from a study of BPS instantons wrapping the separate components of $Σ_{\cup}$. Our analysis hinges on a novel computation of effective divisors in $X$ that are not inherited from effective divisors of the toric variety.

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