Minimal surfaces and weak gravity
Minimal surfaces and weak gravity
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DOI：
10.1007/jhep03(2020)021
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发表时间：
2019-06
影响因子：
5.4
通讯作者：
M. Demirtaş;Cody Long;L. McAllister;M. Stillman
中科院分区：
文献类型：
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作者：
M. Demirtaş;Cody Long;L. McAllister;M. Stillman
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型弦理论的紧化中，我们考虑由全纯圈和反全纯圈的并环表示的同调类[H]∈ H4（X，H）.应用于轴子荷的WGC的瞬子形式意味着一个非BPS欧几里德D3-膜包裹着最小体积的代表性的B3-膜的作用的上界。我们给出了一个环面簇中超曲面的定向折叠X和超平面H（）：全纯分量和反全纯分量重组形成一个小得多的圈。特别地，应用于X的子格WGC意味着大的重组，无论子格多么稀疏。因此，包裹着BPS的非BPS瞬子比包裹着BPS的独立成分的BPS瞬子更重要。我们的分析取决于一个新的计算有效因子在X中，不是继承有效因子的复曲面品种。
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]∈ H 4 (X, ℝ) represented by a union Σ∪ 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 min of [Σ]. We give an explicit example of an orientifold X of a hypersurface in a toric variety, and a hyperplane H⊂ H 4 (X, ℝ), such that for any [Σ]∈ H that satisfies the WGC, the minimal volume obeys Vol (Σ min)≪ Vol (Σ∪): 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 min are then more important than would be predicted from a study of BPS instantons wrapping the separate components of Σ∪. Our analysis hinges on a novel computation of effective divisors in X that are not inherited from effective divisors of the toric variety.