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arXiv 2004.10768hep-th
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利用BPS极值黑洞合并弱引力和距离猜想

Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes

Naomi Gendler, Irene Valenzuela

备注：
66 pages, 10 figures; v2: typos corrected, references added
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摘要：

我们分析了在卡-丘三重上IIB型弦论的$\mathcal{N}=2$紧化的一般无限距离极限下BPS态的荷质结构，并利用所得结果改进了多重规范场和标量场下的沼泽地猜想.我们表明，BPS界与黑洞的极值界在这些无限远的限制，和BPS状态的电荷质量矢量位于退化椭球只有两个非退化方向，无论模或规范场的数量。我们提供了数值的主要半径的椭球体的分类的奇点，正在接近。我们使用这些发现来告知沼泽地距离猜想，该猜想指出，一个状态塔沿着测地线轨迹向无限场距离呈指数变化。我们把一般的边界上的质量衰减率$λ$的这座塔的黑洞极值界，这在我们的设置意味着$λ\geq 1/\sqrt{6}$。我们希望这个框架能够持续超过$\mathcal{N}=2$，只要规范耦合变得小的无限场距离限制。

英文摘要：

We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of $\mathcal{N}=2$ compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate $λ$ of this tower in terms of the black hole extremality bound, which in our setup implies $λ\geq 1/\sqrt{6}$. We expect this framework to persist beyond $\mathcal{N}=2$ as long as a gauge coupling becomes small in the infinite field distance limit.

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