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arXiv 1606.08438hep-th
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三维空间中的弱引力猜想

The Weak Gravity Conjecture in three dimensions

Miguel Montero, Gary Shiu, Pablo Soler

摘要:

我们研究了弱耦合$U(1)$理论在$AdS_3$,其相关的带电BTZ解决方案,和他们的带电光谱。我们发现全息对偶二维CFT的模不变性和规范群的紧致性共同暗示了共形维数显著低于黑洞阈值的带电算符的存在。我们认为这是三维空间中弱引力猜想(WGC)的一种形式。我们还探讨了在我们的讨论中出现的一个特定的离散$\mathbb{Z}_N$对称性的模不变性所构成的约束。在这种情况下,模不变性并不保证轻$\mathbb{Z}_N$荷电态的存在。我们还强调了我们的讨论和通常的启发式论点的基础上的黑洞残留物的WGC之间的差异。

英文摘要:

We study weakly coupled $U(1)$ theories in $AdS_3$, their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together imply the existence of charged operators with conformal dimension significantly below the black hole threshold. We regard this as a form of the Weak Gravity Conjecture (WGC) in three dimensions. We also explore the constraints posed by modular invariance on a particular discrete $\mathbb{Z}_N$ symmetry which arises in our discussion. In this case, modular invariance does not guarantee the existence of light $\mathbb{Z}_N$-charged states. We also highlight the differences between our discussion and the usual heuristic arguments for the WGC based on black hole remnants.

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