The weak gravity conjecture in three dimensions

DOI10.1007/JHEP10(2016)159zbMATH Open1390.83123arXiv1606.08438OpenAlexW3121895384WikidataQ63353851 ScholiaQ63353851MaRDI QIDQ1636396

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Publication date: 12 June 2018

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Abstract: We study weakly coupled $U(1)$ theories in $Ad{S}_3$, 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.

Full work available at URL: https://arxiv.org/abs/1606.08438

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