Abstract
Motivated by the weak gravity conjecture, [Phys. Rev. D 104 (2021) 126005] conjectured that in any CFT, the minimal operator dimension at fixed charge is a convex function of the charge. In this letter we construct a counterexample to this convexity conjecture, which is a clockwork-like model with some modifications to make it a weakly-coupled CFT. We also discuss further possible applications of this model and some modified versions of the conjecture which are not ruled out by the counterexample.
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Acknowledgments
We would first like to thank Ofer Aharony and Eran Palti for many interesting discussions, and especially for their patience and for helping to disprove many previous attempts at counterexamples. We are also grateful to Simeon Hellerman for helpful discussions which initialised the project. We would also like to thank Shota Komatsu, Miguel Montero, Domenico Orlando and Sridip Pal for illuminating discussions. MW is grateful to the conference “Large charge aux Diablerets” where this work began, and AS is grateful to the Abu Dhabi meeting on theoretical physics where this work was finished. MW is supported by Grant-in-Aid for JSPS Fellows (No. 22J00752).
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Sharon, A., Watanabe, M. A counterexample to the CFT convexity conjecture. J. High Energ. Phys. 2023, 202 (2023). https://doi.org/10.1007/JHEP05(2023)202
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DOI: https://doi.org/10.1007/JHEP05(2023)202