Abstract
In the Einstein-Maxwell-charged scalar system with a negative cosmological constant in arbitrary dimensions higher than three, there exists a horizonless charged soliton solution, which we construct explicitly for an arbitrary mass of the scalar in perturbative series in small charge. We find that the stability of the soliton is determined by the validity of the AdS weak gravity conjecture. The existence of a stable soliton might endanger the convexity of the (free) energy as a function of the charge because the phase transition between the soliton and the extremal Reissner-Nordstrom black hole would be discontinuous. We, however, argue that the existence of the hairy black hole solution circumvents the violation of convexity. The thermodynamic properties of the hairy black hole show that the phase transition becomes continuous irrespective of whether the AdS weak gravity conjecture holds. When it holds, the phase transition occurs between the soliton and the hairy black hole, and when it is violated, the phase transition occurs between the extremal Reissner-Nordstrom black hole and the hairy black hole.
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Acknowledgments
The authors would like to thank Yoshihiko Abe, Nick Dorey, and Toshifumi Noumi for fruitful discussions. T.I. is supported in part by JSPS KAKENHI Grant Number 19K03871. Y.N. is in part supported by JSPS KAKENHI Grant Number 21K03581.
The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University, where this work was initiated during the YITP workshop “Strings and Fields 2023”.
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Ishii, T., Nakayama, Y. Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS. J. High Energ. Phys. 2024, 197 (2024). https://doi.org/10.1007/JHEP05(2024)197
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DOI: https://doi.org/10.1007/JHEP05(2024)197