Abstract
We consider BPS states in M theory compactified on a Calabi-Yau threefold with one Kähler parameter, and investigate their relation to black holes and black rings. On the microscopic side, a characterization of the BPS degeneracy can be obtained from the non-perturbative part of the topological string free energy according to the Gopakumar-Vafa conjecture. On the macroscopic side, the Wald entropy of relevant black objects in the four-dimensional IIA description is computed from the perturbative part of the same topological string free energy following the work of Cardoso-de Wit-Mohaupt and then lifted to five-dimensional M theory through the Gaiotto-Strominger-Yin correspondence. For a given value of the M2 brane charge, we find that for small angular momenta, the microscopic BPS degeneracy matches the entropy of a rotating black hole, whereas an apparent transition occurs at a critical value of the angular momentum. Beyond this value, we find encouraging evidence that the microscopic counting is well approximated by the entropy of a black ring. We conclude by formulating a new puzzle involving the corrections due to degenerate worldsheet instantons.
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Acknowledgments
We thank Xi Yin for the initial collaboration. We thank Shiraz Minwalla, Cumrun Vafa, and Xi Yin for valuable feedback on a preliminary version of the manuscript. Also, we would like to thank Yiming Chen, Michael B. Green, Daniel Jafferis, Manki Kim, Neil D. Lambert, Jan Manschot, Samir D. Mathur, Sameer Murthy, Hirosi Ooguri, Fernando Quevedo, Harvey S. Reall, Jorge E. Santos, Andrew Strominger, and Zhi-Zhen Wang for helpful discussions. YL is supported by the Simons Collaboration Grant on the Non-Perturbative Bootstrap. IH is supported by the Harvard Quantum Initiative Fellowship.
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Halder, I., Lin, YH. Black hole/black ring transition. J. High Energ. Phys. 2024, 193 (2024). https://doi.org/10.1007/JHEP01(2024)193
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DOI: https://doi.org/10.1007/JHEP01(2024)193