Abstract
Supersymmetric elementary string states in the compactified heterotic string theory are described by small black holes that have zero area event horizon. In this paper we compute the supersymmetric index of such elementary string states using gravitational path integral. The dominant contribution to the path integral comes from an Euclidean rotating black hole solution of the supergravity theory with a finite area event horizon, but the logarithm of the index, computed from the saddle point, vanishes. Nevertheless we show that the solution is singular on certain subspaces of the horizon where higher derivative corrections can be important, and once the higher derivative corrections are taken into account the solution could yield a finite result for the logarithm of the index whose form agrees with the microscopic results up to an overall numerical constant. While the numerical constant is not determined in our analysis, we show that it is independent of the details of the compactification and even the number of non-compact dimensions, in agreement with the microscopic results.
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Acknowledgments
We would like to thank A H Anupam for discussions and collaboration during the initial stages of this work. CC thanks David Turton and Shasha Tyukov for discussions. AS thanks Sameer Murthy for discussions. AV thanks David Chow for email correspondence. PS would like to thank the Raman Research Institute and the International Centre for Theoretical Sciences for their kind hospitality during the initial stages of this work. CC is supported by the STFC consolidated grant (ST/X000583/1) “New Frontiers in Particle Physics, Cosmology and Gravity”. A.S. is supported by ICTS-Infosys Madhava Chair Professorship and the J.C. Bose fellowship of the Department of Science and Technology.
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Chowdhury, C., Sen, A., Shanmugapriya, P. et al. Supersymmetric index for small black holes. J. High Energ. Phys. 2024, 136 (2024). https://doi.org/10.1007/JHEP04(2024)136
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DOI: https://doi.org/10.1007/JHEP04(2024)136