Abstract
Supersymmetric localization has led to remarkable progress in computing quantum corrections to BPS black hole entropy. The program has been successful especially for computing perturbative corrections to the Bekenstein-Hawking area formula. In this work, we consider non-perturbative corrections related to polar states in the Rademacher expansion, which describes the entropy in the microcanonical ensemble. We propose that these non-perturbative effects can be identified with a new family of saddles in the localization of the quantum entropy path integral. We argue that these saddles, which are euclidean AdS2 × S1 × S2 geometries, arise after turning on singular fluxes in M-theory on a Calabi-Yau. They cease to exist after a certain amount of flux, resulting in a finite number of geometries; the bound on that number is in precise agreement with the stringy exclusion principle. Localization of supergravity on these backgrounds gives rise to a finite tail of Bessel functions in agreement with the Rademacher expansion. As a check of our proposal, we test our results against well known microscopic formulas for one-eighth and one-quarter BPS black holes in \( \mathcal{N}=8 \) and \( \mathcal{N}=4 \) string theory respectively, finding agreement. Our method breaks down precisely when mock-modular effects are expected in the entropy of one-quarter BPS dyons and we comment upon this. Furthermore, we mention possible applications of these results, including an exact formula for the entropy of four dimensional \( \mathcal{N}=2 \) black holes.
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Gomes, J. Quantum black hole entropy, localization and the stringy exclusion principle. J. High Energ. Phys. 2018, 132 (2018). https://doi.org/10.1007/JHEP09(2018)132
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DOI: https://doi.org/10.1007/JHEP09(2018)132