Abstract
We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to ℤ N orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter-BPS black holes in \( \mathcal{N}=4 \) supergravity and one-eighth BPS black holes in \( \mathcal{N}=8 \) supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half-BPS black holes in \( \mathcal{N}=2 \) supergravity depends non-trivially on the ℤ N orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on ℤ N orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to ℤ N orbifolds of hyperboloids to an expression involving the Harish-Chandra character of sl (2, R), a result which is of possible mathematical interest.
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Gupta, R.K., Lal, S. & Thakur, S. Logarithmic corrections to extremal black hole entropy in \( \mathcal{N}=2 \), 4 and 8 supergravity. J. High Energ. Phys. 2014, 72 (2014). https://doi.org/10.1007/JHEP11(2014)072
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DOI: https://doi.org/10.1007/JHEP11(2014)072