Abstract
We use the techniques of supersymmetric localization to compute the BPS black hole entropy in \( \mathcal{N}=2 \) supergravity. We focus on the n v + 1 vector multiplets on the black hole near horizon background which is AdS2 × S2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one-loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one-loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one-loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.
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Gupta, R.K., Ito, Y. & Jeon, I. Supersymmetric localization for BPS black hole entropy: 1-loop partition function from vector multiplets. J. High Energ. Phys. 2015, 197 (2015). https://doi.org/10.1007/JHEP11(2015)197
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DOI: https://doi.org/10.1007/JHEP11(2015)197