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All solutions of the localization equations for \( \mathcal{N}=2 \) quantum black hole entropy

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Abstract

We find the most general bosonic solution to the localization equations describing the contributions to the quantum entropy of supersymmetric black holes in four dimensional \( \mathcal{N}=2 \) supergravity coupled to n v vector multiplets. This requires the analysis of the BPS equations of the corresponding off-shell supergravity (including fluctuations of the auxiliary fields) with AdS 2 × S 2 attractor boundary conditions. Our work completes and extends the results of arXiv:1012.0265 that were obtained for the vector multiplet sector, to include the fluctuations of all the fields of the off-shell supergravity. We find that, when the auxiliary SU(2) gauge field strength vanishes, the most general supersymmetric configuration preserving four supercharges is labelled by n v + 1 real parameters corresponding to the excitations of the conformal mode of the graviton and the scalars of the n v vector multiplets. In the general case, the localization manifold is labelled by an additional SU(2) triplet of one-forms and a scalar function.

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  1. NIKHEF theory group, Science Park 105, 1098 XG, Amsterdam, The Netherlands

    Rajesh Kumar Gupta & Sameer Murthy

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  1. Rajesh Kumar Gupta
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Correspondence to Rajesh Kumar Gupta.

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ArXiv ePrint: 1208.6221

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Gupta, R.K., Murthy, S. All solutions of the localization equations for \( \mathcal{N}=2 \) quantum black hole entropy. J. High Energ. Phys. 2013, 141 (2013). https://doi.org/10.1007/JHEP02(2013)141

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  • DOI: https://doi.org/10.1007/JHEP02(2013)141

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