Abstract
Supersymmetric terms in the effective action of \( \mathcal{N}=2 \) supergravity in four dimensions are generically classified into chiral-superspace integrals and full-superspace integrals. For a theory of \( \mathcal{N}=2 \) vector multiplets coupled to supergravity, a special class of couplings is given by chiral-superspace integrals that are governed by a holomorphic prepotential function. The quantum entropy of BPS black holes in such theories depends on the prepotential according to a known integral formula. We show, using techniques of localization, that a large class of full-superspace integrals in the effective action of \( \mathcal{N}=2 \) supergravity do not contribute to the quantum entropy of BPS black holes at any level in the derivative expansion. Our work extends similar results for semi-classical supersymmetric black hole entropy, and goes towards providing an explanation of why the prepotential terms capture the exact microscopic quantum black hole entropy.
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ArXiv ePrint: 1306.3796
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Murthy, S., Reys, V. Quantum black hole entropy and the holomorphic prepotential of \( \mathcal{N}=2 \) supergravity. J. High Energ. Phys. 2013, 99 (2013). https://doi.org/10.1007/JHEP10(2013)099
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DOI: https://doi.org/10.1007/JHEP10(2013)099