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We study the one-loop corrections to the effective on-shell action of N=2supergravity in the background of the Reissner-Nordstrom black hole. In theextreme case the contributions from graviton, gravitino and photon to theone-loop corrections to the entropy are shown to cancel. This gives the firstexplicit example of the supersymmetric non-renormalization theorem for theon-shell action (entropy) for BPS configurations which admit Killing spinors.We display the residual supersymmetry of the perturbations of a generalsupersymmetric theory in a bosonic BPS background.Comment: 13 Pages, LaTe

One-loop supergravity corrections to black hole entropy and residual supersymmetry