ONE-LOOP SUPERGRAVITY CORRECTIONS TO BLACK-HOLE ENTROPY AND RESIDUAL SUPERSYMMETRY

We study the one-loop corrections to the effective on-shell action of N=2 supergravity in the background of the Reissner-Nordstrom black hol e. In the extreme case the contributions from the graviton, gravitino, and photon to the one-loop corrections to the entropy are shown to ca ncel. This gives the first explicit example of the supersymmetric nonr enormalization theorem for the on-shell action (entropy) for BPS confi gurations which admit Killing spinors. We display the residual supersy mmetry of the perturbations of a general supersymmetric theory in a bo sonic BPS background.