One-Loop Supergravity Corrections to the Black Hole Entropy and Residual Supersymmetry

TL;DR

This paper calculates one-loop quantum corrections to black hole entropy in N=2 supergravity, demonstrating a non-renormalization property for BPS black holes due to residual supersymmetry, with explicit cancellations among quantum fields.

Contribution

It provides the first explicit example of supersymmetric non-renormalization of the on-shell action for BPS black holes with Killing spinors, including detailed analysis of residual supersymmetry.

Findings

Graviton, gravitino, and photon contributions cancel in the extremal case.

Demonstrates residual supersymmetry in perturbations around BPS backgrounds.

Provides explicit evidence for non-renormalization theorems in supergravity.

Abstract

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