FERMION ZERO MODES AND BLACK-HOLE HYPERMULTIPLETS WITH RIGID SUPERSYMMETRY

TL;DR

This paper investigates zero modes of gravitini and dilatini in extreme black-hole solutions within supergravity theories, demonstrating their normalizability, duality invariance, and the supersymmetric structure of multi-black-hole backgrounds.

Contribution

It provides a detailed analysis of fermionic zero modes in black-hole backgrounds and introduces a rigid supersymmetry framework for multi-black-hole solutions in N=2 supergravity.

Findings

Gravitini zero modes are normalizable on extreme Reissner-Nordstrom black holes.

Fermionic zero modes have finite, duality-invariant norms.

The N=2 hypermultiplet action is shown to be rigidly supersymmetric in multi-black-hole backgrounds.

Abstract

The gravitini zero modes riding on top of the extreme Reissner-Nordstrom black-hole solution of N=2 supergravity are shown to be normalizable. The gravitini and dilatini zero modes of axion-dilaton extreme black-hole solutions of N=4 supergravity are also given and found to have finite norms. These norms are duality invariant. The finiteness and positivity of the norms in both cases are found to be correlated with the Witten-Israel-Nester construction; however, we have replaced the Witten condition by the pure-spin-3/2 constraint on the gravitini. We compare our calculation of the norms with the calculations which provide the moduli space metric for extreme black holes. The action of the N=2 hypermultiplet with an off-shell central charge describes the solitons of N=2 supergravity. This action, in the Majumdar-Papapetrou multi-black-hole background, is shown to be N=2 rigidly supersymmetric.