N=8 BPS Black Holes with 1/2 or 1/4 Supersymmetry and Solvable Lie Algebra Decompositions

TL;DR

This paper constructs explicit BPS black hole solutions in N=8 supergravity that preserve 1/2 or 1/4 of supersymmetry, linking these solutions to specific decompositions of a 70-dimensional solvable Lie algebra.

Contribution

It introduces a systematic method to derive BPS black hole solutions with higher supersymmetry fractions using Lie algebra decompositions, extending previous work on 1/8 supersymmetry cases.

Findings

Different Lie algebra decompositions correspond to distinct scalar field behaviors.

Solutions exhibit unique fixed points at the horizon depending on the decomposition.

The structure of scalar evolution is directly related to the preserved supersymmetry fraction.

Abstract

In the context of N=8 supergravity we construct the general form of BPS 0--branes that preserve either 1/2 or 1/4 of the original supersymmetry. We show how such solutions are related to suitable decompositions of the 70 dimensional solvable Lie algebra that describes the scalar field sector. We compare our new results to those obtained in a previous paper for the case of 1/8 supersymmetry preserving black holes. Each of the three cases is based on a different solvable Lie algebra decomposition and leads to a different structure of the scalar field evolution and of their fixed values at the horizon of the black hole.