Maurer-Cartan Equations and Black Hole Superpotentials in N =8 Supergravity

TL;DR

This paper derives the non-BPS extremal black hole superpotential in N=8, d=4 supergravity using Maurer-Cartan equations, providing an independent approach from previous methods that involved dimensional reduction.

Contribution

It introduces a novel derivation of the superpotential directly in four dimensions using Maurer-Cartan equations, avoiding dimensional reduction techniques.

Findings

Superpotential successfully derived in d=4 supergravity

Method offers an independent derivation from previous dimensional reduction approaches

Enhances understanding of black hole solutions in N=8 supergravity

Abstract

We retrieve the non-BPS extremal black hole superpotential of N=8, d=4 supergravity by using the Maurer-Cartan equations of the symmetric space E_7(7)/SU(8). This superpotential was recently obtained with different 3- and 4-dimensional techniques. The present derivation is independent on the reduction to d=3.