N=8 BPS black holes preserving 1/8 supersymmetry

TL;DR

This paper provides an exact solution for 1/8 BPS black holes in N=8 supergravity, detailing their scalar fields, gauge fields, and entropy, with a focus on their embedding in special Kähler geometry and the Solvable Lie Algebra formalism.

Contribution

It offers a detailed analysis and explicit solution of 1/8 BPS black holes within N=8 supergravity, connecting group-theoretical methods with supergravity solutions.

Findings

Exact scalar and gauge field solutions with non-trivial radial dependence.

U-duality invariant entropy expression.

Embedding in special Kähler manifold of the T^6/Z^3 orbifold.

Abstract

In the context of N=8 supergravity we consider BPS black-holes that preserve 1/8 supersymmetry. It was shown in a previous paper that, modulo U-duality transformations of E_{7(7)} the most general solution of this type can be reduced to a black-hole of the STU model. In this paper we analize this solution in detail, considering in particular its embedding in one of the possible Special K\"ahler manifold compatible with the consistent truncations to N=2 supergravity, this manifold being the moduli space of the T^6/Z^3 orbifold, that is: SU(3,3)/SU(3)*U(3). This construction requires a crucial use of the Solvable Lie Algebra formalism. Once the group-theoretical analisys is done, starting from a static, spherically symmetric ans\"atz, we find an exact solution for all the scalars (both dilaton and axion-like) and for gauge fields, together with their already known charge-dependent fixed values, which yield a U-duality invariant entropy. We give also a complete translation dictionary between the Solvable Lie Algebra and the Special K\"ahler formalisms in order to let comparison with other papers on similar issues being more immediate. Although the explicit solution is given in a simplified case where the equations turn out to be more manageable, it encodes all the features of the more general one, namely it has non-vanishing entropy and the scalar fields have a non-trivial radial dependence.