Universality of the superpotential for d = 4 extremal black holes

TL;DR

This paper develops a universal method to derive the superpotential for extremal black holes in N=2 supergravity, applicable to BPS and non-BPS cases, and demonstrates its use in specific models and the full N=8 theory.

Contribution

It introduces a general strategy to obtain the superpotential W for extremal black holes in symmetric space supergravities, extending previous U-duality invariant constructions.

Findings

Explicit superpotentials for st^2 and stu models.

Solution of gradient flows for these models.

Applicability to full N=8 supergravity.

Abstract

We provide a general strategy to obtain the superpotential W for both BPS and non-BPS extremal black holes in N=2 four dimensional supergravities based on symmetric spaces. This extends the construction of W in terms of U-duality invariants that was presented in previous work on the $t^3$ model. As an application, we explicitly provide W and the solutions to the related gradient flows for the $st^2$ and stu models. The procedure is shown to hold also for the full N=8 theory. The role of flat directions in moduli space is clarified.