d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms

TL;DR

This paper extends the black hole attractor mechanism in N=2 supergravity to include Fayet-Iliopoulos terms, analyzing stability and critical points across different models and symplectic frames, with implications beyond supersymmetry.

Contribution

It generalizes the attractor mechanism to gauged supergravity without hypermultiplets and explores stability in various models and frames, including non-supersymmetric contexts.

Findings

Attractor points are semi-positive definite in Hessian analysis.

The framework applies to multiple symplectic frames and extends to higher dimensions.

Fayet-Iliopoulos terms influence the structure of black hole solutions.

Abstract

We generalize the description of the d=4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d>4, as well. Thence, we work out the example of the stu model of N=2 supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and D0-D6 BH charge configurations, and in three different symplectic frames: the SO(1,1)^{2}, SO(2,2) covariant and SO(8)-truncated ones. The attractive nature of the critical points, related to the semi-positive definiteness of the Hessian matrix, is also studied.