Conformal Symmetries for Extremal Black Holes with General Asymptotic Scalars in STU Supergravity

TL;DR

This paper constructs the most general BPS black hole solutions in STU supergravity with arbitrary scalar asymptotics, revealing a conformal symmetry that maps solutions within a fourteen-parameter family.

Contribution

It provides the first comprehensive construction of general BPS black holes with arbitrary asymptotic scalars in STU supergravity, including a conformal inversion symmetry.

Findings

Constructed the most general BPS black holes with arbitrary scalar asymptotics.

Identified a conformal inversion symmetry of the Couch-Torrence type.

Presented simplified solutions suitable for further studies.

Abstract

We present a construction of the most general BPS black holes of STU supergravity (${\cal N}=2$ supersymmetric $D=4$ supergravity coupled to three vector super-multiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.