Static BPS black holes in U(1) gauged supergravity

TL;DR

This work addresses the challenge of classifying static $1/4$-BPS AdS$_4$ black holes in Fayet-Iliopoulos gauged $ ext{N}=2$ supergravity with symmetric scalar manifolds. By leveraging very special geometry, the authors simplify the BPS flow to depend on a single covariant scalar combination and show that the full flow can be reconstructed from the attractor data, encoded in a real symplectic vector $oldsymbol{B}$ that satisfies $(1/4) I_4'(oldsymbol{B},oldsymbol{B},G)=oldsymbol{ extGamma}$ with horizon constraints. The paper provides a unified, duality-covariant framework for static AdS$_4$ BPS solutions, derives explicit first-order flow equations for the radial evolution, and demonstrates that attractor geometries lift to full black holes with entropy $oldsymbol{ ext{E}}=rac{}{} oldsymbol{ ext{E}}=oldsymbol{ ext{E}}=oldsymbol{ ext{E}}=oldsymbol{ ext{E}}=oldsymbol{ ext{E}}=oldsymbol{ ext{E}}=oldsymbol{ ext{E}}=oldsymbol{ ext{E}}$, i.e., $oldsymbol{ ext{E}}= ext{}\pi ig(I_4(oldsymbol{B})ig)^{1/2}$. Explicit STU-model examples, including the $t^3$ truncation and general STU charge configurations, illustrate the existence of rich dyonic BPS branches with finite horizons and, in some cases, nontrivial axions. The approach yields concrete algebraic constraints determined by the quartic invariant $I_4$ and offers a path to generalize to stationary solutions or theories with hypermultiplets on symmetric manifolds, thereby expanding analytic control over gauged AdS$_4$ black holes and their holographic implications.

Abstract

We consider the flow equations for $1/4$-BPS asymptotically AdS$_4$ static black holes in Fayet-Iliopoulos gauged supergravity, using very special geometry identities to obtain a simplified form in the most general case. Under mild assumptions on the form of the solution, we analyse the flow equations and find an explicit solution for arbitrary gauging and charge vectors within the chosen ansatz. Comparing with the corresponding attractor equations, we find that the solution is given in terms of exactly the same vector of parameters, implying that all regular attractors can be extended to full black hole solutions. We present explicit examples of black hole solutions with all complex scalars and charges allowed by the ansatz turned on, within the STU model and its truncations.