Dyonic AdS black holes in maximal gauged supergravity

TL;DR

This paper constructs two new families of dyonic AdS black holes in four-dimensional maximal gauged supergravity: static solutions in $\mathcal{N}=2$, $\mathrm{U}(1)^4$ with four electric and four magnetic charges, and rotating solutions in $\mathcal{N}=2$, $\mathrm{U}(1)^2$ with two electric and two magnetic charges. The static class is obtained by gauging a previously known asymptotically flat STU-type solution via $R\to R+g^2W^2$, yielding a 10-parameter family, including planar and hyperbolic horizons, while the rotating class generalizes dyonic Kerr–Newman–AdS within a pairwise-equal truncation and, in several subcases, reduces to Kerr–Newman–AdS or ungauged solutions. A major focus is the thermodynamics of dyonic AdS black holes, showing that a consistent first law depends on the chosen boundary conditions for the gauge fields, with a detailed symplectic-structure analysis identifying three classes of admissible mixed boundary conditions and clarifying when the mass is integrable. The paper also uncovers hidden symmetries in the rotating solutions in the form of Killing tensors with torsion (KYT) in two conformal frames, enabling separability of the Hamilton–Jacobi and Klein–Gordon equations and highlighting rich geometric structures underlying these new black holes. The results have potential implications for AdS/CFT applications with finite density and magnetic fields and illuminate the interplay between boundary data, conserved charges, and integrability in gauged supergravity. All constructions are expressed in terms of precise metric ansätze, charge parameterizations, and explicit relations between ungauged and gauged frames, with explicit but compact forms provided for the rotating and static sectors. The work suggests natural extensions to fully eight-charge rotating AdS black holes and invites further exploration of the holographic and supersymmetric properties of these dyonic configurations.

Abstract

We present two new classes of dyonic anti-de Sitter black hole solutions of 4-dimensional maximal N=8, SO(8) gauged supergravity. They are: (1) static black holes of N=2, U(1)^4 gauged supergravity with 4 electric and 4 magnetic charges, with spherical, planar or hyperbolic horizons; and (2) rotating black holes of N=2, U(1)^2 gauged supergravity with 2 electric and 2 magnetic charges. We study their thermodynamics, and point out that the formulation of a consistent thermodynamics for dyonic anti-de Sitter black holes is dependent on the existence of boundary conditions for the gauge fields. We identify several distinct classes of boundary conditions for gauge fields in U(1)^4 supergravity. We study a general family of metrics containing the rotating solutions, and find Killing-Yano tensors with torsion in two conformal frames, which underlie separability.