Black holes admitting a Freudenthal dual

Abstract

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.

32 pages revtex, 10 tables; minor corrections, references added

References in corpus (51)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Unity of Superstring Dualities
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Counting Dyons in N=4 String Theory
• Solitonic Strings and BPS Saturated Dyonic Black Holes
• Four Dimensional String/String/String Triality
• New Connections Between 4D and 5D Black Holes
• Precision Counting of Small Black Holes
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
• STU Black Holes and String Triality
• E(7) Symmetric Area of the Black Hole Horizon
• General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus
• Counting BPS Blackholes in Toroidal Type II String Theory
• Massive String States as Extreme Black Holes
• Branes, central charges and U-duality invariant BPS conditions
• Black Holes and U-Duality
• Charge Orbits of Symmetric Special Geometries and Attractors
• String triality, black hole entropy and Cayley's hyperdeterminant
• Comments on the Spectrum of CHL Dyons
• Black Holes, Qubits and Octonions
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Strings, Black Holes, and Quantum Information
• Counting Dyons in N=8 String Theory
• Magic Supergravities, N= 8 and Black Hole Composites
• Stringy Black Holes and the Geometry of Entanglement
• E_7 and the tripartite entanglement of seven qubits
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• Bound States of Black Holes and Other $P$-Branes
• N=8 Dyon Partition Function and Walls of Marginal Stability
• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Freudenthal triple classification of three-qubit entanglement
• Multiplet Structures of BPS Solitons
• Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two
• E_6 and the bipartite entanglement of three qutrits
• Attractors with Vanishing Central Charge
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• Regular BPS black holes: macroscopic and microscopic description of the generating solution
• Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
• A three-qubit interpretation of BPS and non-BPS STU black holes
• Wall Crossing Formula for N=4 Dyons: A Macroscopic Derivation
• Jordan algebras, exceptional groups, and higher composition laws
• Special entangled quantum systems and the Freudenthal construction
• U-duality Invariant Dyon Spectrum in type II on T^6
• Hidden symmetries of the Nambu-Goto action
• S-duality Action on Discrete T-duality Invariants
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• Microscopic entropy of the most general four-dimensional BPS black hole
• The generating solution of regular N=8 BPS black holes
• Unitary invariants of qubit systems
• Duality, Central Charges and Entropy of Extremal BPS Black Holes

Cited by in corpus (52)

• The black-hole/qubit correspondence: an up-to-date review
• Are all supergravity theories Yang-Mills squared?
• Freudenthal triple classification of three-qubit entanglement
• Degeneration of Groups of Type E7 and Minimal Coupling in Supergravity
• Freudenthal Duality and Generalized Special Geometry
• STU Black Holes as Four Qubit Systems
• Arithmetic of N=8 Black Holes
• The Freudenthal gauge symmetry of the black holes of N=2,d=4 supergravity
• Small Orbits
• Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
• Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity
• Freudenthal Dual Lagrangians
• Qubits from extra dimensions
• N=2 SUGRA BPS Multi-center solutions, quadratic prepotentials and Freudenthal transformations
• Entanglement classification of three fermions with up to nine single-particle states
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• Black Hole Nilpotent Orbits and Tits Satake Universality Classes
• Dualities Near the Horizon
• Hitchin functionals are related to measures of entanglement
• Exceptional Reductions
• Jordan C*-Algebras and Supergravity
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Two-Center Black Holes, Qubits and Elliptic Curves
• Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes
• Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
• The attractor mechanism as a distillation procedure
• Jordan Pairs, E6 and U-Duality in Five Dimensions
• Extremal Black Holes as Qudits
• Black holes and equivariant charge vectors in N=2,d=4 supergravity
• Nonlinear symmetries of black hole entropy in gauged supergravity
• Black holes and general Freudenthal transformations
• A Kind of Magic
• Attractors and first order formalism in five dimensions revisited
• Black Holes and Higher Composition Laws
• Entropy of non-extremal STU black holes: the F-invariant unveiled
• Classification of simple linearly compact Kantor triple systems over the complex numbers
• Real weights, bound states and duality orbits
• Magic Coset Decompositions
• The supersymmetric black holes of N=8 supergravity
• Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity
• Quantum Gravity Needs Supersymmetry
• Freudenthal ranks: GHZ vs. W
• Multi-Centered Invariants, Plethysm and Grassmannians
• Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
• Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces
• Peccei-Quinn Transformations and Black Holes : Orbit Transmutations and Entanglement Generation
• On Symmetries of Extremal Black Holes with One and Two Centers
• U-Duality and the Leech Lattice
• Supersymmetric Black Holes and Freudenthal Duality
• Perturbative and Non-Perturbative Aspects of N=8 Supergravity
• Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
• Freudenthal Duality in Conformal Field Theory