Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity

Abstract

One would often like to know when two a priori distinct extremal black p-brane solutions are in fact U-duality related. In the classical supergravity limit the answer for a large class of theories has been known for some time. However, in the full quantum theory the U-duality group is broken to a discrete subgroup and the question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of N=8 supergravity in four, five and six dimensions. The purpose of this note is to present and clarify what is currently known about these discrete orbits while at the same time filling in some of the details not yet appearing in the literature. To this end we exploit the mathematical framework of integral Jordan algebras and Freudenthal triple systems. The charge vector of the dyonic black string in D=6 is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. The situation in four dimensions is less clear: while black holes preserving more than 1/8 of the supersymmetries may be fully classified by known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes a complete classification is known. All projective black holes are E_{7(7)}(Z) related to a four or five charge canonical form determined uniquely by the set of known arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the charge vectors of black holes with a given leading-order entropy.

43 pages, 8 tables; minor corrections, references added; version to appear in Class. Quantum Grav

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Cited by in corpus (22)

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• On the Black-Hole/Qubit Correspondence
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• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• Global symmetries of Yang-Mills squared in various dimensions
• Small Orbits
• Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity
• Branes, Weights and Central Charges
• Freudenthal Dual Lagrangians
• Exceptional Reductions
• Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
• Topics in Cubic Special Geometry
• Iwasawa N=8 Attractors
• A Kind of Magic
• Small Black Hole Constituents and Horizontal Symmetry
• Orbits in Non-Supersymmetric Magic Theories
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Real weights, bound states and duality orbits
• Freudenthal ranks: GHZ vs. W
• Peccei-Quinn Transformations and Black Holes : Orbit Transmutations and Entanglement Generation
• Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
• Jordan meets Freudenthal. A Black Hole Exceptional Story