Small Orbits

Abstract

We study both the "large" and "small" U-duality charge orbits of extremal black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras and their associated Freudenthal triple systems, in order to derive the minimal charge representatives, their stabilizers and the associated "moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2 and N = 4 theories coupled to an arbitrary number of vector multiplets, as well as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered as part of the general N = 2 sequence, albeit with an additional triality symmetry, the ST^2 and T^3 models demand a separate treatment, since their representative Jordan algebras are Euclidean or only admit non-zero elements of rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter coupled N = 3, and "pure" N = 5 theories.

40 pages, 9 tables. References added. Expanded comments added to sections III. C. 1. and III. F. 3

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Cited by in corpus (22)

• Gauged Supergravities
• The black-hole/qubit correspondence: an up-to-date review
• Are all supergravity theories Yang-Mills squared?
• Freudenthal Dual Lagrangians
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Integrable Scalar Cosmologies II. Can they fit into Gauged Extended Supergavity or be encoded in N=1 superpotentials?
• Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
• Jordan Pairs, E6 and U-Duality in Five Dimensions
• Black holes and general Freudenthal transformations
• A Kind of Magic
• Orbits in Non-Supersymmetric Magic Theories
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Real weights, bound states and duality orbits
• Sextonions, Zorn Matrices, and ${\mathbf{e}}_{7\frac{1}{2}}$
• Fermions, Wigs, and Attractors
• Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
• Iwasawa nilpotency degree of non compact symmetric cosets in N-extended Supergravity
• Peccei-Quinn Transformations and Black Holes : Orbit Transmutations and Entanglement Generation
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• Jordan meets Freudenthal. A Black Hole Exceptional Story
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• On Symmetries of Extremal Black Holes with One and Two Centers