4d/5d Correspondence for the Black Hole Potential and its Critical Points

Abstract

We express the d=4, N=2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d=5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of attractors and the respective entropies. These are related by simple formulae, interpolating between four and five dimensions, depending on the volume modulus and on the 4d magnetic (or electric) charges, and holding true also for generic field configurations and for non-symmetric cubic geometries.

1+24 pages; v2: references added, minor improvements; v3: further minor improvements and clarifications

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Cited by in corpus (45)

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• stu Black Holes Unveiled
• Erice Lectures on Black Holes and Attractors
• Twin Supergravities from Yang-Mills Squared
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• First order flows for N=2 extremal black holes and duality invariants
• Universality of the superpotential for d = 4 extremal black holes
• Non-BPS Attractors in 5d and 6d Extended Supergravity
• Holographic RG flow dual to attractor flow in extremal black holes
• Attractors in Black
• Separation of Attractors in 1-modulus Quantum Corrected Special Geometry
• Small Orbits
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• Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
• 5D Black Holes and Non-linear Sigma Models
• Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity
• More on N=8 Attractors
• Quantum Lift of Non-BPS Flat Directions
• Dualities Near the Horizon
• Intersecting Attractors
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• On Quantum Special Kaehler Geometry
• Black string first order flow in N=2, d=5 abelian gauged supergravity
• Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
• A Note on Exact Solutions and Attractor Mechanism for Non-BPS Black Holes
• 5d/4d U-dualities and N=8 black holes
• Special Geometry, Hessian Structures and Applications
• Topics in Cubic Special Geometry
• Multiple Single-Centered Attractors
• On the Uniqueness of Supersymmetric Attractors
• On the correspondence between black holes, domain walls and fluxes
• Attractors and first order formalism in five dimensions revisited
• Black holes and general Freudenthal transformations
• Extremal Black Brane Attractors on The Elliptic Curve
• d-Geometries Revisited
• SAM Lectures on Extremal Black Holes in d=4 Extended Supergravity
• Real weights, bound states and duality orbits
• First-order attractor flow equations for supersymmetric black rings in N=2, D=5 supergravity
• Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification
• Attractor Flows in st^2 Black Holes
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• Jordan meets Freudenthal. A Black Hole Exceptional Story
• No Fermionic Wigs for BPS Attractors in 5 Dimensions
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• On the Supersymmetry of Bianchi attractors in Gauged supergravity