Extremal Black Hole and Flux Vacua Attractors

Abstract

These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $C{Y}_3$ and its orientifolded version, associated with $\frac{C{Y}_3\times T^2}{{\mathbb{Z}}_2}$. Finally, recent results on the U-duality orbits and moduli spaces of non-BPS extremal black hole attractors in $3⩽N⩽8$, d=4 supergravities are reported.

1+74 pages, 2 Tables. Contribution to the Proceedings of the Winter School on Attractor Mechanism 2006 (SAM2006), 20-24 March 2006, INFN-LNF, Frascati, Italy

References in corpus (16)

• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
• Stationary black holes and attractor mechanism
• Magic Supergravities, N= 8 and Black Hole Composites
• On some properties of the Attractor Equations
• N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
• New Attractors, Entropy Function and Black Hole Partition Function
• Critical points of the Black-Hole potential for homogeneous special geometries
• Attractors with Vanishing Central Charge
• BPS Microstates and the Open Topological String Wave Function
• N=2 Supersymmetric Black Attractors in Six and Seven Dimensions
• New attractor mechanism for spherically symmetric extremal black holes
• Separation of Attractors in 1-modulus Quantum Corrected Special Geometry
• Non-Kaehler attracting manifolds
• The Attractor Mechanism in Gauss-Bonnet Gravity
• On the critical points of the entropic principle

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• d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms
• Holographic RG flow dual to attractor flow in extremal black holes
• Attractors in Black
• More on N=8 Attractors
• Quantum Lift of Non-BPS Flat Directions
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• BPS and non BPS 7D Black Attractors in M-Theory on K3
• Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
• On Black Objects in Type IIA Superstring Theory on Calabi-Yau Manifolds
• On special geometry of the moduli space of string vacua with fluxes
• Intersecting Black Attractors in 8D N=1 Supergravity
• Geometric Design and Stability of Power Networks
• Charge Orbits and Moduli Spaces of Black Hole Attractors
• Perturbative and Non-Perturbative Aspects of N=8 Supergravity
• Stable Bianchi III attractor in $U(1{)}_R$ gauged supergravity