Supersymmetric AdS_4 black holes and attractors (0911.4926v1)

Abstract: Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets were classified, we construct the first examples of genuine supersymmetric black holes in AdS_4 with nonconstant scalar fields. This is done for various choices of the prepotential, amongst others for the STU model. These solutions permit to study the BPS attractor flow in AdS. We also determine the most general supersymmetric static near-horizon geometry and obtain the attractor equations in gauged supergravity. As a general feature we find the presence of flat directions in the black hole potential, i.e., generically the values of the moduli on the horizon are not completely specified by the charges. For one of the considered prepotentials, the resulting moduli space is determined explicitely. Still, in all cases, we find that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.

• The paper constructs explicit supersymmetric AdS4 black holes with nonconstant scalar fields using attractor equations in N=2 gauged supergravity.
• The study reveals that scalar field moduli can exhibit flat directions at the horizon, showing cases where charges do not entirely fix their values.
• Detailed models, including the STU model, provide insights into attractor mechanisms and their implications for quantum gravity and the AdS/CFT correspondence.

Overview of "Supersymmetric AdS Black Holes and Attractors"

The paper by Sergio L. Cacciatori and Dietmar Klemm explores the construction of genuine supersymmetric black holes with non-trivial scalar fields in four-dimensional anti-de Sitter space (AdS$_4$) within the framework of N=2, D=4 gauged supergravity. This work builds upon prior classifications of timelike supersymmetric solutions, namely the systematic approach outlined in earlier research, and attempts to broaden the understanding of black hole solutions that preserve supersymmetry. The authors expand the exploration of solutions under various prepotentials, including detailed examinations within the STU model, and they investigate the implications of the BPS (Bogomol'nyi-Prasad-Sommerfield) attractor flow in AdS$_4$.

Supersymmetric Black Hole Solutions

One key focus of the paper is constructing static BPS black holes with nonconstant scalar fields by leveraging a set of known attractor equations in gauged supergravity. The paper examines various prepotential forms, such as the STU model's internal mechanics, providing examples of BPS black hole configurations. The authors highlight several significant insights regarding moduli spaces, noting that in some instances, the moduli values at the horizon are not completely determined by the black hole's charges, leading to the existence of flat directions in the black hole potential.

Detailed Examples and Models

The paper thoroughly dissects multiple models to demonstrate the applicability and limitations of their approach:

• SU(1,1)/U(1) Model: Introduces solutions with a single vector multiplet, emphasizing constraints where moduli remain unfixed by charges, thereby existing in a nontrivial moduli space.
• STU Model: Explores this model with several prepotential variations, showcasing solutions with all nonconstant scalars while asserting certain expected charge-dependent quantization conditions.
• General Model Analysis: A near-horizon approach outlines attractor equations, offering potential pathways to determine scalar moduli in terms of charges.

Implications and Future Directions

The findings in this paper have both theoretical and practical implications. The ability to construct explicit supersymmetric solutions in AdS space has significant bearings on understanding quantum gravity and the AdS/CFT correspondence. Furthermore, insights into the attractor mechanism provide promising avenues for exploring how scalar fields settle into constant charge-dependent values, a quintessential feature of black holes in string theory.

Several open questions remain, particularly regarding the general invertibility of the attractor equations in gauged supergravity cases and a deeper understanding of the dynamics when flat directions in black hole potentials arise. Future research could focus on exploring different gauged supergravity frameworks or extending this work's principles to higher dimensions, enhancing the comprehension of quantum gravity regimes. The results could be pivotal in understanding the microscopic foundation of black hole entropy, a long-standing challenge in theoretical physics.

In summary, this paper significantly contributes to the continuing examination of supersymmetric black holes in AdS space, providing a framework for expanding current theoretical models of quantum gravity and their ramifications in the broader context of string theory.