On Symmetries of Extremal Black Holes with One and Two Centers

  • Sergio Ferrara
  • Alessio Marrani
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 144)


After a brief introduction to the Attractor Mechanism, we review the appearance of groups of type \(E_{7}\) as generalized electric-magnetic duality symmetries in locally supersymmetric theories of gravity, with particular emphasis on the symplectic structure of fluxes in the background of extremal black hole solutions, with one or two centers. In the latter case, the role of an “horizontal” symmetry \(SL_{h}\left( 2,\mathbb{R }\right) \) is elucidated by presenting a set of two-centered relations governing the structure of two-centered invariant polynomials.


Black Hole Event Horizon Black Hole Solution Vector Multiplet Magnetic Charge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The reported results were obtained in different collaborations with Laura Andrianopoli, Leron Borsten, Anna Ceresole, Riccardo D’Auria, Mike Duff, G. W. Gibbons, Murat Günaydin, Renata Kallosh, Emanuele Orazi, William Rubens, Raymond Stora, A. Strominger, Mario Trigiante, and Armen Yeranyan, which we gratefully acknowledge. This work is supported by the ERC Advanced Grant no. 226455, “Supersymmetry, Quantum Gravity and Gauge Fields” (SUPERFIELDS).


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Physics DepartmentTheory Unit, CERNGeneva 23Switzerland
  2. 2.INFN-Laboratori Nazionali di FrascatiFrascatiItaly

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