Dualities near the horizon

• Published in: The journal of high energy physics 2013-11, Vol.2013 (11), p.1-33, Article 56
• Main Authors: Ferrara, Sergio, Marrani, Alessio, Orazi, Emanuele, Trigiante, Mario
• Format: Article
• Language: English
• Subjects: Asymptotic properties; Charge; Classical and Quantum Gravitation; Elementary Particles; Field strength; Flats; High energy physics; Invariants; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; Scalars; String Theory; Vectors (mathematics)
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2013)056

A bstract In 4-dimensional supergravity theories, covariant under symplectic electricmagnetic duality rotations, a significant role is played by the symplectic matrix ( φ ), related to the coupling of scalars φ to vector field-strengths. In particular, this matrix enters the twisted self-duality condition for 2-form field strengths in the symplectic formulation of generalized Maxwell equations in the presence of scalar fields. In this investigation, we compute several properties of this matrix in relation to the attractor mechanism of extremal (asymptotically flat) black holes. At the attractor points with no flat directions (as in the = 2 BPS case), this matrix enjoys a universal form in terms of the dyonic charge vector and the invariants of the corresponding symplectic representation of the duality group G , whenever the scalar manifold is a symmetric space with G simple and non-degenerate of type E 7 . At attractors with flat directions, still depends on flat directions, but not , defining the so-called Freudenthal dual of itself. This allows for a universal expression of the symplectic vector field strengths in terms of , in the near-horizon Bertotti-Robinson black hole geometry.