Dualities Near the Horizon

Abstract

In 4-dimensional supergravity theories, covariant under symplectic electric-magnetic duality rotations, a significant role is played by the symplectic matrix M(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 N = 2 BPS case), this matrix enjoys a universal form in terms of the dyonic charge vector Q and the invariants of the corresponding symplectic representation RQ of the duality group G, whenever the scalar manifold is a symmetric space with G simple and non-degenerate of type E7. At attractors with flat directions, M still depends on flat directions, but not MQ, defining the so-called Freudenthal dual of Q itself. This allows for a universal expression of the symplectic vector field strengths in terms of Q, in the near-horizon Bertotti-Robinson black hole geometry.

1+31 pages, 1 Table; v2 : completely reorganized (and shortened) structure, some Sections removed; various clarifications, formulae, and Refs. added; to appear on JHEP

References in corpus (9)

• Charge Orbits of Symmetric Special Geometries and Attractors
• On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
• Black holes admitting a Freudenthal dual
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• 4d/5d Correspondence for the Black Hole Potential and its Critical Points
• Twin Supergravities
• More on N=8 Attractors
• Exceptional Reductions
• Observations on the Darboux coordinates for rigid special geometry

Cited by in corpus (12)

• Gauged Supergravities
• Symplectic Deformations of Gauged Maximal Supergravity
• Electric-magnetic deformations of D=4 gauged supergravities
• Introductory Lectures on Extended Supergravities and Gaugings
• Nonlinear symmetries of black hole entropy in gauged supergravity
• Black holes and general Freudenthal transformations
• The $c$-map, Tits Satake subalgebras and the search for $\mathcal{N}=2$ inflaton potentials
• Stationary $D=4$ Black Holes in Supergravity: The Issue of Real Nilpotent Orbits
• Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity
• Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification
• Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces
• Supersymmetric Black Holes and Freudenthal Duality