On Invariant Structures of Black Hole Charges

Abstract

We study "minimal degree" complete bases of duality- and "horizontal"- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D=4 Einstein supergravity models with symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R) "horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting maximal manifest covariance) and until order six in the fluxes included. The second class, exhibiting a non-trivial "horizontal" stabilizer SO(2), includes N=2 minimally coupled and N=3 matter coupled theories, with U-duality given by the pseudo-unitary group U(r,s) (related to complex flux representations). Finally, we comment on the formulation of special Kaehler geometry in terms of "generalized" groups of type E7.

1+24 pages; 1 Table. v2 : Eqs. (1.2) and (1.3) added; Eq. (2.87) changed

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Cited by in corpus (11)

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• Rotating attractors and BPS black holes in $Ad{S}_4$
• Octonionic black holes
• Degeneration of Groups of Type E7 and Minimal Coupling in Supergravity
• Static BPS black holes in U(1) gauged supergravity
• Freudenthal Dual Lagrangians
• Real weights, bound states and duality orbits
• Quarter-BPS Black Holes in AdS${}_4$-NUT from $N=2$ Gauged Supergravity
• Multi-Centered First Order Formalism
• Multi-Centered Invariants, Plethysm and Grassmannians
• Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification