Abstract
Dimensional reduction along time offers a powerful way to study stationary solutions of 4D symmetric supergravity models via group-theoretical methods. We apply this approach systematically to extremal, BPS and non-BPS, spherically symmetric black holes, and obtain their “fake superpotential” W. The latter provides first order equations for the radial problem, governs the mass and entropy formula and gives the semi-classical approximation to the radial wave function. To achieve this goal, we note that the Noether charge for the radial evolution must lie in a certain Lagrangian submanifold of a nilpotent orbit of the 3D continuous duality group, and construct a suitable parametrization of this Lagrangian. For general non-BPS extremal black holes in \( \mathcal{N} \) = 8 supergravity, W is obtained by solving a non-standard diagonalization problem, which reduces to a sextic polynomial in W 2 whose coefficients are SU(8) invariant functions of the central charges. By consistent truncation we obtain W for other supergravity models with a symmetric moduli space. In particular, for the one-modulus S 3 model, W 2 is given explicitely as the root of a cubic polynomial. The STU model is investigated in detail and the nilpotency of the Noether charge is checked on explicit solutions.
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ArXiv ePrint: 0908.1742
Unité mixte de recherche du CNRS UMR 7589
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Bossard, G., Michel, Y. & Pioline, B. Extremal black holes, nilpotent orbits and the true fake superpotential. J. High Energ. Phys. 2010, 38 (2010). https://doi.org/10.1007/JHEP01(2010)038
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DOI: https://doi.org/10.1007/JHEP01(2010)038