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, \( \mathbb{R} \)) “horizontal” symmetry which mixes the two centers. The first class encompasses \( \mathcal{N} = {2} \) and \( \mathcal{N} = {4} \) matter-coupled theories, with semisimple U-duality given by SL(2, \( \mathbb{R} \)) × 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 \( \mathcal{N} = {2} \) minimally coupled and \( \mathcal{N} = 3 \) matter coupled theories, with U-duality given by the pseudounitary group U(r,s) (related to complex flux representations). Finally, we comment on the formulation of special Kähler geometry in terms of “generalized” groups of type E 7.
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Ferrara, S., Marrani, A. & Yeranyan, A. On invariant structures of black hole charges. J. High Energ. Phys. 2012, 71 (2012). https://doi.org/10.1007/JHEP02(2012)071
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DOI: https://doi.org/10.1007/JHEP02(2012)071