Adams-Iwasawa N=8 Black Holes

Abstract

We study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames.