2012/01/01 by Sergio Luigi Cacciatori, SERGIO LUIGI CACCIATORI, Bianca Letizia Cerchiai +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cartan decomposition #Cartan subalgebra #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie group #Noncommutative and Quantum Gravity Theories #Scalar (mathematics) #Subalgebra #Symmetry (geometry) #Symmetry group #Symplectic geometry #hep-th
paper · pdf · doi:10.1142/s2010194512006721
published as Int. J. Mod. Phys. Conf. Series 13, 44 (2012) · 11 pages, 1 figure, 1 table, Contribution to the Proceedings of the 'JW2011 Workshop on the Scientific and Human Legacy of Julius Wess', held August 27 - 28, 2011 in Donji Milanovac, Serbia
openalex publication_date 2012/01/01 · arxiv created 2012/02/14 · arxiv updated 2015/04/20 · openalex created_date 2016/09/16 · openalex updated_date 2026/08/05
We study some of the properties of the geometry of the exceptional Lie group E 7(7) , which describes the U-duality of the [Formula: see text], d = 4 supergravity. In particular, based on a symplectic construction of the Lie algebra 𝔢 7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space [Formula: see text], 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 [Formula: see text] as scalar configuration of the "large" ⅛-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 E 7(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.