Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces
arXiv:1509.01031
Abstract
Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was introduced in four-dimensional Maxwell-Einstein theories coupled to a non-linear sigma model of scalar fields. In this short review, I will consider its relation to the U-duality Lie groups of type E7 in extended supergravity theories, and comment on the relation between the Hessian of the black hole entropy and the pseudo-Euclidean, rigid special (pseudo)Kaehler metric of the pre-homogeneous spaces associated to the U-orbits.
1+10 pages, 2 Tables. v2: Eq. (7) added. Talk presented at the Conference "Group Theory, Probability, and the Structure of Spacetime", in honor of V. S. Varadarajan, UCLA Dept. of Mathematics, Nov. 7-9 2014. To appear in a special issue of "p-Adic Numbers, Ultrametric Analysis and Applications"
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