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Freudenthal duality in gravity: from groups of type E 7 to pre-homogeneous spaces

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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 E 7 in extended supergravity theories, and comment on the relation between the Hessian of the black hole entropy and the pseudo-Euclidean, rigid special (pseudo)Kähler metric of the pre-homogeneous spaces associated to the U-orbits.

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Authors and Affiliations

  1. Centro Studi e Ricerche “Enrico Fermi”, Via Panisperna 89A, I-00184, Roma, Italy

    A. Marrani

  2. Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova Via Marzolo 8, I-35131, Padova, Italy

    A. Marrani

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Correspondence to A. Marrani.

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Marrani, A. Freudenthal duality in gravity: from groups of type E 7 to pre-homogeneous spaces. P-Adic Num Ultrametr Anal Appl 7, 322–331 (2015). https://doi.org/10.1134/S207004661504007X

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