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Non-linear Symmetries in Maxwell-Einstein Gravity: From Freudenthal Duality to Pre-homogeneous Vector Spaces

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Lie Theory and Its Applications in Physics (LT 2019)

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Abstract

We review the relation between Freudenthal duality and U-duality Lie groups of type \(E_{7}\) in extended supergravity theories, as well as 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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Notes

  1. 1.

    Here U-duality is referred to as the “continuous” symmetries of [21]. Their discrete versions are the U-duality non-perturbative string theory symmetries introduced by Hull and Townsend [22].

  2. 2.

    For a thorough introduction to special Kähler geometry, see e.g. [34].

  3. 3.

    To be more precise, it is worth mentioning that the actual relevant coset manifold is \(E_{7(7)}/[SU(8)/Z_{2}]\), because spinors transform according to the double cover of the stabilizer of the scalar manifold (see e.g. [35, 36], and Refs. therein).

  4. 4.

    The signature along the \(R^{+}\)-direction is negative [32].

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  1. Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Via Panisperna 89A, 00184, Rome, Italy

    Alessio Marrani

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  1. Alessio Marrani
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Correspondence to Alessio Marrani .

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  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Marrani, A. (2020). Non-linear Symmetries in Maxwell-Einstein Gravity: From Freudenthal Duality to Pre-homogeneous Vector Spaces. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2019. Springer Proceedings in Mathematics & Statistics, vol 335. Springer, Singapore. https://doi.org/10.1007/978-981-15-7775-8_16

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