Dualities near the horizon

Ferrara, S.; Marrani, Alessio; Orazi, Emanuele; Trigiante, Mario

doi:10.1007/jhep11(2013)056

Cited by 16 publications

(19 citation statements)

References 60 publications

(164 reference statements)

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“…As observed in [84], at least for all automorphism groups of reduced FTS's over simple or semisimple rank-3 Jordan algebras it holds that (see e.g. [87])…”

Section: Let Us Consider a Particularly Simple Anti-symplectic Case mentioning

confidence: 75%

Black holes and general Freudenthal transformations

Borsten

Duff

Fernandez-Melgarejo

et al. 2019

J. High Energ. Phys.

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We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type E 7 . GFT can be considered as a 2-parameter, a, b ∈ R, generalisation of Freudenthal duality: x → x F = ax + bx, where x is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole andx is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by a 2 ± b 2 . For any x there exists a one parameter subset of GFT that leave the entropy invariant, a 2 ± b 2 = 1, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by span R {x,x} is closed under GFT and is foliated by the orbits of the Freudenthal rotations. Having introduced the basic definitions and presented their properties in detail, we consider the relation of GFT to the global symmetries or Udualities in the context of supergravity. We consider explicit examples in pure supergravity, axiondilaton theories and N = 2, D = 4 supergravities obtained from D = 5 by dimensional reductions associated to (non-degenerate) reduced FTS's descending from cubic Jordan Algebras.

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“…As observed in [84], at least for all automorphism groups of reduced FTS's over simple or semisimple rank-3 Jordan algebras it holds that (see e.g. [87])…”

Section: Let Us Consider a Particularly Simple Anti-symplectic Case mentioning

confidence: 75%

Black holes and general Freudenthal transformations

Borsten

Duff

Fernandez-Melgarejo

et al. 2019

J. High Energ. Phys.

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“…In this section we shall briefly review the Freudenthal duality in ungauged supergravity [27,29,31], and subsequently generalize it to the gauged case.…”

Section: Freudenthal Dualitymentioning

confidence: 99%

“…It can be defined as an anti-involutive, nonlinear map acting on symplectic spaces, in particular on the representation space in which the electromagnetic charges of the black holes sit. After its introduction in [27] in the context of the so-called U -duality Lie groups of type E 7 [28] in extended supergravity theories, interesting relations between Freudenthal duality, the Hessian matrix of the black hole entropy and the rigid special (pseudo-)Kähler metric of the prehomogeneous vector spaces associated to the Uorbits, were discovered and studied in [29,30]. In [31] Freudenthal duality was proved to be a symmetry not only of the classical Bekenstein-Hawking entropy, but also of the critical points of the black hole potential.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear symmetries of black hole entropy in gauged supergravity

Klemm

Marrani

Petri

et al. 2017

J. High Energ. Phys.

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Freudenthal duality in N = 2, D = 4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential F = −iX 0 X 1 and Fayet-Iliopoulos gauging.

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“…the standard form of this invariant can be expressed in the following manifestly Sp(6, R)-invariant form (see for instance [76])…”

Section: The Quartic Invariant In the 14 ′mentioning

confidence: 99%

Thec-map, Tits Satake subalgebras and the search for N=2 inflaton potentials

2015

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In this paper we address the general problem of including inflationary models exhibiting Starobinskylike potentials into (symmetric) N = 2 supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the N = 2 supergravities we are able to make a general statement on the possible α-attractor models which can obtained upon truncation. We find that in symmetric N = 2 models group theoretical constraints restrict the allowed values of the parameter α to be α = 1, 2 3 , 1 3 . This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric N = 2 supergravities, in particular on the so called c-map connection between Quaternionic Kähler manifolds starting from Special Kähler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically selfcontained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of N = 2 supergravities is reviewed in some detail.

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Dualities near the horizon

Cited by 16 publications

References 60 publications

Black holes and general Freudenthal transformations

Black holes and general Freudenthal transformations

Nonlinear symmetries of black hole entropy in gauged supergravity

Thec-map, Tits Satake subalgebras and the search for N=2 inflaton potentials

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