U-invariants, black-hole entropy and fixed scalars

Andrianopoli, Laura Maria; D’Auria, Riccardo; Ferrara, S.

doi:10.1016/s0370-2693(97)00454-1

Cited by 64 publications

(150 citation statements)

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“…The J H 3 -based theory can either be interpreted as N = 2 or as its "twin" N = 6 [39,41,69,70]; in the former case, the SU(2) commuting factor is the global hyper R-symmetry, whereas in the latter case it is the R-symmetry truncated away in the supersymmetry reduction N = 8 → N = 6 (a further truncation N = 6 → N = 3 is considered in subsection 4.1). In both cases, the truncation condition on the twoform Abelian is given in eq.…”

Section: Further Truncation To Minimal Couplingmentioning

confidence: 99%

Degeneration of groups of type E 7 and minimal coupling in supergravity

Ferrara

Каллош

Marrani

2012

J. High Energ. Phys.

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Abstract:We study properties of D = 4 N 2 extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of N = 1 supergravity. This involves a detailed classification of the "degenerations" of the duality groups of type E 7 , when the corresponding quartic invariant polynomial built from the symplectic irreducible representation of G 4 "degenerates" into a perfect square. With regard to cosmological applications, minimal coupling of vectors in consistent truncation to N = 1 from higher-dimensional or higher-N theory is non-generic. On the other hand, non-minimal coupling involving vectors coupled to scalars and axions is generic. These features of supergravity, following from the electric-magnetic duality, may be useful in other applications, like stabilization of moduli, and in studies of non-perturbative black-hole solutions of supergravity/string theory.

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Section: Further Truncation To Minimal Couplingmentioning

confidence: 99%

Degeneration of groups of type E 7 and minimal coupling in supergravity

Ferrara

Каллош

Marrani

2012

J. High Energ. Phys.

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“…the scalar configuration at the event horizon of the 1=8-BPS extremal BH is given by the origin of E 7ð7Þ SUð8Þ . Some care should be taken with regard to ''flat'' directions [8,19]. Because of the existence of the moduli space SUð6ÞÂSUð2Þ (which is the c map [20] of the vector multiplets' scalar manifold of N ¼ 2, d ¼ 4 ''magic'' supergravity based on J C 3 ), can be set to any real value, without affecting the RN BH entropy (1.1).…”

Section: Kkmentioning

confidence: 99%

“…We recall that the quartic invariant of the U-duality group SLð2; RÞ Â SOð6; nÞ of N ¼ 4, d ¼ 4 supergravity coupled to n vector multiplets is [8] …”

Section: Embedding Of the Axion-dilaton Extremal Bhmentioning

confidence: 99%

“…These are the duality groups of the low energy actions, whose discrete subgroups appear as symmetries of the nonperturbative spectrum of BPS states [2]. These orbits, which have been further studied in ( [3][4][5], correspond to well-defined categories of allowed entropies of extremal BHs in d ¼ 5 and in d ¼ 4, given in terms of the cubic E 6ð6Þ invariant I 3 ( [1,4,6]) and the quartic E 7ð7Þ invariant I 4 ( [7][8][9]). There are three types of orbits depending on whether the BH background preserves 1=2, 1=4, or 1=8 of the original supersymmetry.…”

Section: Introductionmentioning

confidence: 99%

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More onN=8attractors

et al. 2009

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We examine a few simple extremal black hole configurations of N ¼ 8, d ¼ 4 supergravity. We first elucidate the relation between the BPS Reissner-Nördstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N ¼ 8 supergravity.

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“…Moreover, non compact homogeneous spaces and their non compact duality group G appear in the description of the black hole orbits [9,10,11,12] as well as duality invariant Bekenstein-Hawking entropy formula [13,14,15,16] according to the attractor mechanism [17,18,19]. The study of the attractor mechanism in string theory has been pioneered in [20].…”

Section: Introductionmentioning

confidence: 99%

Iwasawa nilpotency degree of non compact symmetric cosets in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} $\end{document}‐extended supergravity

Cacciatori

Cerchiai

Ferrara

et al. 2014

Fortschritte der Physik

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We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU (2) P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian.We consider symmetric scalar manifolds in N−extended supergravity in various space-time dimensions, elucidating various relations with the underlying Jordan algebras and normed Hurwitz algebras. For magic supergravity theories, our results are consistent with the Tits-Satake projection of symmetric spaces and the nilpotency degree turns out to depend only on the space-time dimension of the theory.These results should be helpful within a deeper investigation of the corresponding supergravity theory, e.g. in studying ultraviolet properties of maximal supergravity in various dimensions.

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U-invariants, black-hole entropy and fixed scalars

Cited by 64 publications

References 50 publications

Degeneration of groups of type E 7 and minimal coupling in supergravity

Degeneration of groups of type E 7 and minimal coupling in supergravity

More onN=8attractors

Iwasawa nilpotency degree of non compact symmetric cosets in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} $\end{document}‐extended supergravity

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