Exceptional supergravity theories and the magic square

Günaydın, Murat; Sierra, Germȧn; Townsend, Paul

doi:10.1016/0370-2693(83)90108-9

Cited by 280 publications

(597 citation statements)

References 6 publications

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“…Interestingly, for the magic Maxwell-Einstein supergravities [4], the degrees d and d g of the Iwasawa polynomial only depend 8 on D, and not on q; this seems consistent with the fact that the corresponding homogeneous (symmetric) manifolds are in the same Tits-Satake universality class (see e.g. [64] for a general treatment).…”

Section: Application To Supergravitysupporting

confidence: 57%

“…Note that the scalar manifolds of N = 6 theory coincides with the one of N = 2 magic supergravity based on J H 3 ; in fact, these theories share the very same bosonic sector [62]. M 1,2 (O) is an exceptional Jordan triple system, generated by 2 × 1 vectors over O [4]. Note that, despite the different relevant irrep.…”

Section: Special Kaehler Symmetric Spacementioning

confidence: 88%

“…It should be remarked that, since this is a N = 2, D = 4 theory, G J 3 ,5 is nothing but a non compact, real form of the mcs G F(J 3 ), 4 .…”

Section: Universal Nilpotency Degree Of Axionic Iwasawa Generators Cmentioning

confidence: 99%

“…Such non compact forms of the Lie groups are relevant for supergravity [1,2,3,4,5,6,7,8]. Here the scalar sector of the theory is described by a non linear sigma model based on a non compact symmetric space with negative curvature G/K, where G is non compact and K is its maximal compact subgroup.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Application To Supergravitysupporting

confidence: 57%

Section: Special Kaehler Symmetric Spacementioning

confidence: 88%

“…It should be remarked that, since this is a N = 2, D = 4 theory, G J 3 ,5 is nothing but a non compact, real form of the mcs G F(J 3 ), 4 .…”

Section: Universal Nilpotency Degree Of Axionic Iwasawa Generators Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…For the maximal N = 8 theory with symmetry E 8(8) (and also for the exceptional 'magic' N = 2 supergravity [12] with symmetry E 8(−24) ), one has h = diag[2, 1, 0, −1, −2], so…”

mentioning

confidence: 99%

Black Holes in Supergravity

Stelle

2015

Springer Proceedings in Physics

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A brief review is given of the use of duality symmetries to form orbits of supergravity black-hole solutions and their relation to extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in this analysis uses a timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of BPS solutions are characterized by nilpotent orbits under the duality symmetries, based upon a tri-graded or pentagraded decomposition of the corresponding duality group algebra.Aside from the general mathematical interest in classifying black hole solutions of any kind, the study of families of such solutions is also of current interest because it touches other important issues in theoretical physics. For example, the classification of BPS and non-BPS black holes forms part of a more general study of branes in supergravity and superstring theory. Branes and their intersections, as well as their worldvolume modes and attached string modes, are key elements in phenomenological approaches to the marriage of string theory with particle physics phenomenology. The related study of nonsingular and horizon-free BPS gravitational solitons is also central to the "fuzzball" proposal of BPS solutions as candidate black-hole quantum microstates.The search for supergravity solutions with assumed Killing symmetries can be recast as a Kaluza-Klein problem [1,2,3]. To see this, consider a 4D theory with a nonlinear bosonic symmetry G 4 (e.g. the "duality" symmetry E 7 for maximal N = 8 supergravity). Scalar fields take their values in a target space Φ 4 = G 4 /H 4 , where H 4 is the corresponding linearly realized subgroup, generally the maximal compact subgroup of G 4 (e.g. SU(8) ⊂ E 7 for N = 8 SG). The search will be constrained by the following considerations:• We assume that a solution spacetime is asymptotically flat or asymptotically Taub-NUT and that there is a 'radial' function r which is divergent in the asymptotic region, g µν ∂ µ r∂ ν r ∼ 1 + O(r −1 ).• Searching for stationary solutions amounts to assuming that a solution possesses a timelike Killing vector field κ µ (x). Lie derivatives with respect to κ µ are assumed to vanish on all fields. The Killing vector κ µ will be assumed to have 1

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Cosmological billiards and oxidation

Buyl

Henneaux

Juliá

et al. 2004

Fortschritte der Physik

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We show how the properties of the cosmological billiards provide useful information (spacetime dimension and $p$-form spectrum) on the oxidation endpoint of the oxidation sequence of gravitational theories. We compare this approach to the other available methods: $GL(n,R)$ subgroups and the superalgebras of dualities.Comment: To appear in the Proceedings of the 27th Johns Hopkins Workshop and in the Proceedings of the 36th International Symposium Ahrenshoop; v2: minor error correcte

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Exceptional supergravity theories and the magic square

Cited by 280 publications

References 6 publications

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

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

Black Holes in Supergravity

Cosmological billiards and oxidation

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