The<i>E</i><sub>11</sub>origin of all maximal supergravities

Riccioni, Fabio; West, Peter

doi:10.1088/1126-6708/2007/07/063

Cited by 139 publications

(265 citation statements)

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“…In the level decomposition of the Borcherds algebra with respect to g, the representation content on level p coincides with r p , up to level D − 2 [4,12,13]. The same is true for E 11 if the level decomposition is done with respect to g ⊕ sl D , and restricted to tensors that are antisymmetric under sl D [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 85%

Tensor hierarchies, Borcherds algebras and E 11

Palmkvist

2012

J. High Energ. Phys.

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Gauge deformations of maximal supergravity in D = 11 − n dimensions generically give rise to a tensor hierarchy of p-form fields that transform in specific representations of the global symmetry group E n . We derive the formulas defining the hierarchy from a Borcherds superalgebra corresponding to E n . This explains why the E n representations in the tensor hierarchies also appear in the level decomposition of the Borcherds superalgebra. We show that the indefinite Kac-Moody algebra E 11 can be used equivalently to determine these representations, up to p = D, and for arbitrarily large p if E 11 is replaced by E r with sufficiently large rank r. * Also affiliated to:

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Section: Introductionmentioning

confidence: 85%

Tensor hierarchies, Borcherds algebras and E 11

Palmkvist

2012

J. High Energ. Phys.

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“…It is well known, for instance, that D = 11 supergravity, or the effective action of type II string theory, compactified on a d torus T d (T (d−1) ) has an E d (R) duality, for d ≤ 10, see [1] and references therein. For the full compactified theory on T 11 it is conjectured that E 11 could be the duality group [2], which actually could be a symmetry of the full M-theory, independently of the compactification [3].…”

Section: Introductionmentioning

confidence: 99%

On the exceptional generalised Lie derivative for d ≥ 7

Rosabal

2015

J. High Energ. Phys.

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In this work we revisit the E 8 × R + generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the E 7 × R + one. Compared to its E d × R + , d ≤ 7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E 8 group, are needed to have a well defined theory. We discuss the implications of the structure of the E 8 × R + generalised transformation on the construction of the d = 8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.

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“…In this sense, one can understand why type IIB supergravity in D = 10 (along with its SL(2, R) U -duality) has not been considered : it has no 1-form potentials. As discussed in [70,71,66], the relevant 1-form U -irrep. can be predicted by exploiting the infinite-dimensional (Kac-Moody extended) algebra E 11 .…”

Section: Application To Supergravitymentioning

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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TheE₁₁origin of all maximal supergravities

Cited by 139 publications

References 68 publications

Tensor hierarchies, Borcherds algebras and E 11

Tensor hierarchies, Borcherds algebras and E 11

On the exceptional generalised Lie derivative for d ≥ 7

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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TheE11origin of all maximal supergravities

Cited by 139 publications

References 68 publications

Tensor hierarchies, Borcherds algebras and E 11

Tensor hierarchies, Borcherds algebras and E 11

On the exceptional generalised Lie derivative for d ≥ 7

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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TheE₁₁origin of all maximal supergravities