E11, SL(32) and central charges

West, Peter

doi:10.1016/j.physletb.2003.09.059

Cited by 202 publications

(521 citation statements)

References 12 publications

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“…This same construction is central to the E 11 programme of West and others [20][21][22][23][24][25]. As such the duality manifest form of the Bosonic sector of supergravity is somewhat of a truncation of the E 11 theory, a fact used to construct the RR sector of double field theory in ref.…”

Section: Of the O(d D)/o(d) × O(d)mentioning

confidence: 96%

Global aspects of double geometry

Berman

Cederwall

Perry³

2014

J. High Energ. Phys.

123

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Abstract:We consider the concept of a generalised manifold in the O(d, d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are defined. Triple overlaps are trivial concerning their action on coordinates, but non-trivial on fields, including the generalised metric. A generalised manifold is an ordinary manifold, but the generalised metric on the manifold carries a gerbe structure. We show how the abelian behaviour of the gerbe is embedded in the non-abelian T-duality group. We also comment on possibilities and difficulties in the U-duality setting.

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Section: Of the O(d D)/o(d) × O(d)mentioning

confidence: 96%

Global aspects of double geometry

Berman

Cederwall

Perry³

2014

J. High Energ. Phys.

123

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“…The work of de Wit and Nicolai presents a reformulation of D = 11 supergravity that abandons manifest 11-dimensional covariance, using a Kaluza-Klein inspired 4 + 7 or 3 + 8 splitting of the coordinates, but which exhibits an enhanced local Lorentz symmetry in accordance with the (composite) gauge symmetries appearing in the D = 4 or D = 3 coset models [40,41]. However, it did not manifest the exceptional groups, and further work in [42] suggested that additional coordinates should be introduced in order to achieve this, an idea that also features prominently in the proposal of [43]. Later work in [44] gave a manifestly E 7(7) covariant formulation for a certain 7-dimensional truncation of D = 11 supergravity by introducing coordinates in the 56 of E 7 (7) .…”

Section: Jhep09(2013)080mentioning

confidence: 99%

U-duality covariant gravity

Hohm¹,

Samtleben

2013

J. High Energ. Phys.

107

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Abstract:We extend the techniques of double field theory to more general gravity theories and U-duality symmetries, having in mind applications to the complete D = 11 supergravity. In this paper we work out a (3 + 3)-dimensional 'U-duality covariantization' of D = 4 Einstein gravity, in which the Ehlers group SL(2, R) is realized geometrically, acting in the 3 representation on half of the coordinates. We include the full (2 + 1)-dimensional metric, while the 'internal vielbein' is a coset representative of SL(2, R)/SO(2) and transforms under gauge transformations via generalized Lie derivatives. In addition, we introduce a gauge connection of the 'C-bracket', and a gauge connection of SL(2, R), albeit subject to constraints. The action takes the form of (2 + 1)-dimensional gravity coupled to a Chern-Simons-matter theory but encodes the complete D = 4 Einstein gravity. We comment on generalizations, such as an 'E 8(8) covariantization' of M-theory.

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“…The importance of the rank three generator in the context of M5-brane dynamics was already stressed in [33] and also features in [21] where it is seen as part of K(E 11 ). However, it is an open question whether there exists a vector-spinor-type representation of K(E 11 ), which would be analogous to (11) and thus also compatible with [32].…”

mentioning

confidence: 94%

“…Here, K(E 10 ) is the maximal compact subgroup of E 10 . Further evidence for the rôle of the one-dimensional non-linear sigma model E 10 /K(E 10 ) in M-theory was provided in [13][14][15][16].An earlier and conceptually different proposal aiming at capturing hidden symmetries of M-theory, and based on the very-extended Kac-Moody group E 11 , was made in [17,18] and further developed in [19][20][21]. A proposal combining the ideas of [18] and [11] was put forward in [22][23][24].…”

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confidence: 99%

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Hidden symmetries and the fermionic sector of eleven-dimensional supergravity

2006

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We study the hidden symmetries of the fermionic sector of D = 11 supergravity, and the rôle of K(E 10 ) as a generalised 'R-symmetry'. We find a consistent model of a massless spinning particle on an E 10 /K(E 10 ) coset manifold whose dynamics can be mapped onto the fermionic and bosonic dynamics of D = 11 supergravity in the near space-like singularity limit. This E 10 -invariant superparticle dynamics might provide the basis of a new definition of M-theory, and might describe the 'de-emergence' of spacetime near a cosmological singularity. Eleven-dimensional supergravity (SUGRA 11 ) [1] is believed to be the low-energy limit of the elusive 'M-theory', which is, hopefully, a unified framework encompassing the various known string theories. Understanding the symmetries of SUGRA 11 is therefore important for reaching a satisfactory formulation of M-theory. Many years ago it was found that the toroidal dimensional reduction of SUGRA 11 to lower dimensions leads to the emergence of unexpected ('hidden') symmetry groups, notably E 7 in the reduction to four noncompactified spacetime dimensions [2], E 8 in the reduction to D = 3 [2-5], and the affine Kac-Moody group E 9 in the reduction to D = 2 [6,7]. It was also conjectured [8] that the hyperbolic Kac-Moody group E 10 might appear when reducing SUGRA 11 to only one (time-like) dimension.Recently, the consideration, à la Belinskii, Khalatnikov and Lifshitz [9], of the near space-like singularity limit 1 of generic inhomogeneous bosonic eleven-dimensional supergravity solutions has uncovered some striking evidence for the hidden rôle of E 10 [10,11]. Ref.[11] related the gradient expansion * Corresponding author.E-mail address: axel.kleinschmidt@aei.mpg.de (A. Kleinschmidt). 1 This limit can also be viewed as a small tension limit, α → ∞.(∂ x ∂ t ), which organises the near space-like singularity limit [12], to an algebraic expansion in the height of positive roots of E 10 . A main conjecture of [11] was the existence of a correspondence between the time evolution, around any given spatial point x, of the supergravity bosonic fields g (11) MN (t, x), A (11) MNP (t, x), together with their infinite towers of spatial gradients, on the one hand, and the dynamics of a structureless massless particle on the infinite-dimensional coset space E 10 /K(E 10 ) on the other hand. Here, K(E 10 ) is the maximal compact subgroup of E 10 . Further evidence for the rôle of the one-dimensional non-linear sigma model E 10 /K(E 10 ) in M-theory was provided in [13][14][15][16].An earlier and conceptually different proposal aiming at capturing hidden symmetries of M-theory, and based on the very-extended Kac-Moody group E 11 , was made in [17,18] and further developed in [19][20][21]. A proposal combining the ideas of [18] and [11] was put forward in [22][23][24].In this Letter, we extend the bosonic coset construction of [11] to the full supergravity theory by including fermionic variables; more specifically, we provide evidence for the existence of a correspondence between th...

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E11, SL(32) and central charges

Cited by 202 publications

References 12 publications

Global aspects of double geometry

Global aspects of double geometry

U-duality covariant gravity

Hidden symmetries and the fermionic sector of eleven-dimensional supergravity

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