<i>E</i>
                    <sub>11</sub>
                    and M theory

West, Peter

doi:10.1088/0264-9381/18/21/305

Cited by 446 publications

(1,009 citation statements)

References 37 publications

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“…This agreement has been considered somewhat mysterious, since neither U n+1 or E 11 appears in the construction of the tensor hierarchy. On the other hand, it is in line with the ideas of gauging as a probe of M-theory degrees of freedom [1,2], and of Borcherds or Kac-Moody algebras as symmetries in M-theory [3][4][5].…”

Section: Resultssupporting

confidence: 64%

“…General gauge deformations of the lower-dimensional theories have been systematically studied in recent years as a way of exploring the M-theory degrees of freedom beyond supergravity [1,2]. These studies have exhibited features that also appear in other approaches to M-theory, developed during the last decade, where possible symmetries based on Kac-Moody or Borcherds algebras have been investigated [3][4][5]. The present work is an attempt to relate the different approaches to each other via the features that they share.…”

Section: Introductionmentioning

confidence: 99%

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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: Resultssupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Tensor hierarchies, Borcherds algebras and E 11

Palmkvist

2012

J. High Energ. Phys.

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“…, 8, that in three dimensions are dual to the Kaluza-Klein vectors A µ m . As the latter originate from components of the D " 11 metric, this amounts to including in the theory components of a 'dual graviton' [23][24][25][26] at the full non-linear level, something that is considered impossible on the grounds of the no-go theorems in [27,28]. In EFT this problem is resolved due to the presence of the extra E 8p8q gauge symmetry from (1.3).…”

Section: Introductionmentioning

confidence: 99%

Exceptional field theory. III.E8(8)

2014

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We develop exceptional field theory for E 8p8q , defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E 8p8q . The fields transform under E 8p8q generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an 'internal' dreibein and an E 8p8q -valued 'zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E 8p8q E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E 8p8q gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to D " 11 or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.

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“…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].…”

mentioning

confidence: 99%

“…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].…”

mentioning

confidence: 99%

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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E ₁₁ and M theory

Cited by 446 publications

References 37 publications

Tensor hierarchies, Borcherds algebras and E 11

Tensor hierarchies, Borcherds algebras and E 11

Exceptional field theory. III.E8(8)

Hidden symmetries and the fermionic sector of eleven-dimensional supergravity

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E 11 and M theory

Cited by 446 publications

References 37 publications

Tensor hierarchies, Borcherds algebras and E 11

Tensor hierarchies, Borcherds algebras and E 11

Exceptional field theory. III.E8(8)

Hidden symmetries and the fermionic sector of eleven-dimensional supergravity

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E ₁₁ and M theory