The local symmetries of M-theory and their formulation in generalised geometry

Berman, David S.; Godazgar, Hadi; Godazgar, Mahdi; Perry, Malcolm J.

doi:10.1007/jhep01(2012)012

Cited by 160 publications

(245 citation statements)

References 75 publications

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“…(The case of d = 4 was first considered in [37,19,29,38].) Concretely, we write the generalised vector index M as an antisymmetric pair [mn] of GL + (d + 1, R) indices, where m, n = 1, .…”

Section: The Set-upmentioning

confidence: 99%

Spheres, Generalised Parallelisability and Consistent Truncations

Lee

Strickland‐Constable

Waldram

2017

Fortschritte der Physik

162

363

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We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten-and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a frame algebra with constant coefficients. The consistent truncation then arises as a generalised version of a conventional Scherk-Schwarz reduction with the frame algebra encoding the embedding tensor of the reduced theory. The key new result is that all round-sphere S d geometries admit such generalised parallelisations with an SO(d + 1) frame algebra. Thus we show that the remarkable consistent truncations on S 3 , S 4 , S 5 and S 7 are in fact simply generalised Scherk-Schwarz reductions. This description leads directly to the standard non-linear scalar-field ansatze and as an application we give the full scalar-field ansatz for the type IIB truncation on S 5 .

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“…(The case of d = 4 was first considered in [37,19,29,38].) Concretely, we write the generalised vector index M as an antisymmetric pair [mn] of GL + (d + 1, R) indices, where m, n = 1, .…”

Section: The Set-upmentioning

confidence: 99%

Spheres, Generalised Parallelisability and Consistent Truncations

Lee

Strickland‐Constable

Waldram

2017

Fortschritte der Physik

162

363

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“…Finally we end with some comments on the extension of these ideas to the extended, exceptional geometries that occur in M-theory where the full U-duality groups are made a manifest symmetry [58,[60][61][62][63][64][65][66][67][68][69][70][71][72][73].…”

Section: Jhep09(2014)066mentioning

confidence: 99%

“…[58,[60][61][62][63][64][65][66][67][68][69][70][71][72][73]. We refer the reader to those papers or the reviews [16,17] for an introduction.…”

Section: Jhep09(2014)066mentioning

confidence: 99%

Global aspects of double geometry

Berman

Cederwall

Perry³

2014

J. High Energ. Phys.

Self Cite

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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“…In addition, we will have to introduce extra fields and constraints, but the extra fields can be eliminated once the constraints are solved. After the advent of DFT, there have already been quite a number of papers extending the techniques developed here to various U-duality groups [45][46][47][48][49][50][51] (see also [52,53] for earlier results). The actions given in this context exhibit manifest E n(n) symmetry for n ≤ 7 and describe truncations of D = 11 supergravity.…”

Section: Jhep09(2013)080mentioning

confidence: 99%

“…In particular, the specific actions of [45][46][47] carry terms that are zero when det M = 1 and cannot show up in our construction.…”

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 local symmetries of M-theory and their formulation in generalised geometry

Cited by 160 publications

References 75 publications

Spheres, Generalised Parallelisability and Consistent Truncations

Spheres, Generalised Parallelisability and Consistent Truncations

Global aspects of double geometry

U-duality covariant gravity

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