E8 geometry

Cederwall, Martin; Rosabal, J. A.

doi:10.1007/jhep07(2015)007

Cited by 41 publications

(67 citation statements)

References 54 publications

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“…We use the term "ancillary transformations" for these extra gauge symmetries. Such transformations have already been shown to be important in a number of situations [2,42,45,46,49]. Eq.…”

Section: Jhep02(2018)071mentioning

confidence: 97%

“…The parameters of generalised diffeomorphisms at degree 0 and lower become irrelevant; such transformations can always be absorbed in an ancillary transformation. The pattern from E 8 exceptional geometry [45,46] is repeated. The precise content of "matter" fields depends on details.…”

Section: Jhep02(2018)071mentioning

confidence: 99%

“…Some important examples of exceptional field theory for high rank groups (E 8 , E 9 ) exhibit the presence of additional constrained local transformations [2,42,45,46,49], for which we use the term ancillary transformations. However, the classifications in refs.…”

Section: Introductionmentioning

confidence: 99%

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Extended geometries

Cederwall

Palmkvist

2018

J. High Energ. Phys.

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We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section constraint. Generically, additional ("ancillary") gauge transformations are present, and we give a concrete criterion determining when they appear. A universal form of the (pseudo-)action determines the dynamics in all cases without ancillary transformations, and also for a restricted set of cases based on the adjoint representation of a finite-dimensional simple Lie group. Our construction reproduces (the internal sector of) all previously considered cases of double and exceptional field theories.

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“…We use the term "ancillary transformations" for these extra gauge symmetries. Such transformations have already been shown to be important in a number of situations [2,42,45,46,49]. Eq.…”

Section: Jhep02(2018)071mentioning

confidence: 97%

Section: Jhep02(2018)071mentioning

confidence: 99%

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Extended geometries

Cederwall

Palmkvist

2018

J. High Energ. Phys.

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“…Here, L ∇ refers to generalized Lie derivatives (2.9) with partial derivatives replaced by covariant ones ∇ = ∂ − Γ. Following [22], this suggests to rather define torsion as the part of the Christoffel connection that transforms covariantly under the generalized diffeomorphisms. With the transformation of (2.13) under (2.9) given by which can be made explicit with the form of the projector (A.4).…”

Section: Jhep09(2016)168mentioning

confidence: 99%

“…It is thus tempting to wonder if already in exceptional field theory, and before reduction, the constrained gauge connection can be considered as a function of the remaining fields such as [22] …”

Section: Jhep09(2016)168mentioning

confidence: 99%

E8(8) exceptional field theory: geometry, fermions and supersymmetry

Baguet

Samtleben

2016

J. High Energ. Phys.

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We present the supersymmetric extension of the recently constructed E 8(8) exceptional field theory -the manifestly U-duality covariant formulation of the untruncated ten-and eleven-dimensional supergravities. This theory is formulated on a (3+248) dimensional spacetime (modulo section constraint) in which the extended coordinates transform in the adjoint representation of E 8(8) . All bosonic fields are E 8(8) tensors and transform under internal generalized diffeomorphisms. The fermions are tensors under the generalized Lorentz group SO(1, 2) × SO(16), where SO(16) is the maximal compact subgroup of E 8(8) . Vanishing generalized torsion determines the corresponding spin connections to the extent they are required to formulate the field equations and supersymmetry transformation laws. We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms. In particular, the covariantly constrained gauge vectors of E 8(8) exceptional field theory combine with the standard supergravity fields into a single supermultiplet. We give the complete extended Lagrangian and show its invariance under supersymmetry. Upon solution of the section constraint the theory reduces to full D=11 or type IIB supergravity.

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Exceptional Calabi–Yau spaces: the geometry of backgrounds with flux

Ashmore

Waldram

2017

Fortschritte der Physik

174

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In this paper we define the analogue of Calabi–Yau geometry for generic D=4, N=2 flux backgrounds in type II supergravity and M‐theory. We show that solutions of the Killing spinor equations are in one‐to‐one correspondence with integrable, globally defined structures in E7(7)×double-struckR+ generalised geometry. Such “exceptional Calabi–Yau” geometries are determined by two generalised objects that parametrise hyper‐ and vector‐multiplet degrees of freedom and generalise conventional complex, symplectic and hyper‐Kähler geometries. The integrability conditions for both hyper‐ and vector‐multiplet structures are given by the vanishing of moment maps for the “generalised diffeomorphism group” of diffeomorphisms combined with gauge transformations. We give a number of explicit examples and discuss the structure of the moduli spaces of solutions. We then extend our construction to D=5 and D=6 flux backgrounds preserving eight supercharges, where similar structures appear, and finally discuss the analogous structures in Ofalse(d,dfalse)×double-struckR+ generalised geometry.

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E8 geometry

Cited by 41 publications

References 54 publications

Extended geometries

Extended geometries

E8(8) exceptional field theory: geometry, fermions and supersymmetry

Exceptional Calabi–Yau spaces: the geometry of backgrounds with flux

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