On section conditions of E 7(+7) exceptional field theory and superparticle in N = 8 $$ \mathcal{N}=8 $$ central charge superspace

Bandos, Igor A.

doi:10.1007/jhep01(2016)132

Cited by 6 publications

(21 citation statements)

References 69 publications

(157 reference statements)

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“…This may help clarify the general restrictions on the extra gauge field A M and how they relate to restrictions (especially the imposition of the section condition) on the generalised momenta p M . Here there could be a link with the superparticle models of [54,55].…”

Section: Other Directionsmentioning

confidence: 99%

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Particle actions and brane tensions from double and exceptional geometry

Blair

2017

J. High Energ. Phys.

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Massless particles in n+1 dimensions lead to massive particles in n dimensions on Kaluza-Klein reduction. In string theory, wrapped branes lead to multiplets of massive particles in n dimensions, in representations of a duality group G. By encoding the masses of these particles in auxiliary worldline scalars, also transforming under G, we write an action which resembles that for a massless particle on an extended spacetime. We associate this extended spacetime with that appearing in double field theory and exceptional field theory, and formulate a version of the action which is invariant under the generalised diffeomorphism symmetry of these theories. This provides a higher-dimensional perspective on the origin of mass and tension in string theory and M-theory. Finally, we consider the reduction of exceptional field theory on a twisted torus, which is known to give the massive IIA theory of Romans. In this case, our particle action leads naturally to the action for a D0 brane in massive IIA. Here an extra vector field is present on the worldline, whose origin in exceptional field theory is a vector field introduced to ensure invariance under generalised diffeomorphisms.

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Section: Other Directionsmentioning

confidence: 99%

“…One attempt is [53]. The papers [54,55] study a superparticle model in which the section condition of EFT appears.…”

Section: Introductionmentioning

confidence: 99%

Particle actions and brane tensions from double and exceptional geometry

Blair

2017

J. High Energ. Phys.

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“…As was shown in [24], N cannot be greater than d, but we can always choose N = d or N = d − 1, which correspond to the M-theory section and the type IIB section, respectively.…”

Section: Generalized Lie Derivativementioning

confidence: 99%

“…* The gauge algebra of the generalized diffeomorphism is closed if the following section conditions are satisfied [11,22]:where Ω IJ is the antisymmetric tensor intrinsic to the E 7(7) group. Under the section condition, all fields can depend on at most d coordinates (see [24] for a proof in the E 7(7) EFT).In the above conventional formulation, the Y -tensor and the section condition strongly depend on the dimension d, and when we consider applications of the E d(d) EFT, we need to specify the dimension d explicitly. A hypothetical "underlying EFT" (or 11D EFT), which reproduces all E d(d) EFTs (d ≤ 8) from simple truncations, has been proposed in [25], but the program has not been completed yet.…”

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confidence: 99%

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η-symbols in exceptional field theory

Sakatani

Uehara

2017

Progress of Theoretical and Experimental Physics

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We present the universal form of η-symbols that can be applied to an arbitrary E d (d) exceptional field theory (EFT) up to d = 7. We then express the Y -tensor, which governs the gauge algebra of EFT, as a quadratic form of the η-symbols. The usual definition of the Y -tensor strongly depends on the dimension of the compactification torus while it is not the case for our Y -tensor. Furthermore, using the η-symbols, we propose a universal form of the linear section equation. In particular, in the SL(5) EFT, we explicitly show the equivalence to the known linear section equation. * The gauge algebra of the generalized diffeomorphism is closed if the following section conditions are satisfied [11,22]:where Ω IJ is the antisymmetric tensor intrinsic to the E 7(7) group. Under the section condition, all fields can depend on at most d coordinates (see [24] for a proof in the E 7(7) EFT).In the above conventional formulation, the Y -tensor and the section condition strongly depend on the dimension d, and when we consider applications of the E d(d) EFT, we need to specify the dimension d explicitly. A hypothetical "underlying EFT" (or 11D EFT), which reproduces all E d(d) EFTs (d ≤ 8) from simple truncations, has been proposed in [25], but the program has not been completed yet. In this paper, we investigate such uniform formulations from a different approach. In our approach, the Y -tensor is expressed in terms of SL(d) [or SL(d − 1)] tensors and E d(d) tensors are not used. Accordingly, the truncation to lower d can be easily performed.The present paper is organized as follows. In section 2, we introduce η-symbols as a natural generalization of the O(d, d)-invariant metric η IJ in DFT and explain how the η-symbols are related to branes in M-theory/type IIB theory. The Y -tensor is expressed by using the ηsymbols and the Ω-tensor. In section 3, we find the explicit form of the η-symbols and the Ω-tensor. In section 4, we show the explicit form of the section condition and the generalized Lie derivative. In section 5, we propose a new linear section equation, and show that it reproduces the known linear section equation [11] in the case of the SL(5) EFT. Section 6 is devoted to conclusions and discussion.

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E7(7) exceptional field theory in superspace

Butter

Samtleben

Sezgin

2019

J. High Energ. Phys.

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We formulate the locally supersymmetric E 7(7) exceptional field theory in a (4 + 56|32) dimensional superspace, corresponding to a 4D N = 8 "external" superspace augmented with an "internal" 56-dimensional space. This entails the unification of external diffeomorphisms and local supersymmetry transformations into superdiffeomorphisms. The solutions to the superspace Bianchi identities lead to on-shell duality equations for the p-form field strengths for p ≤ 4. The reduction to component fields provides a complete description of the on-shell supersymmetric theory. As an application of our results, we perform a generalized Scherk-Schwarz reduction and obtain the superspace formulation of maximal gauged supergravity in four dimensions parametrized by an embedding tensor.

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On section conditions of E 7(+7) exceptional field theory and superparticle in N = 8 $$ \mathcal{N}=8 $$ central charge superspace

Cited by 6 publications

References 69 publications

Particle actions and brane tensions from double and exceptional geometry

Particle actions and brane tensions from double and exceptional geometry

η-symbols in exceptional field theory

E7(7) exceptional field theory in superspace

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