| 1. |
- Bossard, Guillaume, et al.
(author)
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Beyond E11
- 2017
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In: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :5
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Journal article (peer-reviewed)abstract
- We study the non-linear realisation of E-11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E-11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E-11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E-11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.
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| 2. |
- Bossard, Guillaume, et al.
(author)
-
Extended geometry of magical supergravities
- 2023
-
In: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :5
-
Journal article (peer-reviewed)abstract
- We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived.
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| 3. |
- Bossard, Guillaume, et al.
(author)
-
Generalised diffeomorphisms for E9
- 2017
-
In: Physical Review D - Particles, Fields, Gravitation and Cosmology. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 96, s. 106022-
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Journal article (peer-reviewed)abstract
- We construct generalised diffeomorphisms for E9 exceptional field theory. The trans- formations, which like in the E8 case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism alge- bra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordi- nate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalised Scherk–Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.
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