| 1. |
- Cederwall, Martin, 1961
(författare)
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SL(5) Supersymmetry
- 2021
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Ingår i: Fortschritte der Physik. - : Wiley. - 0015-8208 .- 1521-3978. ; 69:11-12
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Tidskriftsartikel (refereegranskat)abstract
- We consider supersymmetry in five dimensions, where the fermionic parameters are a 2-form under (Formula presented.). Supermultiplets are investigated using the pure spinor superfield formalism, and are found to be closely related to infinite-dimensional extensions of the supersymmetry algebra: the Borcherds superalgebra (Formula presented.), the tensor hierarchy algebra (Formula presented.) and the exceptional superalgebra E(5, 10). A theorem relating (Formula presented.) and E(5, 10) to all levels is given.
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| 2. |
- Cederwall, Martin, 1961
(författare)
-
Superspace formulation of exotic supergravities in six dimensions
- 2021
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2021:3
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Tidskriftsartikel (refereegranskat)abstract
- We provide a linearised superfield description of the exotic non-metric N = (4, 0) supergravity in D = 6, by using a pure spinor superfield formalism. The basic field Ψ is a ghost number 2 scalar, transforming in the same R-symmetry module as the tensor fields. Partial results for the N = (1, 3) model are presented.
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| 3. |
- Cederwall, Martin, 1961, et al.
(författare)
-
Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra
- 2020
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Ingår i: Journal of High Energy Physics. - : Springer. - 1029-8479 .- 1126-6708. ; 2020:2
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Tidskriftsartikel (refereegranskat)abstract
- Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics, especially in extended geometry and gauged supergravity. We further develop the recently proposed definition of tensor hierarchy algebras in terms of generators and relations encoded in a Dynkin diagram (which coincides with the diagram for a related Borcherds superalgebra). We apply it to cases where a grey node is added to the Dynkin diagram of a rank r + 1 Kac-Moody algebra g(+), which in turn is an extension of a rank r finite-dimensional semisimple simply laced Lie algebra g. The algebras are specified by g together with a dominant integral weight lambda. As a by-product, a remarkable identity involving representation matrices for arbitrary integral highest weight representations of g is proven. An accompanying paper [1] describes the application of tensor hierarchy algebras to the gauge structure and dynamics in models of extended geometry.
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| 4. |
- Cederwall, Martin, 1961, et al.
(författare)
-
Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics
- 2020
-
Ingår i: Journal of High Energy Physics. - : Springer. - 1029-8479 .- 1126-6708. ; 2020:2
-
Tidskriftsartikel (refereegranskat)abstract
- The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns out to be a tensor hierarchy algebra rather than a Borcherds superalgebra. This tensor hierarchy algebra is a non-contragredient superalgebra, generically infinite-dimensional, which is a double extension of the structure algebra of the extended geometry. We use it to perform a (partial) analysis of the gauge structure in terms of an L∞ algebra for extended geometries based on finite-dimensional structure groups. An invariant pseudo-action is also given in these cases. We comment on the continuation to infinite-dimensional structure groups. An accompanying paper [1] deals with the mathematical construction of the tensor hierarchy algebras.
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