Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra

Cederwall, Martin; Palmkvist, Jakob

doi:10.1007/jhep02(2020)144

Cited by 16 publications

(49 citation statements)

References 18 publications

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“…[7]. This construction is extended in the accompanying paper [1] to W (g + ) and S(g + ) for finite-dimensional g.…”

Section: Jhep02(2020)145mentioning

confidence: 94%

“…The superalgebra S turns out to be appropriate for the description of extended geometry; the extra elements in W = W (g + ) are not required. Both W and S can be described by the same Dynkin diagram as B, but with different assignment of generators and relations [1]. This doubly extended diagram was described in the preceding section and is given schematically in figure 2.…”

Section: Jhep02(2020)145mentioning

confidence: 99%

“…Accordingly, also the study of the THA's, restricted to finite-dimensional g + in [7], needs to be extended. This extended study is carried out in the accompanying paper [1].…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 describes the THA S(g + ) with focus on a particularly useful double grading. For more detail, we refer to the companion paper [1]. We then perform a detailed investigation of the ancillary transformations, as obtained from the THA, in section 4.…”

Section: Introductionmentioning

confidence: 99%

“…The accompanying paper [1] deals with the construction of the THA's from generators and relations, and other purely algebraic aspects. In order for both papers to be reasonably self-contained, their contents have a certain overlap.…”

Section: Introductionmentioning

confidence: 99%

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Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Cederwall

Palmkvist

2020

J. High Energ. Phys.

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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 [ ] deals with the mathematical construction of the tensor hierarchy algebras.

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“…[7]. This construction is extended in the accompanying paper [1] to W (g + ) and S(g + ) for finite-dimensional g.…”

Section: Jhep02(2020)145mentioning

confidence: 94%

Section: Jhep02(2020)145mentioning

confidence: 99%

“…Accordingly, also the study of the THA's, restricted to finite-dimensional g + in [7], needs to be extended. This extended study is carried out in the accompanying paper [1].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Cederwall

Palmkvist

2020

J. High Energ. Phys.

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SL(5) Supersymmetry

Cederwall

2021

Fortschritte der Physik

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We consider supersymmetry in five dimensions, where the fermionic parameters are a 2-form under SL(5). 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 ℬ(E 4 ), the tensor hierarchy algebra S(E 4 ) and the exceptional superalgebra E(5, 10). A theorem relating ℬ(E 4 ) and E(5, 10) to all levels is given. Introduction and OverviewSupersymmetry provides an extension of bosonic space-time symmetries with fermionic generators. These are generically spinors under space-time rotations (and may also transform under R-symmetry). In certain situations, supersymmetry generators in non-spinorial modules may be considered. The main example is provided by "twisting", where one considers a fermionic generator which is a singlet under some subalgebra.More generically, one may a priori consider an assignment where supersymmetry generators come in a module S of a spacetime "structure group" G, which we think of as corresponding to the double cover of the Lorentz group together with R-symmetry. A supersymmetry algebra will take the form 1 [Q a , Q b ] = c ab m P m , with some invariant tensor c, and the rest of the brackets vanishing. The only condition is that the symmetric product ∨ 2 S contains the vector representation V.Presently, we will consider one specific such assignment, namely when the structure group is G = SL(5), V = 5 and S = 10. The supersymmetry algebra then is 2 [Q mn , Q pq ] = 2𝜖 mnpqr 𝜕 r ,(1.1

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On exceptional QP-manifolds

Osten

2024

J. High Energ. Phys.

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The connection between two recent descriptions of tensor hierarchies — namely, infinity-enhanced Leibniz algebroids, given by Bonezzi & Hohm and Lavau & Palmkvist, and the p-brane QP-manifolds constructed by Arvanitakis — is made precise. This is done by presenting a duality-covariant version of latter.The construction is based on the QP-manifold T⋆[n]T[1]M × ℋ[n], where M corresponds to the internal manifold of a supergravity compactification and ℋ[n] to a degree-shifted version of the infinity-enhanced Leibniz algebroid. Imposing that the canonical Q-structure on T⋆[n]T[1]M is the derivative operator on ℋ leads to a set of constraints. Solutions to these constraints correspond to $$ \frac{1}{2} $$ 1 2 -BPS p-branes, suggesting that this is a new incarnation of a brane scan. Reduction w.r.t. to these constraints reproduces the known p-brane QP-manifolds. This is shown explicitly for the SL(3)×SL(2)- and SL(5)-theories.Furthermore, this setting is used to speculate about exceptional ‘extended spaces’ and QP-manifolds associated to Leibniz algebras. A proposal is made to realise differential graded manifolds associated to Leibniz algebras as non-Poisson subspaces (i.e. not Poisson reductions) of QP-manifolds similar to the above. Two examples for this proposal are discussed: generalised fluxes (including the dilaton flux) of O(d, d) and the 3-bracket flux for the SL(5)-theory.

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Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra

Cited by 16 publications

References 18 publications

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

SL(5) Supersymmetry

On exceptional QP-manifolds

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