| 1. |
- Bossard, Guillaume, et al.
(författare)
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Generalised diffeomorphisms for E9
- 2017
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Ingår i: Physical Review D - Particles, Fields, Gravitation and Cosmology. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 96, s. 106022-
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Tidskriftsartikel (refereegranskat)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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| 2. |
- Carbone, Lisa, et al.
(författare)
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Generators and relations for (generalised) Cartan type superalgebras
- 2019
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Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 1194:1
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Konferensbidrag (refereegranskat)abstract
- In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, A(n-1,0) = s (1|n) can be constructed by adding a "gray" node to the Dynkin diagram of An-1 = s (n), corresponding to an odd null root. The Cartan superalgebras constitute a difierent class, where the simplest example is Wpnq, the derivation algebra of the Grassmann algebra on n generators. Here we present a novel construction of Wpnq, from the same Dynkin diagram as A(n-1,0), but with additional generators and relations.
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| 3. |
- Carbone, Lisa, et al.
(författare)
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Generators and relations for Lie superalgebras of Cartan type
- 2019
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 52:5
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Tidskriftsartikel (refereegranskat)abstract
- We give an analog of a Chevalley-Serre presentation for the Lie superalgebras W(n) and S(n) of Cartan type. These are part of a wider class of Lie superalgebras, the so-called tensor hierarchy algebras, denoted W(g) and S(g), where g denotes the Kac-Moody algebra A(r), D-r or E-r. Then W(A(n-1)) and S(A(n-1)) are the Lie superalgebras W(n) and S(n). The algebras W(g) and S(g) are constructed from the Dynkin diagram of the Borcherds-Kac-Moody superalgebras B(g) obtained by adding a single grey node (representing an odd null root) to the Dynkin diagram of g. We redefine the algebras W(A(r)) and S(A(r)) in terms of Chevalley generators and defining relations. We prove that all relations follow from the defining ones at level >= -2. The analogous definitions of the algebras in the D- and E-series are given. In the latter case the full set of defining relations is conjectured.
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| 4. |
- Cederwall, Martin, 1961
(författare)
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Algebraic structures in exceptional geometry
- 2018
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Singapore : Springer Singapore. - 2194-1017 .- 2194-1009. ; 255:2018, s. 31-41
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Konferensbidrag (refereegranskat)abstract
- Exceptional field theory (EFT) gives a geometric underpinning of the U-duality symmetries of M-theory. In this talk I give an overview of the surprisingly rich algebraic structures which naturally appear in the context of EFT. This includes Borcherds superalgebras, Cartan type superalgebras (tensor hierarchy algebras) and L∞ algebras. This is the written version of a talk based mainly on refs. [1-6], presented at ISQS25, Prague, June 2017, at QTS-10/LT-12, Varna, June 2017, at SQS 2017, Dubna, Aug. 2017, and at the 9th Mathematical Physics Meeting, Belgrade, Sept. 2017.
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| 5. |
- Cederwall, Martin, 1961
(författare)
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Algebraic Structures in Extended Geometry
- 2018
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Ingår i: Physics of Particles and Nuclei. - 1063-7796. ; 49:5, s. 873-878
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Tidskriftsartikel (refereegranskat)abstract
- Extended geometry is a unifying framework including exceptional field theory (XFT) and double field theory (DFT). It gives a geometric underpinning of the duality symmetries of M-theory. In this talk I give an overview of the surprisingly rich algebraic structures which naturally appear in the context of extended geometry. This includes Borcherds superalgebras, Cartan type superalgebras (tensor hierarchy algebras) and L-infinity algebras. This is the written version of a talk based mainly on [1-6], presented at SQS 2017, Dubna, Aug. 2017.
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| 6. |
- Cederwall, Martin, 1961
(författare)
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An off-shell superspace reformulation of D=4, N=4 super-Yang–Mills theory
- 2017
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- D = 4, N = 4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D = 10 theory. That superspace, in particular the choice of pure spinor variables, is less suitable for dealing with fields that are inherently 4-dimensional, such as the superfields based on the scalars, which are gauge-covariant, and traces of powers of scalars, which are gauge-invariant. We give a reformulation of D = 4, N = 4 super-Yang-Mills theory in N = 4 superspace, using inherently 4-dimensional pure spinors. All local degrees of freedom reside in a superfield based on the physical scalars. The formalism should be suited for calculations of correlators of traces of scalar superfields.
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| 7. |
- Cederwall, Martin, 1961
(författare)
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An Off-Shell Superspace Reformulation of D = 4, N = 4 Super-Yang–Mills Theory
- 2018
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Ingår i: Fortschritte der Physik. - : Wiley. - 0015-8208 .- 1521-3978. ; 66:1
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Tidskriftsartikel (refereegranskat)abstract
- D = 4, N = 4 super-Yang–Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D = 10 theory. That superspace, in particular the choice of pure spinor variables, is less suitable for dealing with fields that are inherently 4-dimensional, such as the superfields based on the scalars, which are gauge-covariant, and traces of powers of scalars, which are gauge-invariant. We give a reformulation of D = 4, N = 4 super-Yang–Mills theory in N = 4 superspace, using inherently 4-dimensional pure spinors. All local degrees of freedom reside in a superfield based on the physical scalars. The formalism should be suited for calculations of correlators of traces of scalar superfields.
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| 8. |
- Cederwall, Martin, 1961
(författare)
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Double supergeometry
- 2016
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2016:6
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Tidskriftsartikel (refereegranskat)abstract
- A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D=10 as the main example. The formalism is based on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group. Covariance under generalised super-diffeomorphisms is manifest. Ordinary superspace is obtained as a solution of the orthosymplectic section condition. A systematic study of curved superspace Bianchi identities is performed, and a relation to a double pure spinor superfield cohomology is established. A Ramond-Ramond superfield is constructed as an infinite-dimensional orthosymplectic spinor. Such objects in minimal orbits under the OSp supergroup ("pure spinors") define super-sections.
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| 9. |
- Cederwall, Martin, 1961, et al.
(författare)
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E (8) geometry
- 2015
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2015:7, s. 1-22
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Tidskriftsartikel (refereegranskat)abstract
- We investigate exceptional generalised diffeomorphisms based on E (8(8)) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL(n + 1) is sketched. Some related issues are discussed.
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| 10. |
- Cederwall, Martin, 1961, et al.
(författare)
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E8 geometry
- 2015
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We investigate exceptional generalised diffeomorphisms based on E_8(8) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL(n+1) is sketched. Some related issues are discussed.
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